Meta tags:
Headings (most frequently used words):
cross, validation, bootstrap, jackknife, resampling, statistics, contents, permutation, tests, see, also, references, literature, external, links, monte, carlo, software, comparison, of, and,
Text of the page (most frequently used words):
the (174), and (55), bootstrap (39), for (37), #jackknife (35), #statistics (32), data (28), variance (27), this (24), with (24), validation (24), cross (22), regression (22), sample (22), statistical (19), resampling (17), estimator (17), distribution (17), test (16), analysis (16), method (16), model (15), edit (15), sampling (14), methods (13), estimate (13), used (12), that (12), from (11), time (11), estimation (11), correlation (11), statistic (11), tests (11), permutation (11), inference (10), are (10), wikipedia (9), series (9), linear (9), probability (9), random (9), than (9), more (9), main (9), when (9), non (8), monte (8), carlo (8), population (8), mean (8), size (8), transformation (8), plot (8), not (8), can (8), one (8), may (7), applications (7), median (7), chart (7), hypothesis (7), set (7), bootstrapping (7), applied (7), bias (7), estimates (7), subsampling (7), article (7), other (6), log (6), likelihood (6), standard (6), interval (6), parametric (6), testing (6), prediction (6), based (6), springer (6), samples (6), delete (6), page (5), rank (5), models (5), squares (5), general (5), normal (5), coefficient (5), multiple (5), randomization (5), confidence (5), estimating (5), empirical (5), links (5), doi (5), pierre (5), del (5), moral (5), also (5), both (5), such (5), consistent (5), each (5), out (5), toggle (4), table (4), contents (4), search (4), under (4), terms (4), using (4), inc (4), use (4), was (4), nonparametric (4), control (4), function (4), least (4), box (4), multivariate (4), predictors (4), bayesian (4), ratio (4), power (4), estimators (4), point (4), family (4), experiment (4), error (4), normalization (4), line (4), without (4), results (4), comparison (4), 2007 (4), isbn (4), particle (4), 978 (4), observation (4), only (4), but (4), repeated (4), original (4), distributed (4), square (4), value (4), uses (4), hide (4), move (4), sidebar (4), view (3), articles (3), index (3), information (3), design (3), studies (3), bioinformatics (3), product (3), survival (3), partial (3), exponential (3), factor (3), classification (3), discriminant (3), degrees (3), freedom (3), robust (3), adaptive (3), errors (3), maximum (3), alternative (3), lehmann (3), plug (3), unbiased (3), distance (3), moments (3), parameter (3), study (3), designs (3), approximation (3), replication (3), reduction (3), scatter (3), central (3), package (3), variability (3), two (3), functions (3), simulation (3), their (3), external (3), 2013 (3), monographs (3), wolter (3), introduction (3), shao (3), 1995 (3), 1946 (3), royal (3), society (3), held (3), jstor (3), journal (3), tukey (3), mathematical (3), quenouille (3), 1949 (3), variate (3), see (3), usually (3), weights (3), whereas (3), basic (3), there (3), coefficients (3), could (3), assumptions (3), observations (3), same (3), interest (3), been (3), case (3), many (3), rate (3), resample (3), where (3), example (3), often (3), tools (3), languages (2), contact (2), about (2), privacy (2), policy (2), available (2), apply (2), commons (2), attribution (2), july (2), categories (2), needing (2), words (2), phrases (2), quotes (2), attributed (2), all (2), short (2), description (2), wikidata (2), https (2), national (2), mathematics (2), portal (2), system (2), environmental (2), official (2), quality (2), engineering (2), clinical (2), first (2), limit (2), spectral (2), density (2), frequency (2), domain (2), autoregressive (2), vector (2), specific (2), structural (2), seasonal (2), adjustment (2), stationarity (2), distributions (2), cluster (2), principal (2), manova (2), contingency (2), categorical (2), anova (2), poisson (2), generalized (2), equations (2), determination (2), pearson (2), moment (2), posterior (2), way (2), sum (2), hodges (2), selection (2), chi (2), fit (2), score (2), comparisons (2), most (2), powerful (2), theorem (2), minimum (2), optimal (2), decision (2), location (2), scale (2), shape (2), trial (2), randomized (2), controlled (2), experiments (2), survey (2), methodology (2), missing (2), cleaning (2), feature (2), scaling (2), transform (2), forest (2), dependence (2), dispersion (2), deviation (2), range (2), variation (2), geometric (2), arithmetic (2), continuous (2), interactive (2), demonstration (2), within (2), between (2), microarray (2), adjustments (2), version (2), software (2), pdf (2), chapman (2), hall (2), crc (2), press (2), field (2), integration (2), 2004 (2), feynman (2), kac (2), formulae (2), genealogical (2), interacting (2), good (2), literature (2), verbyla (2), evaluating (2), accuracy (2), 1007 (2), bibcode (2), encyclopedia (2), computational (2), biology (2), mahalanobis (2), 1958 (2), its (2), wiley (2), references (2), genetic (2), algorithm (2), complex (2), schemes (2), stratification (2), theoretical (2), aspects (2), special (2), particularly (2), means (2), ratios (2), medians (2), quantiles (2), become (2), practical (2), disadvantage (2), jackknifing (2), brr (2), requires (2), originally (2), intervals (2), hand (2), then (2), while (2), rather (2), seen (2), similar (2), differences (2), gives (2), result (2), popular (2), have (2), idea (2), physics (2), like (2), proposed (2), instead (2), itself (2), tends (2), half (2), possibly (2), new (2), replicates (2), extended (2), assuming (2), identically (2), valid (2), conditions (2), convergence (2), limiting (2), tend (2), smaller (2), has (2), cases (2), accurate (2), replacement (2), how (2), leaves (2), added (2), subsets (2), validating (2), sets (2), related (2), replace (2), measures (2), functionals (2), principle (2), null (2), appearance (2), upload (2), file (2), changes (2), history (2), read (2), subsection (2), create (2), account (2), donate (2), menu (2), add, topic, mobile, cookie, statement, developers, code, conduct, legal, safety, contacts, disclaimers, text, additional, site, you, agree, registered, trademark, profit, organization, wikimedia, foundation, creative, sharealike, license, rendered, parsoid, last, edited, 2025, utc, hidden, september, 2022, matches, retrieved, org, php, title, resampling_, oldid, 1298730845, yale, lux, israel, bnf, france, united, states, authority, databases, wikiproject, category, kriging, geostatistics, geographic, cartography, spatial, psychometrics, accounts, jurimetrics, econometrics, demography, crime, census, actuarial, science, social, identification, reliability, process, probabilistic, chemometrics, medical, epidemiology, trials, biostatistics, nelson, aalen, hazard, hitting, accelerated, failure, aft, proportional, hazards, kaplan, meier, whittle, wavelet, fourier, autoregression, var, conditional, heteroskedasticity, arch, arima, jenkins, arma, xcf, pacf, autocorrelation, acf, breusch, godfrey, durbin, watson, ljung, johansen, dickey, fuller, granger, causality, break, cointegration, smoothing, trend, decomposition, elliptical, equation, canonical, components, cochran, mantel, haenszel, mcnemar, graphical, cohen, kappa, ancova, partition, regressions, binomial, logistic, bernoulli, families, homoscedasticity, heteroscedasticity, isotonic, semiparametric, nonlinear, ordinary, simple, template, splines, mars, simultaneous, mixed, effects, residuals, confounding, variable, bayes, credible, prior, van, der, waerden, ordered, jonckheere, terpstra, friedman, kruskal, wallis, mann, whitney, signed, wilcoxon, sign, bic, aic, normality, shapiro, wilk, jarque, bera, lilliefors, anderson, darling, kolmogorov, smirnov, squared, goodness, student, wald, lagrange, multiplier, uniformly, tails, hypotheses, tolerance, pivot, scheffé, rao, blackwellization, frequentist, sensitivity, robustness, asymptotics, divergence, efficiency, loss, functional, sufficiency, completeness, monotone, space, specification, order, theory, quasi, natural, sectional, cohort, observational, down, stochastic, scientific, assignment, interaction, factorial, blocking, questionnaire, opinion, poll, stratified, effect, collection, detrending, differencing, preprocessing, component, dimensionality, truncation, winsorizing, outlier, unit, min, max, standardization, fisher, anscombe, stabilizing, yeo, johnson, cox, transformations, processing, ecdf, matrix, heatmap, violin, stem, leaf, display, run, radar, pie, histogram, fan, correlogram, biplot, bar, graphics, spearman, kendall, grouped, summary, tables, count, skewness, kurtosis, percentile, interquartile, average, absolute, mode, lehmer, heinz, heronian, harmonic, cubic, contraharmonic, center, descriptive, outline, permtest, compare, groups, bioconductor, genomics, evaluate, outcomes, retrieval, paired, evaluation, trec, samplingvarest, implements, some, statistics101, program, datasets, book, davison, hinkley, 1997, cup, angelo, canty, brian, ripley, 2010, plus, boot, jiang, simon, adjusted, approach, stat, med, dec, 