# roysPval: Roy's largest root exact test In pcev: Principal Component of Explained Variance

## Description

In the classical domain of PCEV applicability this function uses Johnstone's approximation to the null distribution of ' Roy's Largest Root statistic. It uses a location-scale variant of the Tracy-Wildom distribution of order 1.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```roysPval(pcevObj, ...) ## Default S3 method: roysPval(pcevObj, ...) ## S3 method for class 'PcevClassical' roysPval(pcevObj, shrink, index, ...) ## S3 method for class 'PcevSingular' roysPval(pcevObj, shrink, index, nperm, ...) ## S3 method for class 'PcevBlock' roysPval(pcevObj, shrink, index, ...) ```

## Arguments

 `pcevObj` A pcev object of class `PcevClassical` or `PcevBlock` `...` Extra parameters. `shrink` Should we use a shrinkage estimate of the residual variance? `index` If `pcevObj` is of class `PcevBlock`, `index` is a vector describing the block to which individual response variables correspond `nperm` Number of permutations for Tracy-Widom empirical estimate.

## Details

For singular PCEV, where number of variables is higher than the number of observations, one can choose between two aprroximations. First one, called 'Wishart', is based on the first term of expansion of the joint distribution of roots for singular beta ensemble. Second version of test, `estimation = "TW"`, assumes that largest root statistics follows Tracy-Wildom as in classical case. See vignette for the domains of the applicability of these tests.

Note that if `shrink` is set to `TRUE`, the location-scale parameters are estimated using a small number of permutations.

pcev documentation built on Oct. 13, 2017, 1:40 a.m.