标准伽玛分布族参数的EB估计的收敛速度

本文构造了标准伽玛分布族参数的EB估计，并给出了该估计的收敛速度。在适当的条件下，该速度可以分别充分接近于1／2和1。     

分析传动误差的时序模型法

介绍了齿轮传动链误差的时序建模及其几种典型时序谱估计的比较,并提出一种适于表示传动误差的时序模型。     

COMPONENTS OF VARIANCE MODELS WITH TRANSFORMATIONS

Power transformations are a popular way to improve the agreement between the observations and the assumptions in a statistical model. In this paper it is assumed that the data, after appropriate power transformation Λ, satisfies a variance components model, with independent Gaussian components. The focus is on inference for quantities which have an interpretation regardless of the choice of Λ (Carroll & Ruppert, 1981) – in particular the intraclass correlation coefficient ρ, the predicted probability of a new observation being less than a specified value and the predicted quantile. It is shown that, in the case Λ= 0, the asymptotic variance of ρ is the same, whether or not one treats Δ as estimated or as known. This supports an empirical conjecture of Solomon (1985). For predicted probabilities and predicted quantiles the variance when A is estimated is shown to be only slightly greater than the variance assuming Δ is known, except in the tails of the distribution where there can be substantial difference between the two variances.     

JAMES-STEIN RULE ESTIMATORS IN LINEAR REGRESSION MODELS WITH MULTIVARIATE-t DISTRIBUTED ERROR

This paper considers estimation of β in the regression model y =Xβ+μ, where the error components in μ have the jointly multivariate Student-t distribution. A family of James-Stein type estimators (characterised by nonstochastic scalars) is presented. Sufficient conditions involving only X are given, under which these estimators are better (with respect to the risk under a general quadratic loss function) than the usual minimum variance unbiased estimator (MVUE) of β. Approximate expressions for the bias, the risk, the mean square error matrix and the variance-covariance matrix for the estimators in this family are obtained. A necessary and sufficient condition for the dominance of this family over MVUE is also given.     

Protection against outliers in empirical bayes estimation

The proven optimality properties of empirical Bayes estimators and their documented successful performance in practice have made them popular. Although many statisticians have used these estimators since the landmark paper of James and Stein (1961), relatively few have proposed techniques for protecting them from the effects of outlying observations or outlying parameters. One notable series of studies in protection against outlying parameters was conducted by Efron and Morris (1971, 1972, 1975). In the fully Bayesian case, a general discussion on robust procedures can be found in Berger (1984, 1985). Here we implement and evaluate a different approach for outlier protection in a random-effects model which is based on appropriate specification of the prior distribution. When unusual parameters are present, we estimate the prior as a step function, as suggested by Laird and Louis (1987). This procedure is evaluated empirically, using a number of simulated data sets to compare the effects of the step-function prior with those of the normal and Laplace priors on the prediction of small-area proportions.     

A product-limit estimator for use with length-biased data

The following life-testing situation is considered. At some time in the distant past, n objects, from a population with life distribution F, were put in use; whenever an object failed, it was promptly replaced. At some time τ, long after the start of the process, a statistician starts observing the n objects in use at that time; he knows the age of each of those n objects, and observes each of them for a fixed length of time? ∞, or until failure, whichever occurs first. In the case where T is finite, some of the observations may be censored; in the case where T =∞, there is no censoring. The total life of an object in use at time ∞ is a length-biased observation from F. A nonparametric estimator of the (cumulative) hazard function is proposed, and is used to construct an estimator of F which is of the product-limit type. Strong uniform consistency results (for n → ∞) are obtained. An “Aalen-Johansen” identity, satisfied by any pair of life distributions and their (cumulative) hazard functions, is used in obtaining rate-of-convergence results.     

Obtaining cancer risk factor prevalence estimates in small areas: combining data from two surveys

Summary.  Cancer surveillance research requires accurate estimates of risk factors at the small area level. These risk factors are often obtained from surveys such as the National Health Interview Survey (NHIS) or the Behavioral Risk Factors Surveillance System (BRFSS). The NHIS is a nationally representative, face-to-face survey with a high response rate; however, it cannot produce state or substate estimates of risk factor prevalence because the sample sizes are too small and small area identifiers are unavailable to the public. The BRFSS is a state level telephone survey that excludes non-telephone households and has a lower response rate, but it does provide reasonable sample sizes in all states and many counties and has publicly available small area identifiers (counties). We propose a novel extension of dual-frame estimation using propensity scores that allows the complementary strengths of each survey to compensate for the weakness of the other. We apply this method to obtain 1999–2000 county level estimates of adult male smoking prevalence and mammogram usage rates among females who were 40 years old and older. We consider evidence that these NHIS-adjusted estimates reduce the effects of selection bias and non-telephone coverage in the BRFSS. Data from the Current Population Survey Tobacco Use Supplement are also used to evaluate the performance of this approach. A hybrid estimator that selects one of the two estimators on the basis of the mean-square error is also considered.     

Bayesian nonparametric survival analysis for grouped data

A Bayesian nonparametric estimate of the survival distribution is derived under a particular sampling scheme for grouped data that includes the possibility of censoring. The estimate uses the prior information to smooth the data, giving an estimate which is continuous. As special cases survival estimates for life tables are obtained and the estimate of Susarla and Van Ryzin (1976) is derived. As the weight of the prior information tends to zero, the Bayesian estimate reduces to a continuous version of the nonparametric maximum-likelihood estimate. An empirical Bayes modification of the procedure is illustrated on a data set from Cutler and Ederer (1958).     

一种产品失效时间的預測方法

在可靠性工程中,产品的失效时间预测无论在时间、财力、物力“人力上都具有很大的意义。本文提出了一种其寿命分布服从指数分布的产品失效时间的预测方法。该方法利用抽样样品数、有限的产品失效数以及观察到的失效时间所提供的信息,通过数据累加方式进行数据生成,然后建立预测模型,从而对失效时间进行预测。同时,还可以得到指数分布参数的点估计值。     

准EL算法下ARMAX模型的阶估计

本文给出了一种推广的 BIC 准则,根据对准 EL 算法的估计和对 ARMAX 模型变形后的全项f_(n 1)的估计所得到的有关结果,讨论了一种确定 ARMAX 模型阶数的方法。并给出了在推广的BIC 准则意义下关于 ARMAX 模型阶数的最优估计和阶估计的收敛性。同时,也得到了该模型系数矩阵估计的收敛性和收敛速度。