Small-sample inference for the comparison of means of log-normal distributions

We propose a likelihood-based test for comparing the means of two or more log-normal distributions, with possibly unequal variances. A modification to the likelihood ratio test is needed when sample sizes are small. The performance of the proposed procedures is compared with the F-ratio test using Monte Carlo simulations.     

Higher order inference for the consensus mean in inter-laboratory studies

In inter-laboratory studies, a fundamental problem of interest is inference concerning the consensus mean, when the measurements are made by several laboratories which may exhibit different within-laboratory variances, apart from the between laboratory variability. A heteroscedastic one-way random model is very often used to model this scenario. Under such a model, a modified signed log-likelihood ratio procedure is developed for the interval estimation of the common mean. Furthermore, simulation results are presented to show the accuracy of the proposed confidence interval, especially for small samples. The results are illustrated using an example on the determination of selenium in non-fat milk powder by combining the results of four methods. Here, the sample size is small, and the confidence limits for the common mean obtained by different methods produce very different results. The confidence interval based on the modified signed log-likelihood ratio procedure appears to be quite satisfactory.     

Categorical variables with many categories are preferentially selected in bootstrap‐based model selection procedures for multivariable regression models

Automated variable selection procedures, such as backward elimination, are commonly employed to perform model selection in the context of multivariable regression. The stability of such procedures can be investigated using a bootstrap‐based approach. The idea is to apply the variable selection procedure on a large number of bootstrap samples successively and to examine the obtained models, for instance, in terms of the inclusion of specific predictor variables. In this paper, we aim to investigate a particular important problem affecting this method in the case of categorical predictor variables with different numbers of categories and to give recommendations on how to avoid it. For this purpose, we systematically assess the behavior of automated variable selection based on the likelihood ratio test using either bootstrap samples drawn with replacement or subsamples drawn without replacement from the original dataset. Our study consists of extensive simulations and a real data example from the NHANES study. Our main result is that if automated variable selection is conducted on bootstrap samples, variables with more categories are substantially favored over variables with fewer categories and over metric variables even if none of them have any effect. Importantly, variables with no effect and many categories may be (wrongly) preferred to variables with an effect but few categories. We suggest the use of subsamples instead of bootstrap samples to bypass these drawbacks.     

Normal Approximation of a Discrete Distribution on Exact Test of Uniform Association in a 2 × 3 Table

For the analysis of 2 × 3 tables, TOMIZAWA (1993) considered an exact test of uniform association, which is an extension of independence, and then derived a discrete distribution. This paper gives a normal approximation of the discrete distribution and describes that the normalized statistic can test a one-sided hypothesis on the uniform association. Also it points out that the square of the normalized test statistic is equal to the Pearson's chi-squared statistic for testing the uniform association.     

On the efficiency of score tests for homogeneity in two-component parametric models for discrete data

Summary In many applications of two-component mixture models for discrete data such as zero-inflated models, it is often of interest to conduct inferences for the mixing weights. Score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose. But the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model. In this article, we develop a score test of homogeneity that overcomes the limitations of existing procedures. The technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation. We exploit this decomposition to lay the foundation of the test. Simulation results show that the proposed covariate-adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights. A real-life example in dental caries research is used to illustrate the methodology.