Posts tagged with multivariate

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July 12, 2010

A robust Hotelling test…

Recently I was in need of testing a mean vector. I wrote a few lines of code in R and had it done perfectly. Hotelling test is one of the least interesting test to me. never really figured out why…

At that time I had some time to search more about it. One of the most common things to search for a test is a robust version of it (at least that’s what I search for!). A little search in the 3rd page of google results leads to the following :

One-sample and two-sample robust Hotelling tests with fast and robust bootstrap

The classical Hotelling test for testing if the mean equals a certain value or if two means are equal is modified into a robust one through substitution of the empirical estimates by the MM-estimates of location and scatter. The MM-estimator, using Tukey’s biweight function, is tuned by default to have a breakdown point of 50% and 95% location efficiency. This could be changed through the control argument if desired.

Robust Hotelling T2 test

Performs one and two sample Hotelling T2 tests as well as robust one-sample Hotelling T2 test.

The first uses MM and S estimators while the latter a Minimum Covariance Determinant one. You can get info on those on the links in the end of the post. What might be crucial to you is that MM/S estimators would be more time comsuming compared to MCD. A little demonstation is the following.. Read the rest of this entry »

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February 23, 2010

A quicky..

If you’re (and you should) interested in principal components then take a good look at this. The linked post will take you by hand to do everything from scratch. If you’re not in the mood then the dollowing R functions will help you.

An example.

# Generates sample matrix of five discrete clusters that have
# very different mean and standard deviation values.
z1 <- rnorm(10000, mean=1, sd=1);
z2 <- rnorm(10000, mean=3, sd=3);
z3 <- rnorm(10000, mean=5, sd=5);
z4 <- rnorm(10000, mean=7, sd=7);
z5 <- rnorm(10000, mean=9, sd=9);
mydata <- matrix(c(z1, z2, z3, z4, z5), 2500, 20, byrow=T,
dimnames=list(paste("R", 1:2500, sep=""), paste("C", 1:20, sep="")))

# Performs principal component analysis after scaling the data.
# It returns a list with class "prcomp" that contains five components:
#   (1) the standard deviations (sdev) of the principal components,
#   (2) the matrix of eigenvectors (rotation),
#   (3) the principal component data (x),
#   (4) the centering (center) and
#   (5) scaling (scale) used.
pca <- prcomp(mydata, scale=T)
 Read the rest of this entry »
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November 28, 2009

Probability of hypercubes…

…in R of course!

There is a handy function to do those calculations. Normally (ahh!) you might resolve to a symbolic calculation package (Maple,Mathematica etc.)  but that is not the situation any more. The calculations are done with the mnormt package. Relevant functions exist in other packages as well (R : Distributions)

x <- seq(-2,4,length=21)
y <- 2*x+10
z <- x+cos(y)
mu <- c(1,12,2)
Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
p2 <- sadmvn(lower=rep(-Inf,2), upper=c(2, 11), mu[1:2], Sigma[1:2,1:2])
> p2
[1] 0.3273202
attr(,"error")
[1] 2e-16
attr(,"status")
[1] "normal completion"
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