I've been working on a new book about Simulating Data with SAS. In researching the chapter on simulation of multivariate data, I've noticed that the probability density function (PDF) of multivariate distributions is often specified in a matrix form. Consequently, the multivariate density can usually be computed by using the
I've been a fan of statistical simulation and other kinds of computer experimentation for many years. For me, simulation is a good way to understand how the world of statistics works, and to formulate and test conjectures. Last week, while investigating the efficiency of the power method for finding dominant
When I was at SAS Global Forum last week, a SAS user asked my advice regarding a SAS/IML program that he wrote. One step of the program was taking too long to run and he wondered if I could suggest a way to speed it up. The long-running step was
In a previous post I showed how to implement Stewart's (1980) algorithm for generating random orthogonal matrices in SAS/IML software. By using the algorithm, it is easy to generate a random matrix that contains a specified set of eigenvalues. If D = diag(λ1, ..., λp) is a diagonal matrix and
Because I am writing a new book about simulating data in SAS, I have been doing a lot of reading and research about how to simulate various quantities. Random integers? Check! Random univariate samples? Check! Random multivariate samples? Check! Recently I've been researching how to generate random matrices. I've blogged
Sometimes in matrix computations you need to obtain the values of certain submatrices such as the diagonal elements or the super- or subdiagonal elements. About a year ago, I showed one way to do that: convert subscripts to indices and vice-versa. However, a tip from @RLangTip on Twitter got me
I recently blogged about Mahalanobis distance and what it means geometrically. I also previously showed how Mahalanobis distance can be used to compute outliers in multivariate data. But how do you compute Mahalanobis distance in SAS? Computing Mahalanobis distance with built-in SAS procedures and functions There are several ways to
I have previously blogged about how to convert a covariance matrix into a correlation matrix in SAS (and the other way around). However, I still get questions about it, perhaps because my previous post demonstrated more than one way to accomplish each transformation. To eliminate all confusion, the following SAS/IML
A variance-covariance matrix expresses linear relationships between variables. Given the covariances between variables, did you know that you can write down an invertible linear transformation that "uncorrelates" the variables? Conversely, you can transform a set of uncorrelated variables into variables with given covariances. The transformation that works this magic is
Once again I rediscovered something that I once knew, but had forgotten. Fortunately, this blog is a good place to share little code snippets that I don't want to forget. I needed to compute the diagonal elements of a product of two matrices. In symbols, I have an nxp matrix,
