Tag: Statistical Programming

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Compute within-group multivariate statistics and store them in a list

I recently showed how to compute within-group multivariate statistics by using the SAS/IML language. However, a principal of good software design is to encapsulate functionality and write self-contained functions that compute and return the results. What is the best way to return multiple statistics from a SAS/IML module? A convenient

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How to evaluate the multivariate normal log likelihood

The multivariate normal distribution is used frequently in multivariate statistics and machine learning. In many applications, you need to evaluate the log-likelihood function in order to compare how well different models fit the data. The log-likelihood for a vector x is the natural logarithm of the multivariate normal (MVN) density

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Pooled, within-group, and between-group covariance matrices

A previous article discusses the pooled variance for two or groups of univariate data. The pooled variance is often used during a t test of two independent samples. For multivariate data, the analogous concept is the pooled covariance matrix, which is an average of the sample covariance matrices of the

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The Kolmogorov D distribution and exact critical values

If you have ever run a Kolmogorov-Smirnov test for normality, you have encountered the Kolmogorov D statistic. The Kolmogorov D statistic is used to assess whether a random sample was drawn from a specified distribution. Although it is frequently used to test for normality, the statistic is "distribution free" in

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The Kullback–Leibler divergence between discrete probability distributions

If you have been learning about machine learning or mathematical statistics, you might have heard about the Kullback–Leibler divergence. The Kullback–Leibler divergence is a measure of dissimilarity between two probability distributions. It measures how much one distribution differs from a reference distribution. This article explains the Kullback–Leibler divergence and shows

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Print SAS/IML variables with formats

A SAS/IML programmer asked about the best way to print multiple SAS/IML variables when each variable needs a different format. He wanted the output to resemble the "Parameter Estimates" table that is produced by PROC REG and other SAS/STAT procedures. This article shows four ways to print SAS/IML vectors in

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Predict a random integer: The tradeoff between bias and variance

Books about statistics and machine learning often discuss the tradeoff between bias and variance for an estimator. These discussions are often motivated by a sophisticated predictive model such as a regression or a decision tree. But the basic idea can be seen in much simpler situations. This article presents a

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ROC curves for a binormal sample

In a previous article, I discussed the binormal model for a binary classification problem. This model assumes a set of scores that are normally distributed for each population, and the mean of the scores for the Negative population is less than the mean of scores for the Positive population. I