I've blogged several times about multivariate normality, including how to generate random values from a multivariate normal distribution. But given a set of multivariate data, how can you determine if it is likely to have come from a multivariate normal distribution? The answer, of course, is to run a goodness-of-fit
I recently saw a SAS Knowledge Base article called "How to stop processing your code if a certain condition is met." The article discusses the use of the %RETURN macro statement to abort the execution of a SAS program if some condition occurs. The "condition" is usually an error that
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
In two previous blog posts I worked through examples in the survey article, "Robust statistics for outlier detection," by Peter Rousseeuw and Mia Hubert. Robust estimates of location in a univariate setting are well-known, with the median statistic being the classical example. Robust estimates of scale are less well-known, with
In a previous blog post on robust estimation of location, I worked through some of the examples in the survey article, "Robust statistics for outlier detection," by Peter Rousseeuw and Mia Hubert. I showed that SAS/IML software and PROC UNIVARIATE both support the robust estimators of location that are mentioned
I encountered a wonderful survey article, "Robust statistics for outlier detection," by Peter Rousseeuw and Mia Hubert. Not only are the authors major contributors to the field of robust estimation, but the article is short and very readable. This blog post walks through the examples in the paper and shows
In my recent article on simulating Buffon's needle experiment, I computed the "running mean" of a series of values by using a single call to the CUSUM function in the SAS/IML language. For example, the following SAS/IML statements define a RunningMean function, generate 1,000 random normal values, and compute the
A recent question on a SAS Discussion Forum was "how can you overlay multiple kernel density estimates on a single plot?" There are three ways to do this, depending on your goals and objectives. Overlay different estimates of the same variable Sometimes you have a single variable and want to
