Testing Heterogeneity for Frailty Distribution in Shared Frailty Model

Abstract

The frailties, representing extra variations due to unobserved measurements, are often assumed to be iid in shared frailty models. In medical applications, however, a speculation can arise that a data set might violate the iid assumption. In this paper we investigate this conjecture through an analysis of the kidney infection data in McGilchrist and Aisbett (McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466). As a test procedure, we consider the cusum of squares test which is frequently used for monitoring a variance change in statistical models. Our result strongly sustains the heterogeneity of the frailty distribution.     

Seasonality Tests

This article modifies and extends the test against nonstationary stochastic seasonality proposed by Canova and Hansen. A simplified form of the test statistic in which the nonparametric correction for serial correlation is based on estimates of the spectrum at the seasonal frequencies is considered and shown to have the same asymptotic distribution as the original formulation. Under the null hypothesis, the distribution of the seasonality test statistics is not affected by the inclusion of trends, even when modified to allow for structural breaks, or by the inclusion of regressors with nonseasonal unit roots. A parametric version of the test is proposed, and its performance is compared with that of the nonparametric test using Monte Carlo experiments. A test that allows for breaks in the seasonal pattern is then derived. It is shown that its asymptotic distribution is independent of the break point, and its use is illustrated with a series on U.K. marriages. A general test against any form of permanent seasonality, deterministic or stochastic, is suggested and compared with a Wald test for the significance of fixed seasonal dummies. It is noted that tests constructed in a similar way can be used to detect trading-day effects. An appealing feature of the proposed test statistics is that under the null hypothesis, they all have asymptotic distributions belonging to the Cramér–von Mises family.     

Preliminary test of fit in a general class of conditionally heteroscedastic nonlinear time series

This article is concerned with a general class of conditionally heteroscedastic time series including possibly nonlinear and asymmetric autoregressive conditional heteroscedastic (ARCH) and generalized ARCH models. A problem of preliminary test of fit (PTF, hereafter) within the broad class under consideration is discussed. It is noted that contrary to usual tests in the literature of conditionally heteroscedastic time series, PTF does not require any specification of the conditional variance in advance. Based on the joint limit distributions of sample autocorrelations, a certain Portmanteau-type statistic for PTF is proposed, and its limit is shown to be a chi-square distribution. In addition, some simulation studies, under various innovations, are reported to support our theoretical results.     

Sample Size Formulas for Normal Theory T Tests

Formulas that yield minimum sample size for standard T tests are presented. Although the results are approximations, they usually yield the exact solution. Involving only standard normal quantiles, they could be used in an elementary course.     

Testing equality of conditionally jfclhwdqw exponential distributions

For the models given V = v (a common random stress), X and Y are independently exponentially distributed with failure rates λ₁and λ₂v, testing H₀λ₁λ₂using a random ‘paired’ sample is considered. It is shown that a uniformly most powerful invariant test does not exist even for one sided alternatives; locally most powerful invariant tests are derived and compared with existing procedures. The method is illustrated with reliability data. Finally, the robustness of the tests when the relationships of the failure rates to V is more complex are established.     

Smooth Tests of Copula Specifications

We present a family of smooth tests for the goodness of fit of semiparametric multivariate copula models. The proposed tests are distribution free and can be easily implemented. They are diagnostic and constructive in the sense that when a null distribution is rejected, the test provides useful pointers to alternative copula distributions. We then propose a method of copula density construction, which can be viewed as a multivariate extension of Efron and Tibshirani. We further generalize our methods to the semiparametric copula-based multivariate dynamic models. We report extensive Monte Carlo simulations and three empirical examples to illustrate the effectiveness and usefulness of our method.     

Critical point and power calculations for the studentized range test for generally correlated means

The studentized range test is a widely applied statistical procedure to compare several normal means within the analysis of variance. However, up to now no general methodology is available to perform the all-pair comparisons precisely, such as the computation of p-values or quantiles in the simple unbalanced one-way layout. Instead, a variety of approximations have been proposed in the past. This article focuses on exact computations of simultaneous confidence intervals and exact sample size determinations for all-pair comparisons in the analysis of variance involving arbitrary variance-covariance matrices. General power expressions in closed form are developed and numerical issues concerning the arising multivariate central and noncentral t-distributions are discussed. An application to the usual fixed effects analysis of covariance illustrates the use of the obtained results.     

汉熹平石经《尚书》异文研究

今本《尚书》与汉石经《尚书》之异文包括以下9类,它们是:石经与今本之异文分别为借字和本字、石经与今本之异文分别为本字和借字、石经与今本之异文为同音通用字、石经与今本之异文为古字与今字、石经与今本之异文为一字之异体、石经与今本之异文词异而义同、石经与今本之异文分别为本源字和讹误字、石经与今文之异文源于文字多寡的不同、石经本与今本之异文源于语序的不同。多数异文对文意的理解并没有产生负面影响,仍具有很高的文献价值和史料价值。同时也不能否认,石经《尚书》个别异文的确能起到"一字千金"的作用,对今本《尚书》的解读具有重要的参考价值。     

车行横洞施工对隧道主洞变形的影响

针对隧道车行横洞施工对主洞结构产生影响，以运城 灵宝高速公路中条山隧道工程为依托，采用现场试验和三维有限元仿真的方法，对车行横洞施工阶段主洞的变形规律进行了研究。研究结果表明：车行横洞施工对主洞的影响，在时间上主要表现在交叉口初支拆除和横洞的第1个开挖步，随着横洞开挖深度的增加，主洞结构的变形逐步趋于稳定;车行横洞施工对隧道主洞围岩变形影响主要表现为主洞拱顶下沉量增加和开挖侧拱脚水平位移减小，主洞未开挖侧拱脚水平位移影响不大。     

Likelihood ratio test for simultaneous testing of the mean and the variance of a normal distribution

In this paper, we consider the simultaneous testing of the mean and the variance of a normal distribution. The exact distribution of the likelihood ratio test statistic is obtained, which is not available in the literature. The critical points of the exact test are reported. We also consider some of the other exact and asymptotic tests. The powers of these tests are compared using the Monte Carlo simulations.