SPECTRAL DENSITY ESTIMATION FROM NONLINEARLY OBSERVED DATA

Abstract. The estimation of the spectral density function of a stationary Gaussian process at the input of an instantaneous nonlinearity is considered when the nonlinearity is known and a finite set of observations of the output process is given. A class of spectral estimates is considered and their quadratic-mean consistency is established; precise asymptotic expressions for their bias and covariance are derived and their asymptotic normality is obtained.     

保序回归的大样本性质

利用保序回归与极大似然估计之间的关系,从极大似然估计解的大样本性质出发,得到了保序回归解的两个大样本性质。     

Estimation in Random Coefficient Autoregressive Models

Abstract. We propose the quasi‐maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions.     

ASYMPTOTIC PROPERTIES OF SOME PRELIMINARY ESTIMATORS FOR AUTOREGRESSIVE MOVING AVERAGE TIME SERIES MODELS

Abstract. Some simple preliminary estimators for the coefficients of mixed autoregressive moving average time series models are considered. As the first step the estimators require the fitting of a long autoregression to the data. The first two methods of the paper are non-iterative and generally inefficient. The estimators are Yule-Walker type modifications of the least squares estimators of the coefficients in auxiliary linear regression models derived, respectively, for the coefficients of the long autoregression and for the coefficients of the corresponding long moving average approximation of the model. Both of these estimators are shown to be strongly consistent and their asymptotic distributions are derived. The asymptotic distributions are used in studying the loss in efficiency and in constructing the third estimator of the paper which is an asymptotically efficient two-step estimator. A numerical illustration of the third estimator with real data is given.     

缺失数据下m相依样本的大样本性质

讨论了缺失数据在随机补充方式下均值的估计,证明了估计的相合性和渐进正态性,并给出了经验似然比统计量的渐进分布．     

Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location

Traditionally, a cost-efficient control chart for monitoring product quality characteristic is designed using prior knowledge regarding the process distribution. In practice, however, the functional form of the underlying process distribution is rarely known a priori. Therefore, the nonparametric (distribution-free) charts have gained more attention in the recent years. These nonparametric schemes are statistically designed either with a fixed in-control average run length or a fixed false alarm rate. Robust and cost-efficient designs of nonparametric control charts especially when the true process location parameter is unknown are not adequately addressed in literature. For this purpose, we develop an economically designed nonparametric control chart for monitoring unknown location parameter. This work is based on the Wilcoxon rank sum (hereafter WRS) statistic. Some exact and approximate procedures for evaluation of the optimal design parameters are extensively discussed. Simulation results show that overall performance of the exact procedure based on bootstrapping is highly encouraging and robust for various continuous distributions. An approximate and simplified procedure may be used in some situations. We offer some illustration and concluding remarks.     

On the performance of different capability indices under normal and non-normal distributions

In this article, we have examined the performance of some useful capability indices using normal and non-normal distributions. The confidence intervals are calculated and mean coverage rates are observed for different capability indices. The effects of symmetry and kurtosis of parent distributions are examined on the mean coverage rates of different capability indices. Moreover, we have investigated the robustness (of confidence interval) using the median and percentile-based indices. We have considered the well-known distributions including normal, gamma, t, Weibull, and chi-squared. For these process scenarios, we have observed that some indices resist disturbance only in symmetry of the parent distribution, some resist the disturbance in symmetry and kurtosis of the distribution, and some indices don’t resist against either type of disturbance.     

Approximate Predictive Densities and Their Applications in Generalized Linear Models

Exact calculations of model posterior probabilities or related quantities are often infeasible due to the analytical intractability of predictive densities. Here new approximations for obtaining predictive densities are proposed and contrasted with those based on the Laplace method. Our theory and a numerical study indicate that the proposed methods are easy to implement, computationally efficient, and accurate over a wide range of hyperparameters. In the context of GLMs, we show that they can be employed to facilitate the posterior computation under three general classes of informative priors on regression coefficients. A real example is provided to demonstrate the feasibility and usefulness of the proposed methods in a fully Bayes variable selection procedure.     

A composite likelihood approach for spatially correlated survival data

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory.     

缺失数据下局部M-估计

在缺失响应变量的不完全数据下,对非参数回归模型进行研究.利用稳健的局部线性回归的方法,给出了回归函数m（x）的3个局部线性M-估计：完整数据M-估计,加权M-估计和估计的加权M-估计,证明了3个M-估计有相同的相合性和渐近正态性.模拟研究表明估计的加权M-估计优越于一般的加权估计.