Random effects regression mixtures for analyzing infant habituation

Random effects regression mixture models are a way to classify longitudinal data (or trajectories) having possibly varying lengths. The mixture structure of the traditional random effects regression mixture model arises through the distribution of the random regression coefficients, which is assumed to be a mixture of multivariate normals. An extension of this standard model is presented that accounts for various levels of heterogeneity among the trajectories, depending on their assumed error structure. A standard likelihood ratio test is presented for testing this error structure assumption. Full details of an expectation-conditional maximization algorithm for maximum likelihood estimation are also presented. This model is used to analyze data from an infant habituation experiment, where it is desirable to assess whether infants comprise different populations in terms of their habituation time.     

On the asymptotic behaviour of the recursive Nadaraya–Watson estimator associated with the recursive sliced inverse regression method

We investigate the asymptotic behaviour of the recursive Nadaraya–Watson estimator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya–Watson procedure for the estimation of the regression function which takes into account the previous estimation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya–Watson estimate. We also illustrate our semiparametric estimation procedure on simulated data.     

Copula representation of bivariate L-moments: a new estimation method for multiparameter two-dimensional copula models

Serfling and Xiao [A contribution to multivariate L-moments, L-comoment matrices. J Multivariate Anal. 2007;98:1765–1781] extended the L-moment theory to the multivariate setting. In the present paper, we focus on the two-dimensional random vectors to establish a link between the bivariate L-moments (BLM) and the underlying bivariate copula functions. This connection provides a new estimate of dependence parameters of bivariate statistical data. Extensive simulation study is carried out to compare estimators based on the BLM, the maximum likelihood, the minimum distance and a rank approximate Z-estimation. The obtained results show that, when the sample size increases, BLM-based estimation performs better as far as the bias and computation time are concerned. Moreover, the root-mean-squared error is quite reasonable and less sensitive in general to outliers than those of the above cited methods. Further, the proposed BLM method is an easy-to-use tool for the estimation of multiparameter copula models. A generalization of the BLM estimation method to the multivariate case is discussed.     

Simultaneous sparse model selection and coefficient estimation for heavy-tailed autoregressive processes

We propose a sparse coefficient estimation and automated model selection procedure for autoregressive processes with heavy-tailed innovations based on penalized conditional maximum likelihood. Under mild moment conditions on the innovation processes, the penalized conditional maximum likelihood estimator satisfies a strong consistency, O_P(N^?1/2) consistency, and the oracle properties, where N is the sample size. We have the freedom in choosing penalty functions based on the weak conditions on them. Two penalty functions, least absolute shrinkage and selection operator and smoothly clipped average deviation, are compared. The proposed method provides a distribution-based penalized inference to AR models, which is especially useful when the other estimation methods fail or under perform for AR processes with heavy-tailed innovations [Feigin, Resnick. Pitfalls of fitting autoregressive models for heavy-tailed time series. Extremes. 1999;1:391–422]. A simulation study confirms our theoretical results. At the end, we apply our method to a historical price data of the US Industrial Production Index for consumer goods, and obtain very promising results.     

Enriching Surveys with Supplementary Data and its Application to Studying Wage Regression

We consider the problem of supplementing survey data with additional information from a population. The framework we use is very general; examples are missing data problems, measurement error models and combining data from multiple surveys. We do not require the survey data to be a simple random sample of the population of interest. The key assumption we make is that there exists a set of common variables between the survey and the supplementary data. Thus, the supplementary data serve the dual role of providing adjustments to the survey data for model consistencies and also enriching the survey data for improved efficiency. We propose a semi‐parametric approach using empirical likelihood to combine data from the two sources. The method possesses favourable large and moderate sample properties. We use the method to investigate wage regression using data from the National Longitudinal Survey of Youth Study.     

Cramér Asymptotic Efficiency in a Semiparametric Model

This article is concerned with efficient estimation in a semiparametric model. We consider pseudo maximum likelihood estimation and prove that the proposed estimator is asymptotically efficient in the sense of Cramér; that is, the estimator has the smallest mean squared error.     

Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ Method

Utilizing time series modeling entails estimating the model parameters and dispersion. Classical estimators for autocorrelated observations are sensitive to presence of different types of outliers and lead to bias estimation and misinterpretation. It is important to present robust methods for parameters estimation which are not influenced by contaminations. In this article, an estimation method entitled Iteratively Robust Filtered Fast? τ(IRFFT) is proposed for general autoregressive models. In comparison to other commonly accepted methods, this method is more efficient and has lower sensitivity to contaminations due to having desirable robustness properties. This has been demonstrated by applying MSE, influence function, and breakdown point criteria.     

Maximum likelihood estimation for generalized conditionally autoregressive models of spatial data

Conditionally autoregressive (CAR) models are often used to analyze a spatial process observed over a lattice or a set of irregular regions. The neighborhoods within a CAR model are generally formed deterministically using the inter-distances or boundaries between the regions. To accommodate directional and inherent anisotropy variation, a new class of spatial models is proposed that adaptively determines neighbors based on a bivariate kernel using the distances and angles between the centroid of the regions. The newly proposed model generalizes the usual CAR model in a sense of accounting for adaptively determined weights. Maximum likelihood estimators are derived and simulation studies are presented for the sampling properties of the estimates on the new model, which is compared to the CAR model. Finally the method is illustrated using a data set on the elevated blood lead levels of children under the age of 72 months observed in Virginia in the year of 2000.     

Bayesian optimal sequential design for nonparametric regression via inhomogeneous evolutionary MCMC

We develop a novel computational methodology for Bayesian optimal sequential design for nonparametric regression. This computational methodology, that we call inhomogeneous evolutionary Markov chain Monte Carlo, combines ideas of simulated annealing, genetic or evolutionary algorithms, and Markov chain Monte Carlo. Our framework allows optimality criteria with general utility functions and general classes of priors for the underlying regression function. We illustrate the usefulness of our novel methodology with applications to experimental design for nonparametric function estimation using Gaussian process priors and free-knot cubic splines priors.