let x be a random variable from a normal distribution with unknown mean θ and known variance σ2. in many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. as the usual estimator of θ, i.e., x under the linex loss function is inadmissible, finding some competitors for x becomes worthwhile. the only study in the literature considered the problem of min...

In a recent issue of the Journal, VanderWeele and Vansteelandt (Am J Epidemiol. 2011;174(10):1197-1203) discussed an inverse probability weighting method for case-control studies that could be used to estimate an additive interaction effect, referred to as the "relative excess risk due to interaction." In this article, we reinforce the well-known disadvantages of inverse probability weighting a...

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...

In the first part of this lecture, we will deal with the consistency and asymptotic distribution of maximum likelihood estimator. The second part of the lecture focuses on signal estimation/tracking. An estimator is said to be consistent if it converges to the quantity being estimated. This section speaks about the consistency of MLE and conditions under which MLE is consistent.

This paper describes a recursive method for estimating random coefficient models. Starting with a trial value for the moments of the distribution of coefficients in the population, draws are taken and then weighted to represent draws from the conditional distribution for each sampled agent (i.e., conditional on the agent’s observed dependent variable.) The moments of the weighted draws are calc...

Maximum likelihood methods are by far the most popular methods for deriving statistical estimators. However, parametric likelihoods require distributional specifications. The empirical likelihood is a nonparametric likelihood function that does not require such distributional assumptions, but is otherwise analogous to its parametric counterpart. Both likelihoods assume that the random variables...

Suppose we observe an ergodic Markov chain on the real line, with a parametric model for the autoregression function, i.e. the conditional mean of the transition distribution. If one speciies, in addition, a paramet-ric model for the conditional variance, one can deene a simple estimator for the parameter, the maximum quasi-likelihood estimator. It is robust against misspeciication of the condi...

A discrete statistical model is a subset of probability simplex. Its maximum likelihood estimator (MLE) retraction from that simplex onto the model. We characterize all models for which this rational function. This contribution via real algebraic geometry rests on results Horn uniformization due to Huh and Kapranov. present an algorithm constructing with MLE, we demonstrate it range instances. ...