Projection bounds on expectations of record statistics from restricted families

The projection method is applied to derive sharp moment bounds for the expectations of record statistics based on independent samples from two families of life distributions: the ones with decreasing failure probability and rate.     

The evaluation of general non-centred orthant probabilities

Summary. The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. The approach taken has two stages. In the first stage, it is shown how non-centred orthoscheme probabilities can be evaluated by using a recursive integration method. In the second stage, some ideas of Schläfli and Abrahamson are extended to show that any non-centred orthant probability can be expressed as differences between at most ( m −1)! non-centred orthoscheme probabilities. This approach allows an accurate evaluation of many multivariate normal probabilities which have important applications in statistical practice.     

Component selection in additive quantile regression models

Nonparametric additive models are powerful techniques for multivariate data analysis. Although many procedures have been developed for estimating additive components both in mean regression and quantile regression, the problem of selecting relevant components has not been addressed much especially in quantile regression. We present a doubly-penalized estimation procedure for component selection in additive quantile regression models that combines basis function approximation with a ridge-type penalty and a variant of the smoothly clipped absolute deviation penalty. We show that the proposed estimator identifies relevant and irrelevant components consistently and achieves the nonparametric optimal rate of convergence for the relevant components. We also provide an accurate and efficient computation algorithm to implement the estimator and demonstrate its performance through simulation studies. Finally, we illustrate our method via a real data example to identify important body measurements to predict percentage of body fat of an individual.     

Tests for the umbrella alternative under normality

Consider a one-way layout of the analysis of variance assuming independence, normality, and homogeneity of variance. Test the null hypothesis H_o that the means, j., of each of Amp; columns, i = 1,…, k are equal versus the alternative that they follow an umbrella pattern. That is, the alternative is H₁-H₀ where H₁: μ₁> μ₂>… > μk, and m is known. We derive a class of tests which are unbiased and lie in a nontrivial complete class. We recommend specific tests within the class. A simulation of the power functions of some tests is contrasted with the simulated power function of the likelihood ratio test.     

Bounds for Expectations of Differences of Generalized Order Statistics Based on General and Life Distributions

Let X _? ^(r), r ≥ 1, denote generalized order statistics based on an arbitrary distribution function F with finite pth absolute moment for some 1 ≤ p ≤ ∞. We present sharp upper bounds on E(X _? ^(s) ? X _? ^(r)), 1 ≤ r < s, for F being either general or life distribution. The bounds are expressed in various scale units generated by pth central absolute or raw moments of F, respectively. The distributions achieving the bounds are specified.     

Characterization of the Wishart Distribution on Homogeneous Cones in the Bobecka and Wesolowski Way

The aim of this article is to extend the characterization of the ordinary Wishart on symmetric matrices as given by Bobecka and Weso?owski (2002 Bobecka , K. , Weso?owski , J. ( 2002 ). The Lukacs–Olkin–Rubin theorem without invariance of the “quotient” . Studia Math. 152 : 147 – 160 . [Google Scholar]) to the Wishart distribution on homogeneous cones.     

Testing Equality of Means Under Order Restrictions Using Multiple Contrasts

The likelihood ratio test for equality of ordered means is known to have power characteristics that are generally superior to those of competing procedures. Difficulties in implementing this test have led to the development of alternative approaches, most of which are based on contrasts. While orthogonal contrasts can be chosen to simplify the distribution theory, we propose a class of tests that is easy to implement even if the contrasts used are not orthogonal. An overall measure of significance may be obtained by using Fisher's combination statistic to combine the dependent p-values arising from these contrasts. This method can be easily implemented for testing problems involving unequal sample sizes and any partial order, and has power properties that compare well with those of the likelihood ratio test and other contrast-based tests.     

Generalized Confidence Interval for the Scale Parameter of the Power-Law Process

The power-law process is widely used in the analysis of repairable system reliability. In this article, interval estimation for the scale parameter is investigated under some general conditions. A procedure to derive a generalized confidence interval for the scale parameter is presented. We also study the accuracy of the generalized confidence interval by Monte Carlo simulation. Finally, two examples are shown to illustrate the proposed procedure.     

Statistical inference for a class of life distributions

Life distributions with hazard rate functions of the form r(t) = Ag(t) + Bh(t) are considered. It is assumed that g(t) and h(t) are known and are independent of the unknown parameters A and B. The maximum likelihood estimators are studied for complete and censored samples. The estimation problem is reduced to a solution of one equation with one unknown parameter and it is observed that the solution is unique. The estimation procedure under the assumption of aging is also described. Some comments about the asymptotic variance-covariance matrix are given, and tests of hypo-theses are described for some cases.     

一二八事变蒋介石的对日战略

一二八事变蒋介石实施了积极抵抗、预备交涉的战略方针,采取了有效的战略措施,如京沪防卫与军政部署;迁都洛阳;划分战区;调兵增援;加强沿海防御;构筑第二道防线;制定第二期抵抗作战方案,最终实现了其部分战略目的——在不签订割地条约的前提下与日本达成停战协定。该战略的制约因素包括政治、经济、军事等。总起来说,蒋介石的对日战略部分是有效的,但也存在着消极成分,表现在该战略受制于“攘外必先安内”的政治目标,只进行了有限度的抵抗。并且《淞沪停战协定》规定中国不得在上海至苏州、昆山一带驻军,令中国主权受到了侵犯,未能实现蒋介石的另一部分战略目标——在不签订丧权条约的前提下与日本达成停战协定。