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.
In univariate data analysis, the median is often used as an alternative to the mean because the mean is sensitive to outliers in the data, whereas the median is a robust statistic. For higher-dimensional data, the mean and the centroid are both used to represent the "center" of a cloud
Recently, a colleague struggled to find the source of a run-time error happening somewhere within a very large library of SAS IML function modules. Since the error happens at run time, I told my colleague about how to find the location of a run time error by reading the traceback
In some applications, it is useful to permute the rows or the columns of a matrix. A previous article discusses how random permutation of columns (within each row) are useful in constructing permutation tests. This article shows a simpler situation: Permuting the rows of a matrix to change their order.
It is difficult to evaluate high-dimensional integrals. One numerical technique that can be useful is quasi-Monte Carlo integration. In this article, I show how you can generate quasirandom points in SAS and use them to evaluate a definite integral on a compact region. For simplicity, the example in this article
A previous article shows how to convert a positive integer from base 10 to any other arbitrary base. For example, 15 (base 10) = 120 (base 3) because 15 = 1*32 + 2*31 + 0*30. Representing integers is probably familiar to many readers. But did you know that you can
While many applications of Monte Carlo techniques use pseudorandom numbers, some applications that involve integrals are more accurate when you use quasirandom numbers, which, despite their names, are not random but are deterministic sequences of numbers. Many of these sequences are constructed by representing base-10 numbers in a different base.
Many data analysts are familiar with logistic regression, where the response variable, Y, has two observed values, often represented as Y=0 and Y=1. The case Y=0 encodes that an event did not happen. For example, a patient did not experience some disease or did not die. The opposite case (Y=1)
A previous article discusses various ways to overlay a density curve on a histogram in SAS. SAS provides several procedures that handle this task for common univariate probability distributions such as normal, lognormal, and gamma. If you define and use a less common distribution, you can write a GTL template
SAS has several procedures that can fit a probability distribution to data, plot a histogram, and overlay one or more density estimates: PROC UNIVARIATE in Base SAS enables you to overlay parametric density curves from about 20 common continuous probability distributions, such as normal, lognormal, and gamma. It also enables
The power method is a well-known iterative scheme to approximate the largest eigenvalue (in absolute value) of a symmetric matrix. It is useful in practice when you need only the largest eigenvalue and eigenvector of a large matrix. The method requires only matrix-vector multiplication and vector scaling. There is a