5320, 1002, sim, 2968, pmid, 17624926, brb, nci, nih, gov, techreport, prederr_rev_0407, 9781466504059, systems, 387, 20268, 2nd, edition, 2006, 3rd, birkhauser, litvaitis, 1989, wildlife, habitat, 787, 153448048, s2cid, bf01868317, 1989enman, 783v, 783, management, second, verlag, 281, elsevier, 2018, 544, 811432, abc, proceedings, meeting, 16th, 370, 2981330, 325, 109, quite, large, preliminary, report, 614, 2237363, annals, approximate, 2983696, 1111, 2517, 6161, tb00023, 1986, potential, 1257, 1139, x86, 222, 1986cajfr, 1255v, 1255, canadian, research, 626, 575, 4419, 1902, 4684, 9393, approximations, logan, david, wolesensky, willian, pure, interscience, texts, tracts, john, sons, 2009, chapter, section, surrogate, uniform, generation, pseudoreplication, filter, bagging, aggregating, easier, involve, stages, clustering, varying, response, calibration, post, unequal, found, accounted, precise, consideration, should, smooth, differentiable, totals, proportions, odd, etc, argument, favoring, over, jackknifes, overcome, problem, relaxing, smoothness, requirements, problems, however, furthermore, computations, thus, mainly, recommended, needed, balanced, whether, depend, operational, concerns, specialized, enough, whole, computes, easy, highly, computationally, intensive, subsamples, yield, numerical, which, why, although, huge, insights, difference, users, different, exactly, because, need, verified, several, times, before, publishing, agencies, verification, crucial, number, just, preferred, economics, biological, sciences, dependent, independence, extensions, allow, extension, group, association, better, unimodal, parameters, asymptotically, true, almost, surely, technical, says, populations, variances, behind, lies, systematically, recomputing, leaving, calculated, equivalent, leave, differs, goal, invented, intention, reducing, considered, independently, made, would, approximately, being, calculate, historically, preceded, invention, inventing, extending, foreshadowed, who, suggested, chosen, coined, name, interpenetrating, advantage, much, weaker, compared, particular, sufficient, known, addition, subsample, must, infinity, together, converges, zero, independent, iid, cover, well, resamples, blocks, subsequent, individual, points, leads, does, include, examples, root, typically, ransac, done, approximating, key, sub, deciding, predictor, variables, adding, always, reduces, residual, unchanged, contrast, validated, will, decrease, valuable, increase, worthless, avoids, self, influence, draws, toward, making, appear, really, predicts, form, single, another, fold, splits, into, turn, remaining, training, predict, averaging, predictions, across, yields, overall, measure, employed, repeatedly, building, trees, predictive, constructing, those, doubt, impossible, very, complicated, formulas, calculation, techniques, updating, transitions, reconfiguration, context, sequentially, weighted, allows, low, copies, high, type, algorithms, filters, purpose, deriving, called, odds, proportion, best, rely, resampled, concluded, likely, occur, generating, counterfactual, creation, observed, redirected, free, item, projects, printable, download, print, export, switch, legacy, parser, get, shortened, url, cite, permanent, link, what, here, actions, english, talk, português, polski, 한국어, 日本語, italiano, فارسی, español, deutsch, čeština, català, top, personal, pages, recent, community, learn, help, contribute, current, events, navigation, jump, content,
Text of the page (random words):
xample of the plug in principle the bootstrapping method bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean median proportion odds ratio correlation coefficient or regression coefficient it has been called the plug in principle 1 as it is the method of estimation of functionals of a population distribution by evaluating the same functionals at the empirical distribution based on a sample for example 1 when estimating the population mean this method uses the sample mean to estimate the population median it uses the sample median to estimate the population regression line it uses the sample regression line it may also be used for constructing hypothesis tests it is often used as a robust alternative to inference based on parametric assumptions when those assumptions are in doubt or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors bootstrapping techniques are also used in the updating selection transitions of particle filters genetic type algorithms and related resample reconfiguration monte