Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths

We obtain the rates of pointwise and uniform convergence of multivariate kernel density estimators using a random bandwidth vector obtained by some data-based algorithm. We are able to obtain faster rate for pointwise convergence. The uniform convergence rate is obtained under some moment condition on the marginal distribution. The rates are obtained under i.i.d. and strongly mixing type dependence assumptions.     

Penalized spline joint models for longitudinal and time-to-event data

The joint models for longitudinal data and time-to-event data have recently received numerous attention in clinical and epidemiologic studies. Our interest is in modeling the relationship between event time outcomes and internal time-dependent covariates. In practice, the longitudinal responses often show non linear and fluctuated curves. Therefore, the main aim of this paper is to use penalized splines with a truncated polynomial basis to parameterize the non linear longitudinal process. Then, the linear mixed-effects model is applied to subject-specific curves and to control the smoothing. The association between the dropout process and longitudinal outcomes is modeled through a proportional hazard model. Two types of baseline risk functions are considered, namely a Gompertz distribution and a piecewise constant model. The resulting models are referred to as penalized spline joint models; an extension of the standard joint models. The expectation conditional maximization (ECM) algorithm is applied to estimate the parameters in the proposed models. To validate the proposed algorithm, extensive simulation studies were implemented followed by a case study. In summary, the penalized spline joint models provide a new approach for joint models that have improved the existing standard joint models.     

Some results on generalized ageing classes

In this paper we provide new results about generalized ageing classes on the excess lifetime of a renewal process. We also obtain some characterizations of generalized ageing classes by means of the residual life at random time.     

Monte carlo evidence on the robustness of conditional moment tests in tobit and probit models

This paper numerically examines the size robustness of various conditional moment tests in misspecified tobit and probit models. The misspecifications considered include the incorrect exclusion of regressors, ignored heteroskedasticity and false distributional assumptions. An important feature of the experimental design is that it is based on an existing empirical study and is more realistic than many simulation studies. The tests are seen to have mixed performance depending on both the original null hypothesis being tested and type of misspecification encountered.     

Tests and Confidence Intervals for an Extended Variance Component Using the Modified Likelihood Ratio Statistic

Abstract.  The large deviation modified likelihood ratio statistic is studied for testing a variance component equal to a specified value. Formulas are presented in the general balanced case, whereas in the unbalanced case only the one-way random effects model is studied. Simulation studies are presented, showing that the normal approximation to the large deviation modified likelihood ratio statistic gives confidence intervals for variance components with coverage probabilities very close to the nominal confidence coefficient.     

Approximate optimal allocation in repeated sampling from a finite population

Samples of size n are drawn from a finite population on each of two occasions. On the first occasion a variate x is measured, and on the second a variate y. In estimating the population mean of y, the variance of the best linear unbiased combination of means for matched and unmatched samples is itself minimized, with respect to the sampling design on the second occasion, by a certain degree of matching. This optimal allocation depends on the population correlation coefficient, which previous authors have assumed known. We estimate the correlation from an initial matched sample, then an approximately optimal allocation is completed and an estimator formed which, under a bivariate normal superpopulation model, has model expected mean square error equal, apart from an error of order n^-2, to the minimum enjoyed by any linear, unbiased estimator.     

中国区域经济差异源于FDI？——析二次统计误差的形成

 摘　　要:本文比较分析了两项关于FDI与中国区域经济发展差异的研究成果，通过分析这两项成果间迥异的研究结论和相应的近乎对立的政策主张，剖析了实证研究中可能形成的二次统计误差，提请人们从变量选择、模型方法、数据运用等各个方面，全面关注实证研究的客观性和科学性。     

Random Bernstein Polynomials

Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a "Bernstein–Dirichlet" prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a "changing dimension" parameter space.     

凝聚随机算子的一个不动点定理

利用拓扑度的基本性质，给出了凝聚随机算子的一个不动点定理，由此推广了Altman定理，为进一步研究随机算子方程解的存在唯一性及解的近似方法提供了一个有力的工具。     

AN ALGORITHMIC APPROACH TO BAYESIAN LINEAR MODEL CALCULATIONS

A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects.