Consider a study where the times of occurrences of a recurrent event for n units are monitored. For the ith unit, T(i1), T(i2), …, denote the successive event interoccurrence times and this unit is monitored over a random period [0, τ(i)] with τ(i) independent of the T(ij)s. Over this monitoring period, [Formula: see text] is the random number of event occurrences. The T(ij)s are independent an...

Markov chain algorithms are ubiquitous in machine learning and statistics many other disciplines. Typically, these can be formulated as acceptance rejection methods. In this work, we present a novel estimator applicable to methods, dubbed importance sampling, which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides way correcting discretization error...

We compare several simulation estimators for a performance measure of a process having multiple regeneration sequences. We examine the setting of two regeneration sequences. We compare two existing estimators, the permuted estimator and the semi-regenerative estimator, and two new estimators, a type of U -statistic estimator and a type of V -statistic estimator. The last two estimators are obta...

We present a highly accurate least-squares (LS) alternative to the theoretically optimal maximum likelihood (ML) estimator for homographies between two images. Unlike ML, our estimator is non-iterative and yields a solution even in the presence of large noise. By rigorous error analysis, we derive a “hyperLS” estimator which is unbiased up to second order noise terms. We also introduce a comput...

Typical production objectives in distillation process require the delivery of products whose compositions meet certain specifications. The distillation control system, therefore, must hold product compositions as near the set points as possible in faces of upset. In this project, inferential model predictive control, that utilizes an artificial neural network estimator and model predictive cont...

Abstract. Since Manski’s (1975) seminal work, the maximum score method for discrete choice models has been applied to various econometric problems. Kim and Pollard (1990) established the cube root asymptotics for the maximum score estimator. Since then, however, econometricians posed several open questions and conjectures in the course of generalizing the maximum score approach, such as (a) asy...

We study the problem of estimating the highdimensional Gaussian graphical model where the data are arbitrarily corrupted. We propose a robust estimator for the sparse precision matrix in the highdimensional regime. At the core of our method is a robust covariance matrix estimator, which is based on truncated inner product. We establish the statistical guarantee of our estimator on both estimati...

We study in details the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko [10] for a large class of densities on Rd. We then use the work of Bickel and Breiman [2] to prove a central limit theorem in dimensions 1 and 2. In higher dimensions, we provide a development of the bias in terms of powers of N−2/d. This allows us to use a Richardson extrapolation to build, i...

We propose a nonparametric estimator for the rate of spread of an introduced population. We prove that the limit distribution of the estimator is normal or stable, depending on the behavior of the moment generating function. We show that resampling methods can also be used to approximate the distribution of the estimators. © 2001 Elsevier Science B.V. All rights reserved MSC: primary 62G05; sec...

This paper analyzes many weak moment asymptotics under the possibility of similar moments. The possibility of highly related moments arises when there are many of them. Knight and Fu (2000) designate the issue of similar regressors as the “nearly singular” design in the least squares case. In the nearly singular design, the sample variance converges to a singular limit term. However, Knight and...