The Pareto distribution is often used in many areas of economics to model the right tail of heavytailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution– the maximum likelihood estimator (MLE) – is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years...

The zeta distribution with regression parameters has been rarely used in statistics because of the difficulty of estimating the parameters by traditional maximum likelihood. We propose an alternative method for estimating the parameters based on an iteratively reweighted least-squares algorithm. The quadratic distance estimator (QDE) obtained is consistent, asymptotically unbiased and normally ...

This paper shows how the parameters of a stable GARCH(1, 1) model can be estimated from the autocorrelations of the squared process. Speci®cally, the method applies a minimum distance estimator (MDE) to the sample autocorrelations of the squared realization. The asymptotic ef®ciency of the estimator is calculated from using the ®rst g autocorrelations. The estimator can be surprisingly ef®cient...

The estimation of the total number of defects at early stages of the testing process helps managers to make resource allocation and deadline decisions. The use of nonbayesian approaches has proven to be accurate but presents a certain latency to achieve a reasonable accuracy. Here we describe BayesED3M , a bayesian estimator construct upon an existing MLE (Maximum Likelihood Estimator) named as...

We examine bias corrections which have been proposed for the Fixed Effects Panel Probit model with exogenous regressors, using several different data generating processes to evaluate the performance of the estimators in different situations. We find a best estimator across all cases for coefficient estimates, but when the marginal effects are the quantity of interest no analytical correction is...

MOTIVATION The numerical values of gene expression measured using microarrays are usually presented to the biological end-user as summary statistics of spot pixel data, such as the spot mean, median and mode. Much of the subsequent data analysis reported in the literature, however, uses only one of these spot statistics. This results in sub-optimal estimates of gene expression levels and a need...

The search for conditions for the consistency of maximum likelihood estimators in nonlinear mixed effects models is difficult due to the fact that, in general, the likelihood can only be expressed as an integral over the random effects. For repeated measurements or clustered data, we focus on asymptotic theory for the maximum likelihood estimator for the case where the cluster sizes go to infin...

*Correspondence: [email protected] 2Department of Mathematics and Statistics, UNC Charlotte, 9201 University City Blvd, 28223 Charlotte, USA Full list of author information is available at the end of the article Abstract The maximum likelihood estimator (MLE) of Gini-Simpson’s diversity index (GS) is widely used but suffers from large bias when the number of species is large or infinite. We prop...

Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent aftercurrent. This model is a biophysically plausible al...