carlo methods used in computational physics 2 3 in this context the bootstrap is used to replace sequentially empirical weighted probability measures by empirical measures the bootstrap allows to replace the samples with low weights by copies of the samples with high weights cross validation edit main article cross validation statistics cross validation is a statistical method for validating a predictive model subsets of the data are held out for use as validating sets a model is fit to the remaining data a training set and used to predict for the validation set averaging the quality of the predictions across the validation sets yields an overall measure of prediction accuracy cross validation is employed repeatedly in building decision trees one form of cross validation leaves out a single observation at a time this is similar to the jackknife another k fold cross validation splits the data into k subsets each is held out in turn as the validation set this avoids self influence for comparison in regression analysis methods such as linear regression each y value draws the regression line toward itself making the prediction of that value appear more accurate than it really is cross validation applied to linear regression predicts the y value for each observation without using that observation this is often used for deciding how many predictor variables to use in regression without cross validation adding predictors always reduces the residual sum of squares or possibly leaves it unchanged in contrast the cross validated mean square error will tend to decrease if valuable predictors are added but increase if worthless predictors are added 4 monte carlo cross validation edit main article cross validation statistics repeated random sub sampling validation subsampling is an alternative method for approximating the sampling distribution of an estimator the two key differences to the bootstrap are the resample size is smaller than the sample size and resampling is done without replacement the advantage of subsampling is that it is valid under much weaker conditions compared to the bootstrap in particular a set of sufficient conditions is that the rate of convergence of the estimator is known and that the limiting distribution is continuous in addition the resample or subsample size must tend to infinity together with the sample size but at a smaller rate so that their ratio converges to zero while subsampling was originally proposed for the case of independent and identically distributed iid data only the methodology has been extended to cover time series data as well in this case one resamples blocks of subsequent data rather than individual data points there are many cases of applied interest where subsampling leads to valid inference whereas bootstrapping does not for example such cases include examples where the rate of convergence of the estimator is not the square root of the sample size or when the limiting distribution is non normal when both subsampling and the bootstrap are consistent the bootstrap is typically more accurate ransac is a popular algorithm using subsampling jackknife cross validation edit main article jackknife resampling jackknifing jackknife cross validation is used in statistical inference to estimate the bias and standard error variance of a statistic when a random sample of observations is used to calculate it historically this method preceded the invention of the bootstrap with quenouille inventing this method in 1949 and tukey extending it in 1958 5 6 this method was foreshadowed by mahalanobis who in 1946 suggested repeated estimates of the statistic of interest with half the sample chosen at random 7 he coined the name interpenetrating samples for this method quenouille invented this method with the intention of reducing the bias of the sample estimate tukey extended this method by assuming that if the replicates could be considered identically and independently distributed then an estimate of the variance of the sample parameter could be made and that it would be approximately distributed as a t variate with n 1 degrees of freedom n being the sample size the basic idea behind the jackknife variance estimator lies in systematically recomputing the statistic estimate leaving out one or more observations at a time from the sample set from this new set of replicates of the statistic an estimate for the bias and an estimate for the variance of the statistic can be calculated jackknife is equivalent to the random subsampling leave one out cross validation it