Asymptotic normality of the local linear estimation of the conditional density for functional time-series data

This article focuses on the conditional density of a scalar response variable given a random variable taking values in a semimetric space. The local linear estimators of the conditional density and its derivative are considered. It is assumed that the observations form a stationary α-mixing sequence. Under some regularity conditions, the joint asymptotic normality of the estimators of the conditional density and its derivative is established. The result confirms the prospect in Rachdi et al. (2014 Rachdi, M., A. Laksaci, J. Demongeot, A. Abdali, and F. Madani. 2014. Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data. Computational Statistics and Data Analysis 73 :53–68.[Crossref], [Web of Science ®] , [Google Scholar]) and can be applied in time-series analysis to make predictions and build confidence intervals. The finite-sample behavior of the estimator is investigated by simulations as well.     

Testing factor–covariate interaction in rank repeated-measures analysis of covariance models

This article derives the asymptotic properties of rank-based tests for the covariate effects in rank repeated-measures analysis of covariance (ANCOVA) models (Fan and Zhang 2017 Fan, C., and D. Zhang. 2017. Rank repeated measures analysis of covariance. Communications in Statistics - Theory and Methods 46:1158–83.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) employing generalized estimating equation (GEE) techniques. One interested application of the proposed tests is to check the validity of the assumption of homogeneous covariate effects in different levels of the factors. Performance of the proposed tests has been confirmed by simulation studies and illustrated using the famous seizure count data. While the article mainly focuses on interaction tests, the scope of the proposed tests includes testing any contrast of the covariate effect such as the null of no overall covariate effect.     

Binary discrimination methods for high-dimensional data with a geometric representation

Four binary discrimination methods are studied in the context of high-dimension, low sample size data with an asymptotic geometric representation, when the dimension increases while the sample sizes of the classes are fixed. We show that the methods support vector machine, mean difference, distance-weighted discrimination, and maximal data piling have the same asymptotic behavior as the dimension increases. We study the consistent, inconsistent, and strongly inconsistent cases in terms of angles between the normal vectors of the separating hyperplanes of the methods and the optimal direction for classification. A simulation study is done to assess the theoretical results.     

On the Use of GLS Demeaning in Panel Unit Root Testing

One of the most well-known facts about unit root testing in time series is that the Dickey–Fuller (DF) test based on ordinary least squares (OLS) demeaned data suffers from low power, and that the use of generalized least squares (GLS) demeaning can lead to substantial power gains. Of course, this development has not gone unnoticed in the panel unit root literature. However, while the potential of using GLS demeaning is widely recognized, oddly enough, there are still no theoretical results available to facilitate a formal analysis of such demeaning in the panel data context. The present article can be seen as a reaction to this. The purpose is to evaluate the effect of GLS demeaning when used in conjuncture with the pooled OLS t-test for a unit root, resulting in a panel analog of the time series DF–GLS test. A key finding is that the success of GLS depend critically on the order in which the dependent variable is demeaned and first-differenced. If the variable is demeaned prior to taking first-differences, power is maximized by using GLS demeaning, whereas if the differencing is done first, then OLS demeaning is preferred. Furthermore, even if the former demeaning approach is used, such that GLS is preferred, the asymptotic distribution of the resulting test is independent of the tuning parameters that characterize the local alternative under which the demeaning performed. Hence, the demeaning can just as well be performed under the unit root null hypothesis. In this sense, GLS demeaning under the local alternative is redundant.     

Pseudo Panel Data Models With Cohort Interactive Effects

When genuine panel data samples are not available, repeated cross-sectional surveys can be used to form so-called pseudo panels. In this article, we investigate the properties of linear pseudo panel data estimators with fixed number of cohorts and time observations. We extend standard linear pseudo panel data setup to models with factor residuals by adapting the quasi-differencing approach developed for genuine panels. In a Monte Carlo study, we find that the proposed procedure has good finite sample properties in situations with endogeneity, cohort interactive effects, and near nonidentification. Finally, as an illustration the proposed method is applied to data from Ecuador to study labor supply elasticity. Supplementary materials for this article are available online.     

Variable selection and weighted composite quantile estimation of regression parameters with left-truncated data

In this paper, we consider the weighted composite quantile regression for linear model with left-truncated data. The adaptive penalized procedure for variable selection is proposed. The asymptotic normality and oracle property of the resulting estimators are also established. Simulation studies are conducted to illustrate the finite sample performance of the proposed methods.     

The estimation for Lévy processes in high frequency data

In this article, a generalized Lévy model is proposed and its parameters are estimated in high-frequency data settings. An infinitesimal generator of Lévy processes is used to study the asymptotic properties of the drift and volatility estimators. They are consistent asymptotically and are independent of other parameters making them better than those in Chen et al. (2010 Chen, S. X., Delaigle, A., Hall, P. (2010). Nonparametric estimation for a class of Lévy processes. Journal of Econometrics 157:257–271.[Crossref], [Web of Science ®] , [Google Scholar]). The estimators proposed here also have fast convergence rates and are simple to implement.     

Bayesian methods for dealing with missing data problems

Missing data, a common but challenging issue in most studies, may lead to biased and inefficient inferences if handled inappropriately. As a natural and powerful way for dealing with missing data, Bayesian approach has received much attention in the literature. This paper reviews the recent developments and applications of Bayesian methods for dealing with ignorable and non-ignorable missing data. We firstly introduce missing data mechanisms and Bayesian framework for dealing with missing data, and then introduce missing data models under ignorable and non-ignorable missing data circumstances based on the literature. After that, important issues of Bayesian inference, including prior construction, posterior computation, model comparison and sensitivity analysis, are discussed. Finally, several future issues that deserve further research are summarized and concluded.     

A bivariate distribution with Lomax and geometric margins

We develop a stochastic model describing the joint distribution of $(X,N)$, where $N$ has a geometric distribution while $X$ is the sum of $N$ dependent, heavy-tail Pareto components. Models of this form arise in many applications, ranging from hydro-climatology to finance and insurance. We present fundamental properties of this vector, including marginal and conditional distributions, moments, representations, and parameter estimation. We also include an example from finance, illustrating modeling potential of this new bivariate distribution.