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Mixture models are important in theoretical and applied statistics. Mathematical statistics courses for undergraduate senior or first-year graduate students should expose students to some properties of the mixture model. In current textbooks, the predominant approach to obtain the mixture distribution is based on marginalization of the joint distribution defined by the mixture model. This article proposes the use of moment generating functions (mgf) to obtain the distribution of some mixtures. For mixtures that do not have a mgf, a generalization using characteristic functions is illustrated with an example. The mgf approach tends to be simple and it uses some of the tools already built into the course. Several examples are used to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Based on one observation X from a N(θ, θ) distribution where θ(> 0) is an unknown parameter, this article provides an exact expression of the minimum variance unbiased estimator of θ based on the complete and sufficient statistic ∣X∣. Even though N(θ, θ) belongs to a one-parameter exponential family, I discuss some small surprises and intricacies that are worth noting. [ABSTRACT FROM AUTHOR]

Restricted maximum likelihood (REML) estimation of the parameters of the mixed model has become commonplace, even becoming the default option in many statistical software packages. However, a review of the literature indicates a need to update and clarify model selection techniques under REML, as ambiguities exist on the appropriateness of existing information criteria in this setting. A simulation study as well as an application assisted in gaining an understanding of the performance of information criteria in selecting the best model when using REML estimation. [ABSTRACT FROM AUTHOR]

Treatment effects are commonly analyzed by relating post-treatment (F) measurements with corresponding baseline (B) measurements. As effect measures, absolute difference (D) and percent change (PC) are used more than symmetrized percent change (SPC). However, all these measures alter the dependency structure with B and their distributions can differ from B and F. To examine their interpretability and relative performance, we considered simulations under independence and additive and multiplicative correlation structures for parametric and nonparametric analyses. Under independence, nonparametric analysis on F had the greatest power. Elsewhere, simple ANOVA on SPC had power equal to or greater than alternative analysis methods. [ABSTRACT FROM AUTHOR]

The article reports that a linear algebra perspective can provide a great deal of insight into statistical questions. Researchers presents an analysis of the behavior of the sample correlation coefficient when one of the samples is nearly constant. Linear algebra can give insight into the sample correlation coefficient. They can also be helpful in the study of correlation and covariance of distributions. Some linear algebra texts uses ideas from matrix theory in the context of analysis of variance but they do not point out the relationship between the inner product and covariance.

This classroom paradox is an effective tool to motivate students to accept as fact only those things that are backed by reasonable evidence. A two-player game consists of repeated tosses of a loaded coin, until one of the player's three outcome sequences—for example, Tails, Heads, Tails (THT)—occurs. Player 2 chooses his or her sequence after hearing Player 1's choice. The question is, if we know that the probability of Heads is 70%, does Player 1 or Player 2 have the advantage? To their detriment, nearly all students will want to go first and select HHH, which is not even the best choice for the universally disadvantaged Player 1. This example can be presented at several different levels, tuned to the background of the class. [ABSTRACT FROM AUTHOR]

Professor Mudgeon writes simple linear regression questions so that the numbers always work out nicely. A student uses knowledge of linear models to learn that by constructing errors that are orthogonal to the design matrix, regression coefficients can be set to any desired value. An example is provided to construct data to follow a particular example. [ABSTRACT FROM AUTHOR]

The article discusses various articles published within the issue, including one on statistician Samuel S. Wilks' contributions to statistics and another by W. Edwards Deming on Wilks award.

A response by the author is presented to a letter to the editor about his article "RETHINKING THE PAPER HELICOPTER: COMBINING STATISTICAL AND ENGINEERING KNOWLEDGE" in a previous issue.

A letter to the editor is presented in response the article "RETHINKING THE PAPER HELICOPTER: COMBINING STATISTICAL AND ENGINEERING KNOWLEDGE" in a previous issue.