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.
To get better at something, you need to practice. That maxim applies to sports, music, and programming. If you want to be a better programmer, you need to write many programs. This article provides an example of forming the intersection of items in a SAS/IML list. It then provides several
After my recent articles on simulating data by using copulas, many readers commented about the power of copulas. Yes, they are powerful, and the geometry of copulas is beautiful. However, it is important to be aware of the limitations of copulas. This article creates a bizarre example of bivariate data,
In a previous article, I discussed various ways to solve a least-square linear regression model. I discussed the SWEEP operator (used by many SAS regression routines), the LU-based methods (SOLVE and INV in SAS/IML), and the QR decomposition (CALL QR in SAS/IML). Each method computes the estimates for the regression
In computational statistics, there are often several ways to solve the same problem. For example, there are many ways to solve for the least-squares solution of a linear regression model. A SAS programmer recently mentioned that some open-source software uses the QR algorithm to solve least-squares regression problems and asked
In general, it is hard to simulate multivariate data that has a specified correlation structure. Copulas make that task easier for continuous distributions. A previous article presented the geometry behind a copula and explained copulas in an intuitive way. Although I strongly believe that statistical practitioners should be familiar with
Do you know what a copula is? It is a popular way to simulate multivariate correlated data. The literature for copulas is mathematically formidable, but this article provides an intuitive introduction to copulas by describing the geometry of the transformations that are involved in the simulation process. Although there are
A recent article about how to estimate a two-dimensional distribution function in SAS inspired me to think about a related computation: a 2-D cumulative sum. Suppose you have numbers in a matrix, X. A 2-D cumulative sum is a second matrix, C, such that the C[p,q] gives the sum of
This article shows how to estimate and visualize a two-dimensional cumulative distribution function (CDF) in SAS. SAS has built-in support for this computation. Although the bivariate CDF is not used as much as the univariate CDF, the bivariate version is still a useful tool in understanding the probable values of
This article uses simulation to demonstrate the fact that any continuous distribution can be transformed into the uniform distribution on (0,1). The function that performs this transformation is a familiar one: it is the cumulative distribution function (CDF). A continuous CDF is defined as an integral, so the transformation is
A SAS programmer noticed that his SAS output was not displaying multiple blanks in his strings. He had some strings with leading blanks, others with trailing blanks, and others with multiple blanks in the middle. Yet, every time he used SAS to print the strings to the HTML destination, something
