Buckley–James Type Estimator for Censored Data with Covariates Missing by Design

Abstract. The Buckley–James estimator (BJE) is a well‐known estimator for linear regression models with censored data. Ritov has generalized the BJE to a semiparametric setting and demonstrated that his class of Buckley–James type estimators is asymptotically equivalent to the class of rank‐based estimators proposed by Tsiatis. In this article, we revisit such relationship in censored data with covariates missing by design. By exploring a similar relationship between our proposed class of Buckley–James type estimating functions to the class of rank‐based estimating functions recently generalized by Nan, Kalbfleisch and Yu, we establish asymptotic properties of our proposed estimators. We also conduct numerical studies to compare asymptotic efficiencies from various estimators.     

Data driven smooth test for paired populations

In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.     

On the behaviour of tests based on sample spacings for moderatesamples

We revisit the question about optimal performance of goodness-of-fit tests based on sample spacings. We reveal the importance of centering of the test-statistic and of the sample size when choosing a suitable test-statistic from a family of statistics based on power transformations of sample spacings. In particular, we find that a test-statistic based on empirical estimation of the Hellinger distance between hypothetical and data-supported distribution does possess some optimality properties for moderate sample sizes. These findings confirm earlier statements about the robust behaviour of the test-statistic based on the Hellinger distance and are in contrast to findings about the asymptotic (when sample size approaches infinity) of statistics such as Moran's and/or Greenwood's statistic. We include simulation results that support our findings.     

Approximate Inference for the Factor Loading of a Simple Factor Analysis Model

We study a factor analysis model with two normally distributed observations and one factor. Two approximate conditional inference procedures for the factor loading are developed. The first proposal is a very simple procedure but it is not very accurate. The second proposal gives extremely accurate results even for very small sample size. Moreover, the calculations require only the signed log-likelihood ratio statistic and a measure of the standardized maximum likelihood departure. Simulations are used to study the accuracy of the proposed procedures.     

Goodness‐of‐fit tests for the hyperbolic distribution

The authors give tests of fit for the hyperbolic distribution, based on the Cramér‐von Mises statistic W². They consider the general case with four parameters unknown, and some specific cases where one or two parameters are fixed. They give two examples using stock price data.     

A diagnostic for selecting the threshold in extreme value analysis

A new approach is suggested for choosing the threshold when fitting the Hill estimator of a tail exponent to extreme value data. Our method is based on an easily computed diagnostic, which in turn is founded directly on the Hill estimator itself, 'symmetrized' to remove the effect of the tail exponent but designed to emphasize biases in estimates of that exponent. The attractions of the method are its accuracy, its simplicity and the generality with which it applies. This generality implies that the technique has somewhat different goals from more conventional approaches, which are designed to accommodate the minor component of a postulated two-component Pareto mixture. Our approach does not rely on the second component being Pareto distributed. Nevertheless, in the conventional setting it performs competitively with recently proposed methods, and in more general cases it achieves optimal rates of convergence. A by-product of our development is a very simple and practicable exponential approximation to the distribution of the Hill estimator under departures from the Pareto distribution.     

Testing for Regime Switching

We analyze use of a quasi‐likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime‐switching context. This test exploits mixture properties implied by the regime‐switching process, but ignores certain implied serial correlation properties. When formulated in the natural way, the setting is nonstandard, involving nuisance parameters on the boundary of the parameter space, nuisance parameters identified only under the alternative, or approximations using derivatives higher than second order. We exploit recent advances by Andrews (2001) and contribute to the literature by extending the scope of mixture models, obtaining asymptotic null distributions different from those in the literature. We further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime‐switching tests. We compare the size and power of our statistics to other useful tests for regime switching via Monte Carlo methods and find relatively good performance. We apply our methods to reexamine the classic cartel study of Porter (1983) and reaffirm Porter's findings.     

数字语言实验室对大学英语教学的影响

对比说明了传统语言实验室及数字语言实验室的特点。数据统计分析的结果显示 ,两个班级在数字语言实验室实践前没有显著区别 ,但在实践后 ,使用数字语言实验室的班级在考试中听力和总成绩都高于使用传统语言实验室的班级。阐明了数字语言实验室在听力教学上的优势及对大学英语教学的影响     

提高公共选修课教学质量与控制对策

对江汉大学医学与生命科学院2000－2001学年度第一学期开设的4大类20门公共选修课的教学效果进行了统计分析。结果表明，医学学生的公共选修课学习成绩优秀率以专业临床类较高，专业基础类较低。除专业基础类（B类）与文化基础类（A类）课程存在统计学上的显著性差异外，专业临床类（C类）和人文社科类（D类）与文化基础类课程的教学效果在统计学上均无显著差异，说明教师的教学效果在各课程类别上基本具有一致性。     

ASYMPTOTIC TESTS FOR THE CONTINUOUS TIME MARKOV BRANCHING PROCESS WITH IMMIGRATION

This paper presents limit distributions for the modified score and the likelihood-ratio (LR) statistic for testing a composite hypothesis involving the split intensity and mean of the offspring distribution of the supercritical continuous time Markov branching process allowing immigration (CBPI). The immigration intensity and mean are treated as nuisance parameters.