only differs in the goal 8 for many statistical parameters the jackknife estimate of variance tends asymptotically to the true value almost surely in technical terms one says that the jackknife estimate is consistent the jackknife is consistent for the sample means sample variances central and non central t statistics with possibly non normal populations sample coefficient of variation maximum likelihood estimators least squares estimators correlation coefficients and regression coefficients it is not consistent for the sample median in the case of a unimodal variate the ratio of the jackknife variance to the sample variance tends to be distributed as one half the square of a chi square distribution with two degrees of freedom instead of using the jackknife to estimate the variance it may instead be applied to the log of the variance this transformation may result in better estimates particularly when the distribution of the variance itself may be non normal the jackknife like the original bootstrap is dependent on the independence of the data extensions of the jackknife to allow for dependence in the data have been proposed one such extension is the delete a group method used in association with poisson sampling comparison of bootstrap and jackknife edit both methods the bootstrap and the jackknife estimate the variability of a statistic from the variability of that statistic between subsamples rather than from parametric assumptions for the more general jackknife the delete m observations jackknife the bootstrap can be seen as a random approximation of it both yield similar numerical results which is why each can be seen as approximation to the other although there are huge theoretical differences in their mathematical insights the main practical difference for statistics users is that the bootstrap gives different results when repeated on the same data whereas the jackknife gives exactly the same result each time because of this the jackknife is popular when the estimates need to be verified several times before publishing e g official statistics agencies on the other hand when this verification feature is not crucial and it is of interest not to have a number but just an idea of its distribution the bootstrap is preferred e g studies in physics economics biological sciences whether to use the bootstrap or the jackknife may depend more on operational aspects than on statistical concerns of a survey the jackknife originally used for bias reduction is more of a specialized method and only estimates the variance of the point estimator this can be enough for basic statistical inference e g hypothesis testing confidence intervals the bootstrap on the other hand first estimates the whole distribution of the point estimator and then computes the variance from that while powerful and easy this can become highly computationally intensive the bootstrap can be applied to both variance and distribution estimation problems however the bootstrap variance estimator is not as good as the jackknife or the balanced repeated replication brr variance estimator in terms of the empirical results furthermore the bootstrap variance estimator usually requires more computations than the jackknife or the brr thus the bootstrap is mainly recommended for distribution estimation attribution needed 9 there is a special consideration with the jackknife particularly with the delete 1 observation jackknife it should only be used with smooth differentiable statistics e g totals means proportions ratios odd ratios regression coefficients etc not with medians or quantiles this could become a practical disadvantage this disadvantage is usually the argument favoring bootstrapping over jackknifing more general jackknifes than the delete 1 such as the delete m jackknife or the delete all but 2 hodges lehmann estimator overcome this problem for the medians and quantiles by relaxing the smoothness requirements for consistent variance estimation usually the jackknife is easier to apply to complex sampling schemes than the bootstrap complex sampling schemes may involve stratification multiple stages clustering varying sampling weights non response adjustments calibration post stratification and under unequal probability sampling designs theoretical aspects of both the bootstrap and the jackknife can be found in shao and tu 1995 10 whereas a basic introduction is accounted in wolter 2007 11 the bootstrap estimate of model prediction bias is more precise than jackknife estimates with linear models such as linear discriminant