Testing equality of generalized variances of k multivariate normal populations

Generalized variance is a measure of dispersion of multivariate data. Comparison of dispersion of multivariate data is one of the favorite issues for multivariate quality control, generalized homogeneity of multidimensional scatter, etc. In this article, the problem of testing equality of generalized variances of k multivariate normal populations by using the Bartlett's modified likelihood ratio test (BMLRT) is proposed. Simulations to compare the Type I error rate and power of the BMLRT and the likelihood ratio test (LRT) methods are performed. These simulations show that the BMLRT method has a better chi-square approximation under the null hypothesis. Finally, a practical example is given.     

Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity

A preliminary test estimator of variance in the bivariate normal distribution is proposed after the Pitman–Morgan test of homogeneity of two variances. The bias and mean square error of the estimator are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max–min criterion.     

Comparison of preliminary test estimators based on generalized order statistics from proportional hazard family using Pitman measure of closeness

In this article, based on generalized order statistics from a family of proportional hazard rate model, we use a statistical test to generate a class of preliminary test estimators and shrinkage preliminary test estimators for the proportionality parameter. These estimators are compared under Pitman measure of closeness (PMC) as well as MSE criteria. Although the PMC suffers from non transitivity, in the first class of estimators, it has the transitivity property and we obtain the Pitman-closest estimator. Analytical and graphical methods are used to show the range of parameter in which preliminary test and shrinkage preliminary test estimators perform better than their competitor estimators. Results reveal that when the prior information is not too far from its real value, the proposed estimators are superior based on both mentioned criteria.     

Tests for compound periodicities and estimating a non linear function

We propose two tests for testing compound periodicities which are the uniformly most powerful invariant decision procedures against simple periodicities. The second test can provide an excellent estimation of a compound periodic non linear function from observed data. These tests were compared with the tests proposed by Fisher and Siegel by Monte Carlo studies and we found that all the tests showed high power and high probability of a correct decision when all the amplitudes of underlying periods were the same. However, if there are at least several different periods with unequal amplitudes, then the second test proposed always showed high power and high probability of a correct decision, whereas the tests proposed by Fisher and Siegel gave 0 for the power and 0 for the probability of a correct decision, whatever the standard deviation of pseudo normal random numbers. Overall, the second test proposed is the best of all in view of the probability of a correct decision and power.     

A weighted Harrell–Davis distance test with applications to censored data

Consider the standard treatment-control model with a time-to-event endpoint. We propose a novel interpretable test statistic from a quantile function point of view. The large sample consistency of our estimator is proven for fixed bandwidth values theoretically and validated empirically. A Monte Carlo simulation study also shows that given small sample sizes, utilization of a tuning parameter through the application of a smooth quantile function estimator shows an improvement in efficiency in terms of the MSE when compared to direct application of classic Kaplan–Meier survival function estimator. The procedure is finally illustrated via an application to epithelial ovarian cancer data.     

Asymptotic inference in poverty indices: an empirical processes approach

We derive an empirical poverty index containing most of those proposed in the literature. Then, we study its asymptotic behavior by using empirical processes theory. From the results obtained, we derive a Wald-type test for comparing a vector of theoretical poverty indices to a vector of reference indices. We study the test statistic under the null hypothesis of equality, fixed alternatives, and a sequence of local alternatives. A simulation experiment conducted shows that our test performs well for exponential and Pareto data.     

一类弹性系统的内部精确能控性

该文考虑的是具有分布控制的Timoshenko梁系统的精确能控性.用谱分解方法建立了保守系统的正反向能量不等式,证明了在通常的能量空间中该系统是精确能控的.     

I'm Not a Bad Mother — Stories of Mothering‐on‐the‐Edge

This article is located in the field of custody and day‐to‐day care, with a focus on experiences of mothering where mothers no longer have everyday care of their children. At the time of writing, tens of thousands of mothers live separately from their children in Aotearoa, New Zealand. However, there is a general perception of rarity associated with non‐resident mothers, partly due to their reluctance to speak of loss of custody. In this article, we develop a theoretical discussion around the inside/outside relationships between non‐resident mothers and their children that informs therapeutic practice. We argue that mothers who live apart from their children are situated at the edge or periphery of their children's day‐to‐day lives and experience this as outside the lives of their children. Nevertheless, mothers' stories speak of qualities of (m)othering that have been born of and nurtured by longstanding and long‐term commitment to their children.     

论经济增长的驱动因素:劳动生产效率与产业结构——以江苏省为例

本文利用LMDI指数分解方法建立了人均增长率测算模型。该模型可以分析产业GDP结构、产业劳动力结构、产业全员劳动生产效率以及劳动力占总人口比重等因素对人均GDP增长率的影响。江苏省人均GDP增长率的实证分析,表明产业全员劳动生产率和产业结构是该省2010年实现人均GDP增长率200%的主要影响因素。