This paper is concerned with the construction and analysis of a universal estimator for the regression problem in supervised learning. Universal means that the estimator does not depend on any a priori assumptions about the regression function to be estimated. The universal estimator studied in this paper consists of a least-square fitting procedure using piecewise constant functions on a parti...

Selection of an optimal estimator typically relies on either supervised training samples (pairs of measurements and their associated true values) or a prior probability model for the true values. Here, we consider the problem of obtaining a least squares estimator given a measurement process with known statistics (i.e., a likelihood function) and a set of unsupervised measurements, each arising...

Weidong Min Abstract. This paper presents an algorithm based on shrunken polyhedron and mapping to mesh a convex polyhedron using mixed elements, with mostly hexahedra, but including some tetrahedra, pyramids, and wedges. It is part of a scheme for automatically meshing an arbitrary 3D geometry. The scheme rst decomposes a 3D geometry into a set of convex polyhedra. Then the boundary quadrilate...

In this paper we consider a simplified version of a maximum likelihood time synchronization estimator introduced in [2]. This simplified variant assumes approximately accurate clock rates. We give error bounds for the estimator under the assumption of a maximum timestamping delay, and we show that these error bounds are optimal. Furthermore, we prove consistency of the clock offset estimator fo...

We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a non asymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotro...

In this paper, the state estimation problem for continuous-time linear systems with two types of sampling is considered. First, the optimal state estimator under periodic sampling is presented. Then the state estimator with event-based updates is designed, i.e., when an event occurs the estimator is updated linearly by using the measurement of output, while between the consecutive event times t...

We explore additive models that combine both parametric and nonparamet-ric terms and propose a p n-consistent backktting estimator for the parametric component of the model. The theoretical properties of the estimator are developed for the case with a single nonparametric term and extended to an arbitrary number of nonparametric additive terms. An estimator for the optimal band-width making min...

This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yiel...

Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators ar...

This paper introduces a new biased estimator, namely, almost unbiased Liu estimator (AULE) of β for the multiple linear regression model with heteroscedastics and/or correlated errors and suffers from the problem of multicollinearity. The properties of the proposed estimator is discussed and the performance over the generalized least squares (GLS) estimator, ordinary ridge regression (ORR) esti...