function or multiple regression 12 see also edit bootstrap aggregating bagging confidence distribution genetic algorithm monte carlo method nonparametric statistics particle filter pseudoreplication non uniform random variate generation random permutation replication statistics surrogate data testing references edit 1 2 logan j david and wolesensky willian r mathematical methods in biology pure and applied mathematics a wiley interscience series of texts monographs and tracts john wiley sons inc 2009 chapter 6 statistical inference section 6 6 bootstrap methods del moral pierre 2004 feynman kac formulae genealogical and interacting particle approximations probability and its applications springer p 575 doi 10 1007 978 1 4684 9393 1 isbn 978 1 4419 1902 1 series probability and applications del moral pierre 2013 mean field simulation for monte carlo integration chapman hall crc press p 626 monographs on statistics applied probability verbyla d 1986 potential prediction bias in regression and discriminant analysis canadian journal of forest research 16 6 1255 1257 bibcode 1986cajfr 16 1255v doi 10 1139 x86 222 quenouille m h 1949 approximate tests of correlation in time series journal of the royal statistical society series b 11 1 68 84 doi 10 1111 j 2517 6161 1949 tb00023 x jstor 2983696 tukey j w 1958 bias and confidence in not quite large samples preliminary report annals of mathematical statistics 29 2 614 jstor 2237363 mahalanobis p c 1946 proceedings of a meeting of the royal statistical society held on july 16th 1946 journal of the royal statistical society 109 4 325 370 jstor 2981330 encyclopedia of bioinformatics and computational biology abc of bioinformatics elsevier 2018 08 21 p 544 isbn 978 0 12 811432 2 shao j and tu d 1995 the jackknife and bootstrap springer verlag inc pp 281 shao j tu d 1995 the jackknife and bootstrap springer wolter k m 2007 introduction to variance estimation second ed springer verbyla d litvaitis j 1989 resampling methods for evaluating classification accuracy of wildlife habitat models environmental management 13 6 783 787 bibcode 1989enman 13 783v doi 10 1007 bf01868317 s2cid 153448048 literature edit good p 2006 resampling methods 3rd ed birkhauser wolter k m 2007 introduction to variance estimation 2nd edition springer inc pierre del moral 2004 feynman kac formulae genealogical and interacting particle systems with applications springer series probability and applications isbn 978 0 387 20268 6 pierre del moral 2013 del moral pierre 2013 mean field simulation for monte carlo integration chapman hall crc press monographs on statistics and applied probability isbn 9781466504059 jiang w simon r a comparison of bootstrap methods and an adjusted bootstrap approach for estimating the prediction error in microarray classification stat med 2007 dec 20 26 29 5320 34 doi 10 1002 sim 2968 pmid 17624926 https brb nci nih gov techreport prederr_rev_0407 pdf external links edit software edit angelo canty and brian ripley 2010 boot bootstrap r s plus functions r package version 1 2 43 functions and datasets for bootstrapping from the book bootstrap methods and their applications by a c davison and d v hinkley 1997 cup statistics101 resampling bootstrap monte carlo simulation program r package samplingvarest sampling variance estimation implements functions for estimating the sampling variance of some point estimators paired randomization permutation test for evaluation of trec results randomization permutation tests to evaluate outcomes in information retrieval experiments with and without adjustments for multiple comparisons bioconductor resampling based multiple hypothesis testing with applications to genomics permtest an r package to compare the variability within and distance between two groups within a set of microarray data bootstrap resampling interactive demonstration of hypothesis testing with bootstrap resampling in r permutation test interactive demonstration of hypothesis testing with permutation test in r v t e statistics outline index descriptive statistics continuous data center mean arithmetic arithmetic geometric contraharmonic cubic generalized power geometric harmonic heronian heinz lehmer median mode dispersion average absolute deviation coefficient of variation interquartile range percentile range standard deviation variance shape central limit theorem moments kurtosis l moments skewness count data index of dispersion summary tables contingency table frequency distribution grouped data dependence partial correlation pearson prod...
|
