Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
Did you know that SAS provides built-in support for working with probability distributions that are finite mixtures of normal distributions? This article shows examples of using the "NormalMix" distribution in SAS and describes a trick that enables you to easily work with distributions that have many components. As with all
The CUSUM test has many incarnations. Different areas of statistics use different assumption and test for different hypotheses. This article presents a brief overview of CUSUM tests and gives an example of using the CUSUM test in PROC AUTOREG for autoregressive models in SAS. A CUSUM test uses the cumulative
Many statistical tests use a CUSUM statistic as part of the test. It can be confusing when a researcher refers to "the CUSUM test" without providing details about exactly which CUSUM test is being used. This article describes a CUSUM test for the randomness of a binary sequence. You start
I think every course in exploratory data analysis should begin by studying Anscombe's quartet. Anscombe's quartet is a set of four data sets (N=11) that have nearly identical descriptive statistics but different graphical properties. They are a great reminder of why you should graph your data. You can read about
A quadratic form is a second-degree polynomial that does not have any linear or constant terms. For multivariate polynomials, you can quickly evaluate a quadratic form by using the matrix expression x` A x This computation is straightforward in a matrix language such as SAS/IML. However, some computations in statistics
In numerical linear algebra, there are often multiple ways to solve a problem, and each way is useful in various contexts. In fact, one of the challenges in matrix computations is choosing from among different algorithms, which often vary in their use of memory, data access, and speed. This article
Suppose you need to assign 100 patients equally among 3 treatment groups in a clinical study. Obviously, an equal allocation is impossible because the second number does not evenly divide the first, but you can get close by assigning 34 patients to one group and 33 to the others. Mathematically,
I've previously written about how to deal with nonconvergence when fitting generalized linear regression models. Most generalized linear and mixed models use an iterative optimization process, such as maximum likelihood estimation, to fit parameters. The optimization might not converge, either because the initial guess is poor or because the model
Many SAS procedures support the BY statement, which enables you to perform an analysis for subgroups of the data set. Although the SAS/IML language does not have a built-in "BY statement," there are various techniques that enable you to perform a BY-group analysis. The two I use most often are
In simulation studies, sometimes you need to simulate outliers. For example, in a simulation study of regression techniques, you might want to generate outliers in the explanatory variables to see how the technique handles high-leverage points. This article shows how to generate outliers in multivariate normal data that are a
