On marginal estimation in a semiparametric model for longitudinal data with time-independent covariates

We consider M-estimators for a class of semiparametric mixed-effect models without time-dependent covariates and show that the simple marginal estimation method is generally better than the same M-estimator applied to the de-correlated response based on a known or estimated covariance matrix for each subject.     

Innovation performance across Europe

The innovation performance of firms is primarily determined by their own innovative activities and the interaction with their innovation-related environment. This environment typically differs among countries. We assess empirically these differences on firms' innovation performance. To that end we first estimate the relationship between an aggregate innovation input measure and an aggregate innovation output measure, thereby explicitly controlling for structural differences between countries. We then consider the extent to which firms located in a particular country perform better or worse than this estimated benchmark performance. The analysis is based on a panel dataset that we have constructed from Eurostat's first and second Community Innovation Survey. In order to control for possible data contamination we employ an outlier-robust estimator. It appears that among the fourteen countries considered Italy, Germany and Ireland offer an environment that facilitates most the transformation of innovation-related inputs into commercial outputs while the environment in Denmark is the least facilitating.     

Convergence of stochastic approximation algorithms under irregular conditions

We consider a class of stochastic approximation (SA) algorithms for solving a system of estimating equations. The standard condition for the convergence of the SA algorithms is that the estimating functions are locally Lipschitz continuous. Here, we show that this condition can be relaxed to the extent that the estimating functions are bounded and continuous almost everywhere. As a consequence, the use of the SA algorithm can be extended to some problems with irregular estimating functions. Our theoretical results are illustrated by solving an estimation problem for exponential power mixture models.     

Asymptotic normality of M-estimators in a semiparametric model with longitudinal data

Suppose that the longitudinal observations (Y _ij , X _ij , t _ij ) for i = 1, . . . ,n; j = 1, . . . ,m _i are modeled by the semiparamtric model where β ₀ is a k × 1 vector of unknown parameters, g(·) is an unknown estimated function and e _ij are unobserved disturbances. This article consider M-type regressions which include mean, median and quantile regressions. The M-estimator of the slope parameter β ₀ is obtained through piecewise local polynomial approximation of the nonparametric component. The local M-estimator of g(·) is also obtained by replacing β ₀ in model with its M-estimator and using local linear approximation. The asymptotic distribution of the estimator of β ₀ is derived. The asymptotic distributions of the local M-estimators of g(·) at both interior and boundary points are also established. Various applications of our main results are given. The research is supported in part by National Natural Science Foundation of China (Grant No. 10671089).     

Efficiency. of infinite dimensional M- estimators

It is well-known that maximum likelihood estimators are asymptotically normal with covariance equal to the inverse Fisher information in smooth, finite dimensional parametric models. Thus they are asymptotically efficient. A similar phenomenon has been observed for certain infinite dimensional parameter spaces. We give a simple proof of efficiency, starting from a theorem on asymptotic normality of infinite dimensional M -estimators. The proof avoids the explicit calculation of the Fisher information. We also address Hadamard differentiability of the corresponding M -functionals.     

A Central Limit Theorem for M-estimators by the von Mises Method

Asymptotic normality of M- or maximum likelihood type estimators was established in a classic paper by Huber (1967). Reeds (1976) argued that this could have been obtained simply as an application of the delta-method, using the tool of compactly differentiating von Mises functionals with respect to the empirical distribution function F_n. His proof however contains some errors and has been largely ignored. A corrected version of the proof is given.