The higher order large-deviation approximation for the distribution of the sum of independent discreterandom variables

For a sum of not identic ally but independently distributed discrete random variables, its higher order large-deviation approximation in given. They are compared with the normal and Edge-worth type approximations in various cases. Consequently, the large-deviation approximations give sufficiently accurate results.     

The frisch-waugh theorem and generalized least squares

We discuss the standard linear regression model with nonspherical disturbances, where some regressors are annihilated by considering only the residuals from an auxiliary regression, and where, analogous to the Frisch-Waugh procedure, the original GLS procedure is applied to the transformed data. We call this procedure pseudo-GLS and give conditions for pseudo-GL5 to be equal to genuine GLS. We also show via examples that these conditions are often violated in empirical applications, and that the Frisch-Waugh Theorem still “works” with nonspherical disturbances if efficient estimation is applied to both the original and the transformed data.     

Approximating Matrix-Exponential Distributions by Global Randomization

Abstract

Based on the general concept of randomization, we develop linear-algebraic approximations for continuous probability distributions that involve the exponential of a matrix in their definitions, such as phase types and matrix-exponential distributions. The approximations themselves result in proper probability distributions. For such a global randomization with the Erlang-k distribution, we show that the sequences of true and consistent distribution and density functions converge uniformly on [0, ∞). Furthermore, we study the approximation errors in terms of the power moments and the coefficients of the Taylor series, from which the accuracy of the approximations can be determined apriori. Numerical experiments demonstrate the feasibility of the presented randomization technique – also in comparison with uniformization.     

Variable selection in partially linear hazard regression for multivariate failure time data

The aim of this paper is to explore variable selection approaches in the partially linear proportional hazards model for multivariate failure time data. A new penalised pseudo-partial likelihood method is proposed to select important covariates. Under certain regularity conditions, we establish the rate of convergence and asymptotic normality of the resulting estimates. We further show that the proposed procedure can correctly select the true submodel, as if it was known in advance. Both simulated and real data examples are presented to illustrate the proposed methodology.     

A Bayesian method for query approximation

This study presents statistical techniques to obtain local approximate query answers for aggregate multivariate materialized views thus eliminating the need for repetitive scanning of the source data. In widely distributed management information systems, detailed data do not necessarily reside in the same physical location as the decision-maker; thus, requiring scanning of the source data as needed by the query demand. Decision-making, business intelligence and data analysis could involve multiple data sources, data diversity, aggregates and large amounts of data. Management often confronts delays in information acquisition from remote sites. Management decisions usually involve analyses that require the most precise summary data available. These summaries are readily available from data warehouses and can be used to estimate or approximate data in exchange for a quicker response. An approach to supporting aggregate materialized view management is proposed that reconstructs data sets locally using posterior parameter estimates based on sufficient statistics in a log-linear model with a multinomial likelihood.     

Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data

Abstract. In this article, a naive empirical likelihood ratio is constructed for a non‐parametric regression model with clustered data, by combining the empirical likelihood method and local polynomial fitting. The maximum empirical likelihood estimates for the regression functions and their derivatives are obtained. The asymptotic distributions for the proposed ratio and estimators are established. A bias‐corrected empirical likelihood approach to inference for the parameters of interest is developed, and the residual‐adjusted empirical log‐likelihood ratio is shown to be asymptotically chi‐squared. These results can be used to construct a class of approximate pointwise confidence intervals and simultaneous bands for the regression functions and their derivatives. Owing to our bias correction for the empirical likelihood ratio, the accuracy of the obtained confidence region is not only improved, but also a data‐driven algorithm can be used for selecting an optimal bandwidth to estimate the regression functions and their derivatives. A simulation study is conducted to compare the empirical likelihood method with the normal approximation‐based method in terms of coverage accuracies and average widths of the confidence intervals/bands. An application of this method is illustrated using a real data set.     

部分线性模型非参数部分的多项式类关系的检验

对于部分线性模型中非参数部分是否为多项式函数的检验问题,应该先确定其是否为多项式函数类。通过对部分线性模型的拟合残差进行再光滑,基于其变化的趋势性构造统计量以检验其是否为多项式函数类,给出了计算检验P-值的精确算法和三阶矩χ2逼近方法,模拟例子与实际例子充分显示了本方法的有效性。     

Efficient Bayesian inference for exponential random graph models by correcting the pseudo-posterior distribution

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves the calculation of an intractable normalizing constant. This barrier motivates the consideration of tractable approximations to the likelihood function, such as the pseudolikelihood function, which offers an approach to constructing such an approximation. Naive implementation of what we term a pseudo-posterior resulting from replacing the likelihood function in the posterior distribution by the pseudolikelihood is likely to give misleading inferences. We provide practical guidelines to correct a sample from such a pseudo-posterior distribution so that it is approximately distributed from the target posterior distribution and discuss the computational and statistical efficiency that result from this approach. We illustrate our methodology through the analysis of real-world graphs. Comparisons against the approximate exchange algorithm of Caimo and Friel (2011) are provided, followed by concluding remarks.     

关于多元多项式可约性的讨论

比较了多元多项式与一元多项式的可约性,并给出了艾森斯坦因判别准则在多元情形的推广．     

Bandwidth selector for nonparametric recursive density estimation for spatial data defined by stochastic approximation method

Abstract

In this article we propose an automatic selection of the bandwidth of the recursive kernel density estimators for spatial data defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the MWISE (Mean Weighted Integrated Squared Error), the recursive estimator will be quite similar to the nonrecursive one in terms of estimation error and much better in terms of computational costs. In addition, we obtain the central limit theorem for the nonparametric recursive density estimator under some mild conditions.