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Rick WicklinMay 22, 2019 1

Gershgorin discs and the location of eigenvalues

The eigenvalues of a matrix are not easy to compute. It is remarkable, therefore, that with relatively simple mental arithmetic, you can obtain bounds for the eigenvalues of a matrix of any size. The bounds are provided by using a marvelous mathematical result known as Gershgorin's Disc Theorem. For certain

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Analytics | Programming Tips

Rick WicklinMay 20, 2019 6

Critical values of the Kolmogorov-Smirnov test

Recently I wrote about how to compute the Kolmogorov D statistic, which is used to determine whether a sample has a particular distribution. One of the beautiful facts about modern computational statistics is that if you can compute a statistic, you can use simulation to estimate the sampling distribution of

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Analytics | Learn SAS

Rick WicklinMay 15, 2019 2

What is Kolmogorov's D statistic?

Have you ever run a statistical test to determine whether data are normally distributed? If so, you have probably used Kolmogorov's D statistic. Kolmogorov's D statistic (also called the Kolmogorov-Smirnov statistic) enables you to test whether the empirical distribution of data is different than a reference distribution. The reference distribution

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Analytics | Programming Tips

Rick WicklinMay 8, 2019 3

Discrimination, accuracy, and stability in binary classifiers

At SAS Global Forum 2019, Daymond Ling presented an interesting discussion of binary classifiers in the financial industry. The discussion is motivated by a practical question: If you deploy a predictive model, how can you assess whether the model is no longer working well and needs to be replaced? Daymond

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Analytics | Programming Tips

Rick WicklinMay 6, 2019 1

How to simulate data from a generalized linear model

Here's a simulation tip: When you simulate a fixed-effect generalized linear regression model, don't add a random normal error to the linear predictor. Only the response variable should be random. This tip applies to models that apply a link function to a linear predictor, including logistic regression, Poisson regression, and

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Analytics | Learn SAS

Rick WicklinMay 1, 2019 1

Encodings of CLASS variables in SAS regression procedures: A cheat sheet

SAS regression procedures support several parameterizations of classification variables. When a categorical variable is used as an explanatory variable in a regression model, the procedure generates dummy variables that are used to construct a design matrix for the model. The process of forming columns in a design matrix is called

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Analytics | Programming Tips

Rick WicklinApril 24, 2019 0

A CUSUM test for autregressive models

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

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Analytics | Programming Tips

Rick WicklinApril 10, 2019 3

4 ways to compute an SSCP matrix

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

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Analytics | Data Visualization

Rick WicklinMarch 27, 2019 2

How to simulate multivariate outliers

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

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Analytics | Data Visualization

Rick WicklinMarch 4, 2019 1

Visualize SAT scores in North Carolina

Standardized tests like the SAT and ACT can cause stress for both high school students and their parents, but according to a Wall Street Journal article, the SAT and ACT "provide an invaluable measure of how students are likely to perform in college and beyond." Naturally, students wonder how their

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