Exponential bounds for normal approximation of the number of descents and inversions

In this article, we study two well-known statistics, called descent and inversion. The normal approximation by Stein’s method has been considered. Polynomial non uniform bounds of such approximation were obtained by Chuntee and Neammanee in 2013 Chuntee, W., Neammanee, K. (2013). Bounds on normal approximations for the number of descents and inversion. Commun. Stat. A - Theor.to appear. [Google Scholar]. In this article, we sharpen the bound to the exponential growth by using Stein’s method and techniques from the work of Chen, Shao, and Fang in the same year.     

Efficient estimation of non parametric simultaneous equations models

This paper defines a new procedure to efficiently estimate non parametric simultaneous equations models. The proposed estimation procedure exploits the additive structure and achieves oracle efficiency without the knowledge of unobserved error terms. Furthermore, simulation results show that our new estimator outperforms the existing estimator in terms of mean squared error.     

Berry–Esséen theorem for sample quantiles of asymptotically uncorrelated non reversible Markov chains

We prove Berry–Esséen bound for sample quantiles of Markov chains with spectral gap in L².     

Model-based study of families of exponential-type estimators in presence of non response

Among other types of non sampling errors, non response error (NRE) is an inherent component of any sample survey, which is supposed to be given much attention during the designing and execution stages. With increasing awareness of these estimators, therefore, there is an urge for the development of suitable techniques for controlling them.

This article proposes two families of estimators for population mean in the presence of non response and discuses various properties under model approach, namely polynomial regression model. The families include some existing estimators. Comparison of efficiencies along with the robustness of the estimators under misspecification of models has been empirically discussed.     

Efficient inference for parameters of unobservable periodic autoregressive time series

This paper considers estimating the model coefficients when the observed periodic autoregressive time series is contaminated by a trend. The proposed Yule–Walker estimators are obtained by a two-step procedure. In the first step, the trend is estimated by a weighted local polynomial, and the residuals are obtained by subtracting the trend estimates from the observations; in the second step, the model coefficients are estimated by the well-known Yule–Walker method via the residuals. It is shown that under certain conditions such Yule–Walker estimators are oracally efficient, i.e., they are asymptotically equivalent to those obtained from periodic autoregressive time series without a trend. An easy-to-use implementation procedure is provided. The performance of the estimators is illustrated by simulation studies and real data analysis. In particular, the simulation studies show that the proposed estimator outperforms that obtained from the residuals when the trend is estimated by kernel smoothing without taking the heteroscedasticity into consideration.     

A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions

The computational demand required to perform inference using Markov chain Monte Carlo methods often obstructs a Bayesian analysis. This may be a result of large datasets, complex dependence structures, or expensive computer models. In these instances, the posterior distribution is replaced by a computationally tractable approximation, and inference is based on this working model. However, the error that is introduced by this practice is not well studied. In this paper, we propose a methodology that allows one to examine the impact on statistical inference by quantifying the discrepancy between the intractable and working posterior distributions. This work provides a structure to analyse model approximations with regard to the reliability of inference and computational efficiency. We illustrate our approach through a spatial analysis of yearly total precipitation anomalies where covariance tapering approximations are used to alleviate the computational demand associated with inverting a large, dense covariance matrix.     

Local likelihood smoothing of sample extremes

Trends in sample extremes are of interest in many contexts, an example being environmental statistics. Parametric models are often used to model trends in such data, but they may not be suitable for exploratory data analysis. This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial fitting of the generalized extreme value distribution and related models. The uncertainty of fits is assessed by using resampling methods. The methods are applied to data on extreme temperatures and on record times for the women's 3000 m race.     

Inference in generalized additive mixed modelsby using smoothing splines

Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi-likelihood. Because numerical integration is often required by maximizing the objective functions, double penalized quasi-likelihood is proposed to make approximate inference. Frequentist and Bayesian inferences are compared. A key feature of the method proposed is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model by using existing statistical software. A bias correction procedure is also proposed to improve the performance of double penalized quasi-likelihood for sparse data. We illustrate the method with an application to infectious disease data and we evaluate its performance through simulation.     

Tail Exactness of Multivariate Saddlepoint Approximations

We consider a log-concave density f in R ^m satisfying certain weak conditions, particularly on the Hessian matrix of log f . For such a density, we prove tail exactness of the multivariate saddlepoint approximation. The proof is based on a local limit theorem for the exponential family generated by f . However, the result refers not to asymptotic behaviour under repeated sampling, but to a limiting property at the boundary of the domain of f . Our approach does not apply any complex analysis, but relies totally on convex analysis and exponential models arguments.