Resampling

About: Resampling is a research topic. Over the lifetime, 5428 publications have been published within this topic receiving 242291 citations.

Introduction to Statistics Through Resampling Methods and R/S-PLUS

Abstract: Preface. 1. Variation. 1.1 Variation. 1.2. Collecting Data. 1.3. Summarizing Your Data. 1.4. Types of Data. 1.5. Reporting Your Results. 1.6. Measures of Location. 1.7. Samples and Populations. 1.8. Variation- Within and Between. 1.9. Summary and Review. 2. Probability. 2.1. Probability. 2.2. Binomial. 2.3. Condition Probability. 2.4. Independence. 2.5. Applications to Genetics. 2.6. Summary and Review. 3. Distributions. 3.1. Distribution of Values. 3.2. Discrete Distributions. 3.3. Continuous Distributions. 3.4. Properties of Independence Observations. 3.5. Testing A Hypothesis. 3.6. Estimating Effect Size. 3.7 Summary and Review. 4. Testing Hypotheses. 4.1. One-Sample Problems. 4.2. Comparing Two Samples. 4.3. Which Test Should e Use? 4.4. Summary and Review. 5. Designing an Experiment or Survey. 5.1. The Hawthorne Effect. 5.2. Designing an Experiment or Survey. 5.3. How Large a Sample. 5.4. Meta-Analysis. 5.5. Summary and Review. 6. Analyzing Complex Experiments. 6.1. Changes Measured in Percentages. 6.2. Comparing More Than Two Samples. 6.3. Equalizing Variances. 6.4. Categorical Data. 6.5. Multivariate Analysis. 6.6. Summary and Review. 7. Developing Models. 7.1. Models. 7.2. Regression. 7.3. Fitting a Regression Equation. 7.4. Problems with Regression. 7.5 Quantile Regression. 7.6. Validation. 7.7 Classification and Regression Trees. 7.8 Summary and Review. 8. Reporting Your Findings. 8.1. What to Report. 8.2. Text, Tables, of Graph? 8.3. Summarizing Your Results. 8.4 Reporting Analysis Results. 8.5 Exceptions are the Real Story. 9. Problem Solving. 9.1. Real Life Problems. 9.2. Problem Sets. 9.3. Solutions. Appendix: S-PLUS. Answers to Selected Exercises. Subject Index. Index to R Functions.

On bootstrap hypothesis testing

Abstract: Summary We describe methods for constructing bootstrap hypothesis tests, illustrating our approach using analysis of variance. The importance of pivotalness is discussed. Pivotal statistics usually result in improved accuracy of level. We note that hypothesis tests and confidence intervals call for different methods of resampling, so as to ensure that accurate critical point estimates are obtained in the former case even when data fail to comply with the null hypothesis. Our main points are illustrated by a simulation study and application to three real data sets.

A permutation test sensitive to differences in areas for comparing ROC curves from a paired design

Abstract: The area under the receiver operating characteristic (ROC) curve (AUC) is a widely accepted summary index of the overall performance of diagnostic procedures and the difference between AUCs is often used when comparing two diagnostic systems. We developed an exact non-parametric statistical procedure for comparing two ROC curves in paired design settings. The test which is based on all permutations of the subject specific rank ratings is formally a test for equality of ROC curves that is sensitive to the alternatives of AUC difference. The operating characteristics of the proposed test were evaluated using extensive simulations over a wide range of parameters. The proposed procedure can be easily implemented in experimental ROC data sets. For small samples and for underlying parameters that are common in experimental studies in diagnostic imaging the test possesses good operating characteristics and is more powerful than the conventional non-parametric procedure for AUC comparisons. We also derived an asymptotic version of the test which uses an exact estimate of the variance in the permutation space and provides a good approximation even when the sample sizes are small. This asymptotic procedure is a simple and precise approximation to the exact test and is useful for large sample sizes where the exact test may be computationally burdensome.

Some nonasymptotic results on resampling in high dimension, I: Confidence regions

Abstract: We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a non-asymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two approaches, the first based on a concentration principle (valid for a large class of resampling weights) and the second on a direct resampled quantile, specifically using Rademacher weights. Several intermediate results established in the approach based on concentration principles are of self-interest. We also discuss the question of accuracy when using Monte-Carlo approximations of the resampled quantities. We present an application of these results to the one-sided and two-sided multiple testing problem, in which we derive several resampling-based step-down procedures providing a non-asymptotic FWER control. We compare our different procedures in a simulation study, and we show that they can outperform Bonferroni's or Holm's procedures as soon as the observed vector has sufficiently correlated coordinates.