Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.

An Analysis of Two-Dimensional Image Data Using a Grouping Estimator

Machine learning methods, one type of methods used in artificial intelligence, are now widely used to analyze two-dimensional (2D) images in various fields. In these analyses, estimating the boundary between two regions is basic but important. If the model contains stochastic factors such as random observation errors, determining the boundary is not easy. When the probability distributions are mis-specified, ordinal methods such as probit and logit maximum likelihood estimators (MLE) have large biases. The grouping estimator is a semiparametric estimator based on the grouping of data that does not require specific probability distributions. For 2D images, the grouping is simple. Monte Carlo experiments show that the grouping estimator clearly improves the probit MLE in many cases. The grouping estimator essentially makes the resolution density lower, and the present findings imply that methods using low-resolution image analyses might not be the proper ones in high-density image analyses. It is necessary to combine and compare the results of high- and low-resolution image analyses. The grouping estimator may provide theoretical justifications for such analysis.

Statistical inference for the nonparametric and semiparametric hidden Markov model via the composite likelihood approach

In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture model, and a modified expectation-maximization(EM) algorithm is developed to compute the maximum composite likelihood.We systematically study asymptotic properties for both the nonparametric HMM and the semiparametric HMM. We also propose a generalized likelihood ratio test to choose between the nonparametric HMM and the semiparametric HMM. We derive the asymptotic distribution and prove the Wilk’s phenomenon of the proposed test statistics. Simulation studies and an application in volatility clustering analysis of the volatility index in the Chicago Board Options Exchange(CBOE) are conducted to demonstrate the effectiveness of the proposed methods.

Efficient Estimation and Variable Selection in Dynamic Panel Data Partially Linear Varying Coefficient Models with Incidental Parameter

This paper is concerned with the statistical inference of partially linear varying coefficient dynamic panel data model with incidental parameter, including efficient estimation of the parametric and nonparametric components and consistent determination of the lagged order. For the parametric component, we propose an efficient semiparametric generalized method-of-moments（GMM） estimator and establish its asymptotic normality. For the nonparametric component, B-spline series approximation is employed to estimate the unknown coefficient functions, which are shown to achieve the optimal nonparametric convergence rate. A consistent estimator of the variance of error component is also constructed. In addition, by using the smooth-threshold GMM estimating equations, we propose a variable selection method to identify the significant order of lagged terms automatically and remove the irrelevant regressors by setting their coefficient to zeros. As a result, it can consistently determine the true lagged order and specify the significant exogenous variables. Further studies show that the resulting estimator has the same asymptotic properties as if the true lagged order and significant regressors were known prior, i.e., achieving the oracle property. Numerical experiments are conducted to evaluate the finite sample performance of our procedures. An example of application is also illustrated.

Information geometry in neural spike sequences

An information geometrical method is developed for characterizing or classifying neurons in cortical areas whose spike rates fluctuate in time.The interspike intervals(ISIs)of a spike sequence of a neuron is modeled as a gamma process with a time-variant spike rate,a fixed shape parameter and a fixed absolute refractory period.We formulate the problem of estimating the fixed parameters as semiparametric estimation and apply an information geometrical method to derive the optimal estimators from a statistical viewpoint.

Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

Consider a partially linear regression model with an unknown vector parameter , an unknown function g(·), and unknown heteroscedastic error variances. Chen, You[23] proposed a semiparametric generalized least squares estimator (SGLSE) for , which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].

The Proportional Hazards Model for Multiple Type Recurrent Gap Times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies,and often more than one type of recurrent events is of interest.In this paper,we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covaxiates on the censored event processes of interest.An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions.We examine asymptotic properties of the proposed estimators.Finite sample properties of these estimators are demonstrated by simulations.