A new orthogonality-based estimation for varying-coefficient partially linear models

Varying coefficient partially linear models are usually used for longitudinal data analysis, and an interest is mainly to improve efficiency of regression coefficients. By the orthogonality estimation technology and the quadratic inference function method, we propose a new orthogonality-based estimation method to estimate parameter and nonparametric components in varying coefficient partially linear models with longitudinal data. The proposed procedure can separately estimate the parametric and nonparametric components, and the resulting estimators do not affect each other. Under some mild conditions, we establish some asymptotic properties of the resulting estimators. Furthermore, the finite sample performance of the proposed procedure is assessed by some simulation experiments.     

Inference of Seasonal Long‐memory Time Series with Measurement Error

We consider the Whittle likelihood estimation of seasonal autoregressive fractionally integrated moving‐average models in the presence of an additional measurement error and show that the spectral maximum Whittle likelihood estimator is asymptotically normal. We illustrate by simulation that ignoring measurement errors may result in incorrect inference. Hence, it is pertinent to test for the presence of measurement errors, which we do by developing a likelihood ratio (LR) test within the framework of Whittle likelihood. We derive the non‐standard asymptotic null distribution of this LR test and the limiting distribution of LR test under a sequence of local alternatives. Because in practice, we do not know the order of the seasonal autoregressive fractionally integrated moving‐average model, we consider three modifications of the LR test that takes model uncertainty into account. We study the finite sample properties of the size and the power of the LR test and its modifications. The efficacy of the proposed approach is illustrated by a real‐life example.     

Bayesian analysis of joint mean and covariance models for longitudinal data

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. If misspecification occurs, it may lead to inefficient or biased estimators of parameters in the mean. One of the most commonly used methods for handling the covariance matrix is based on simultaneous modeling of the Cholesky decomposition. Therefore, in this paper, we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a fully Bayesian inference for joint mean and covariance models based on this decomposition. A computational efficient Markov chain Monte Carlo method which combines the Gibbs sampler and Metropolis–Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard deviation estimates. Finally, several simulation studies and a real example are presented to illustrate the proposed methodology.     

Approximate queue length distribution of a discriminatory processor sharing queue with impatient customers

We consider a two-class processor sharing queueing system with impatient customers. The system operates under the discriminatory processor sharing (DPS) scheduling. The arrival process of each class customers is the Poisson process and the service requirement of a customer is exponentially distributed. The reneging rate of a customer is a constant. To analyze the performance of the system, we develop a time scale decomposition approach to approximate the joint queue-length distribution of each class customers. Via a numerical experiment, we show that the time scale decomposition approach gives a fairly good approximation of the queue-length distribution and the expected queue length.     

An Estimation Method of the Pair Potential Function for Gibbs Point Processes on Spheres

An estimation method for pairwise interaction potential of a stationary Gibbs point process is introduced by considering the case of observations located on a sphere. It is based both on Fourier decomposition of the potential and on minimum contrast estimation. It is defined when many independent realizations of the process are available. Consistency and asymptotic normality are proved for the resulting estimators. The method enables derivation of the choice of the potential function by embedded hypotheses testing. The method is applied to independent observations of root locations on internodes around stem of maize roots. The internodes are described as circles and we focus on the interaction function associated with the potential. Since a model with too many components seems to fail, we choose a sequential procedure based on embedded hypotheses testing to build a simpler model.     

Equilibrium Wage Dispersion with Worker and Employer Heterogeneity

We construct and estimate an equilibrium search model with on–the–job–search. Firms make take–it–or–leave–it wage offers to workers conditional on their characteristics and they can respond to the outside job offers received by their employees. Unobserved worker productive heterogeneity is introduced in the form of cross–worker differences in a “competence” parameter. On the other side of the market, firms also are heterogeneous with respect to their marginal productivity of labor. The model delivers a theory of steady–state wage dispersion driven by heterogenous worker abilities and firm productivities, as well as by matching frictions. The structural model is estimated using matched employer and employee French panel data. The exogenous distributions of worker and firm heterogeneity components are nonparametrically estimated. We use this structural estimation to provide a decomposition of cross–employee wage variance. We find that the share of the cross–sectional wage variance that is explained by person effects varies across skill groups. Specifically, this share lies close to 40% for high–skilled white collars, and quickly decreases to 0% as the observed skill level decreases. The contribution of market imperfections to wage dispersion is typically around 50%.     

Selection of linear mixed-effects models for clustered data

We consider model selection for linear mixed-effects models with clustered structure, where conditional Kullback–Leibler (CKL) loss is applied to measure the efficiency of the selection. We estimate the CKL loss by substituting the empirical best linear unbiased predictors (EBLUPs) into random effects with model parameters estimated by maximum likelihood. Although the BLUP approach is commonly used in predicting random effects and future observations, selecting random effects to achieve asymptotic loss efficiency concerning CKL loss is challenging and has not been well studied. In this paper, we propose addressing this difficulty using a conditional generalized information criterion (CGIC) with two tuning parameters. We further consider a challenging but practically relevant situation where the number, $m$, of clusters does not go to infinity with the sample size. Hence the random-effects variances are not consistently estimable. We show that via a novel decomposition of the CKL risk, the CGIC achieves consistency and asymptotic loss efficiency, whether $m$ is fixed or increases to infinity with the sample size. We also conduct numerical experiments to illustrate the theoretical findings.