Local Linear Estimation of Second-order Jump-diffusion Model

In this article, we propose the local linear estimators of the drift coefficient and diffusion coefficient in the second-order jump-diffusion model. We also show the consistency and asymptotic normality of these estimators under mild conditions.     

Two-stage generalized moment method approach for bidimensional random coefficient autoregressive models

ABSTRACT

A two-dimensionally indexed random coefficients autoregressive models (2D ? RCAR) and the corresponding statistical inference are important tools for the analysis of spatial lattice data. The study of such models is motivated by their second-order properties that are similar to those of 2D ? (G)ARCH which play an important role in spatial econometrics. In this article, we study the asymptotic properties of two-stage generalized moment method (2S ? GMM) under general asymptotic framework for 2D ? RCA models. So, the efficiency, strong consistency, the asymptotic normality, and hypothesis tests of 2S ? GMM estimation are derived. A simulation experiment is presented to highlight the theoretical results.     

Estimating multivariate autoregressive moving average models by fitting long autoregressions

Some simple methods for the estimation of mixed multivariate autoregressive moving average time series models are introduced. The methods require the fitting of a long autoregression to the data and the computation of consistent initial estimates for the parameters of the model. After these preliminaries the estimators of the paper are obtained by applying weighted least squares to a multivariate auxiliary regression model. Two types of weight matrices are considered. Both of them yield estimators which are strongly consistent and asymptotically normally distributed. The first estimators are also asymptotically efficient while the second ones are not fully efficient but computationally simple. A simulation study is performed to illustrate the behaviour of the estimators in finite samples.     

Dempster's combination rule and sufficient statistics

In his articles (1966-1968) concerning statistical inference based on lower and upper probabilities, Dempster refers to the connection between Fisher's fiducial argument and his own ideas of statistical inference. Dempster's main concern however focuses on the “Bayesian” aspects of his theory and not on an elaboration of the relation between Fisher's and his ideas. This article attempts to work out the connection between those two approaches and focuses primarily on the question, whether Dempster's combination rule, his upper and lower probabilty based on sufficient statistics and inference based on sufficient statistics in Fisher's sense are consistent. To be adequate to Fisher's reasoning, we deal with absolutely continuous, one parametric families of distributions.This is certainly not the usual assumption in context with Dempster's theory and implies a normative but straightforward definition concerning the underlying conditional distribution; this definition however is done in Dempster's spirit as can be seen from his articles, (1966, 1968,a,b). Under those assumptions it can be shown that - similar to Lindley's results concerning consistency in fiducial reasoning (1958) - the combination rule, Dempster's procedure based on sufficient statistics and fiducial inference by sufficient statistics agree iff the parametric family under consideration can be transformed to location parameter form.     

Generalized least squares estimation of multivariate nonlinear models with missing data

The method of estimated generalized least squares estimation of multiple response models is extended to the randomly missing date case. This estimation procedure is computationally simply when there are many missing data but the number of distinct patterns of missing data for the response vectors is small. The consistency and asymptotic normality of the proposed estimators are established.     

Extended BIC for linear regression models with diverging number of relevant features and high or ultra-high feature spaces

In many conventional scientific investigations with high or ultra-high dimensional feature spaces, the relevant features, though sparse, are large in number compared with classical statistical problems, and the magnitude of their effects tapers off. It is reasonable to model the number of relevant features as a diverging sequence when sample size increases. In this paper, we investigate the properties of the extended Bayes information criterion (EBIC) (Chen and Chen, 2008) for feature selection in linear regression models with diverging number of relevant features in high or ultra-high dimensional feature spaces. The selection consistency of the EBIC in this situation is established. The application of EBIC to feature selection is considered in a SCAD cum EBIC procedure. Simulation studies are conducted to demonstrate the performance of the SCAD cum EBIC procedure in finite sample cases.     

A specification strategy for order determination in arma models

In this paper a specification strategy is proposed for the determination of the orders in ARMA models. The strategy is based on two newly defined concepts: the q-conditioned partial auto-regressive function and the p-conditioned partial moving average function. These concepts are similar to the generalized partial autocorrelation function which has been recently suggested for order determination. The main difference is that they are defined and employed in connection with an asymptotically efficient estimation method instead of the rather inefficient generalized Yule-Walker method. The specification is performed by using sequential Wald type tests. In contrast to the traditional testing of hypotheses, these tests use critical values which increase with the sample size at an appropriate rate     

Consistency of the normal equations

This note provides an alternative proof of consistency of the normal equations by appealing to well-known results in linear programming.