R/ACR.R

In dream: DiffeRential Evolution Adaptive Metropolis

## ACR Upper percentiles critical value for test of single multivariate normal outlier.
## From the method given by Wilks (1963) and approaching to a F distribution
## function by the Yang and Lee (1987) formulation, we provide an m-file to
## get the critical value of the maximun squared Mahalanobis distance to detect
## outliers from a normal multivariate sample.
## 
## Syntax: function x = ACR(p,n,alpha) 
## $$ The function's name is giving as a gratefull to Dr. Alvin C. Rencher for his
## unvaluable contribution to multivariate statistics with his text 'Methods of 
## Multivariate Analysis'.$$
## 
## Inputs:
##' @param p number of independent variables.
##' @param n sample size.
##' @param alpha significance level (default = 0.05).
## 
## Output:
##' @return ACR value of the maximum squared Mahalanobis distance.
## 
## We can generate all the critical values of the maximun squared Mahalanobis
## distance presented on the Table XXXII of by Barnett and Lewis (1978) and 
## Table A.6 of Rencher (2002). Also with any given significance level (alpha).
## 
## Example: For p = 3; n = 25; alpha=0.01;
## 
## Calling on Matlab the function: 
## ACR(p,n,alpha)
## 
## Answer is:
## 
## 13.1753
## 
## Created by A. Trujillo-Ortiz, R. Hernandez-Walls, A. Castro-Perez and K. Barba-Rojo
## Facultad de Ciencias Marinas
## Universidad Autonoma de Baja California
## Apdo. Postal 453
## Ensenada, Baja California
## Mexico.
## atrujo@uabc.mx
## 
## Copyright. August 20, 2006.
## 
## To cite this file, this would be an appropriate format:
## Trujillo-Ortiz, A., R. Hernandez-Walls, A. Castro-Perez and K. Barba-Rojo. (2006).
## ACR:Upper percentiles critical value for test of single multivariate normal outlier.
## A MATLAB file. [WWW document]. URL http://www.mathworks.com/matlabcentral/
## fileexchange/loadFile.do?objectId=12161
## 
## References:
## Barnett, V. and Lewis, T. (1978), Outliers on Statistical Data.
## New-York:John Wiley & Sons.
## Rencher, A. C. (2002), Methods of Multivariate Analysis. 2nd. ed.
## New-Jersey:John Wiley & Sons. Chapter 13 (pp. 408-450).
## Wilks, S. S. (1963), Multivariate Statistical Outliers. Sankhya, 
## Series A, 25: 407-426.
## Yang, S. S. and Lee, Y. (1987), Identification of a Multivariate
## Outlier. Presented at the Annual  Meeting of the American
## Statistical Association, San Francisco, August 1987.
##
ACR <- function(p,n,alpha){

  if (missing(alpha)) alpha <- 0.05

  if (alpha<=0 | alpha>=1) stop("Significance level must be between 0 and 1")

  if (missing(p)|missing(n)) stop("Requires args p and n")

  a <- alpha
  ## F distribution critical value with p and n-p-1 degrees of freedom using the Bonferroni correction
  Fc <- qf(1-a/n,p,n-p-1)
  ACR <- (p*(n-1)^2*Fc)/(n*(n-p-1)+(n*p*Fc))

  return(ACR)
  
} ##ACR