Testing for a change point in a sequence of exponential random variables with repeated values

Two test statistics are proposed for the change-point problem with repeated values when the data follow an exponential distribution. The properties of these two statistics have been studied and their asymptotic distributions under the alternative have been derived. The powers of the two test statistics are compared. Real-data examples are presented to illustrate the application of these tests.     

A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

ABSTRACT

A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some prespecified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser’s directional two-sided test as well as the more recently introduced testing procedure of Jones and Tukey, each equivalent to running two one-sided tests, involve three possible decisions to infer the value of a unidimensional parameter. The latter procedure assumes that a point null hypothesis is impossible (e.g., that two treatments cannot have exactly the same effect), allowing a gain of statistical power. There are, however, situations where a point hypothesis is indeed plausible, for example, when considering hypotheses derived from Einstein’s theories. In this article, we introduce a five-decision rule testing procedure, equivalent to running a traditional two-sided test in addition to two one-sided tests, which combines the advantages of the testing procedures of Kaiser (no assumption on a point hypothesis being impossible) and Jones and Tukey (higher power), allowing for a nonnegligible (typically 20%) reduction of the sample size needed to reach a given statistical power to get a significant result, compared to the traditional approach.     

Revisiting retesting in the estimation of proportions by group testing

In the estimation of a proportion p by group testing (pooled testing), retesting of units within positive groups has received little attention due to the minimal gain in precision compared to testing additional units. If acquisition of additional units is impractical or too expensive, and testing is not destructive, we show that retesting can be a useful option. We propose the retesting of a random grouping of units from positive groups, and compare it with nested halving procedures suggested by others. We develop an estimator of p for our proposed method, and examine its variance properties. Using simulation we compare retesting methods across a range of group testing situations, and show that for most realistic scenarios, our method is more efficient.     

On the mathematics of the Jeffreys–Lindley paradox

This paper is concerned with the well known Jeffreys–Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior for the null hypothesis tends to one when the uncertainty, i.e., the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.     

Hypothesis Testing in a Rayleigh Diffusion Model

Applying the large and moderate deviations for the log-likelihood ratio of the Rayleigh diffusion model, we give the negative regions in testing Rayleigh diffusion model and obtain the decay rates of the error probabilities.     

Assessment of individual bioequivalence using sufficient bootstrap procedure

This paper proposes a sufficient bootstrap method, which uses only the unique observations in the resamples, to assess the individual bioequivalence under 2 × 4 randomized crossover design. The finite sample performance of the proposed method is illustrated by extensive Monte Carlo simulations as well as a real‐experimental data set, and the results are compared with those obtained by the traditional bootstrap technique. Our records reveal that the proposed method is a good competitor or even better than the classical percentile bootstrap confidence limits.     

Improved bonferroni procedures for testing overall and pairwise homogeneity hypotheses

Simes' (1986) improved Bonferroni test is verified by simulations ^?to control the α-level when testing the overall homogeneity hypothesis with all pairwise t statistics in a balanced parallel group design. Similarly, this result was found to hold (for practical purposes) in various underlying distributions other than the normal and in some unbalanced designs. To allow the use of step-up procedures based on pairwise t statistics, simulations were used to verify that Simes' test, when applied to testing multiple subset homogeneity hypotheses with pairwise t statistics also keeps the level ? α. Some robustness as above was found here too. Tables of the simulation results are provided and an example of a step-up Hommel-Shaffer type procedure with pairwise comparisons is given.     

积分变换求梁的变形

本文从求解梁挠度的二阶差分方程出发，通过Z变换，最后推导出计算挠度和转角的简单公式，使计算过程简化。对于变截面梁和复杂受载下，此法尤为简便。同时，这也是处理离散参数的数学方法—Z变换在力学中应用的初步尝试。     

What can we learn from twin studies? A comprehensive evaluation of the equal environments assumption

Twin studies are a major source of information about genetic effects on behavior, but they depend on a controversial assumption known as the equal environments assumption (EEA): that similarity in co-twins’ environments is not predictive of similarity in co-twin outcomes. Although evidence has largely supported the EEA, critics have claimed that environmental similarity has not been measured well, and most studies of the EEA have focused on outcomes related to health and psychology. This article addresses these limitations through (1) a reanalysis of data from the most cited study of the EEA, Loehlin and Nichols (1976), using better measures, and through (2) an analysis of nationally representative twin data from MIDUS using more comprehensive controls on a wider variety of outcomes than previous studies. Results support a middle ground position; it is likely that the EEA is not strictly valid for most outcomes, but the resulting bias is likely modest.