## Tag: Bootstrap and Resampling

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Four essential sampling methods in SAS

Many simulation and resampling tasks use one of four sampling methods. When you draw a random sample from a population, you can sample with or without replacement. At the same time, all individuals in the population might have equal probability of being selected, or some individuals might be more likely

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Sample with replacement and unequal probability in SAS

How do you sample with replacement in SAS when the probability of choosing each observation varies? I was asked this question recently. The programmer thought he could use PROC SURVEYSELECT to generate the samples, but he wasn't sure which sampling technique he should use to sample with unequal probability. This

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Resampling and permutation tests in SAS

My colleagues at the SAS & R blog recently posted an example of how to program a permutation test in SAS and R. Their SAS implementation used Base SAS and was "relatively cumbersome" (their words) when compared with the R code. In today's post I implement the permutation test in

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Permute elements within each row of a matrix

Bootstrap methods and permutation tests are popular and powerful nonparametric methods for testing hypotheses and approximating the sampling distribution of a statistic. I have described a SAS/IML implementation of a bootstrap permutation test for matched pairs of data (an alternative to a matched-pair t test) in my paper "Modern Data

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Sample without replacement in SAS

Last week I showed three ways to sample with replacement in SAS. You can use the SAMPLE function in SAS/IML 12.1 to sample from a finite set or you can use the DATA step or PROC SURVEYSELECT to extract a random sample from a SAS data set. Sampling without replacement

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Sample with replacement in SAS

Randomly choosing a subset of elements is a fundamental operation in statistics and probability. Simple random sampling with replacement is used in bootstrap methods (where the technique is called resampling), permutation tests and simulation. Last week I showed how to use the SAMPLE function in SAS/IML software to sample with

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Sampling with replacement: Now easier than ever in the SAS/IML language

With each release of SAS/IML software, the language provides simple ways to carry out tasks that previously required more effort. In 2010 I blogged about a SAS/IML module that appeared in my book Statistical Programming with SAS/IML Software, which was written by using the SAS/IML 9.2. The blog post showed

Programming Tips
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Output percentiles of multiple variables in a tabular format

A challenge for statistical programmers is getting data into the right form for analysis. For graphing or analyzing data, sometimes the "wide format" (each subject is represented by one row and many variables) is required, but other times the "long format" (observations for each subject span multiple rows) is more

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How to compute p-values for a bootstrap distribution

I was recently asked the following question: I am using bootstrap simulations to compute critical values for a statistical test. Suppose I have test statistic for which I want a p-value. How do I compute this? The answer to this question doesn't require knowing anything about bootstrap methods. An equivalent

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Ranking with confidence: Part 2

In a previous post, I described how to compute means and standard errors for data that I want to rank. The example data (which are available for download) are mean daily delays for 20 US airlines in 2007. The previous post carried out steps 1 and 2 of the method

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Ranking with confidence: Part 1

I recently posted an article about representing uncertainty in rankings on the blog of the ASA Section for Statistical Programmers and Analysts (SSPA). The posting discusses the importance of including confidence intervals or other indicators of uncertainty when you display rankings. Today's article complements the SSPA post by showing how