This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

Analogous to the Donsker theorem on partial cumulative sums of independent random variables, for one-sample rank-order statistics, weak convergence to Brownian motion processes is studied here. This yields a simple proof of the asymptotic normality of the related rank statistics for random sample sizes. Analogous to the Donsker theorem on partial cumulative sums of independent random variables,...

We consider the design of c-optimal experiments for the estimation of a scalar function h(θ) of the parameters θ in a nonlinear regression model. A c-optimal design ξ∗ may be singular, and we derive conditions ensuring the asymptotic normality of the Least-Squares estimator of h(θ) for a singular design over a finite space. As illustrated by an example, the singular designs for which asymptotic...

This paper establishes the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for a GARCH process with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution for the periodic GARCH (P -GARCH) equation. As a result, it is shown that the moment of some posit...

This paper investigates the asymptotic properties of quasi-maximum likelihood (QML) estimators for random-effects panel data transformation models where both the response and (some of) the covariates are subject to transformations for inducing normality, flexible functional form, homoskedasticity, and simple model structure. We develop a QML-type procedure for model estimation and inference. We...

Robust (M-) estimation in linear models generally involves statistical functional processes. For drawing statistical conclusions (in large samples), some (uniform) linear approximations are usually needed for such functionals. In this context, the role of Hadamard differentiability is critically examined in this dissertation. In particular, the concept of the second-order Hadamard differenti-ab...

In this paper we propose an instrumental variables (IV) estimator for a semiparametric outcome model with endogeous discrete treatment variables. The main contribution of our paper is that the identi…cation, consistency and asymptotic normality of our estimator all hold even under misspeci…cation of the treatment model. As expected from Newey and McFadden (1994), the covariance matrix for the p...

In this paper we prove the asymptotic normality and rates of strong convergence of some types of estimators for the regression function in a xed-design regression model. We consider the Gasser-MMller estimator and the Priestley-Chao estimator (univariate and multivariate). The proofs of asymptotic normality are based on a central limit theorem from an earlier paper by the author (1996, Stochast...

If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions of the quadratic forms involving integrals of weighted periodograms. Conditions for asymptotic normality of these weighted sums are simple and resemble Lindeb...