Admissible minimum bias estimation of response surfaces

The minimum bias estimator was introduced as an alternative to the least squares estimator for approximating response functions by low-order polynomials. Here we show how to obtain an admissible estimator with smaller squared bias.     

The general class of chain estimators for the ratio of two means using double sampling

A wider class of chain based estimators for the ratio of two means of a finite population has been proposed by using two auxiliary variables. Singh et al.(1994) is a particular case of this class.     

Influence analysis in multivariate linear general models

In this paper we obtain several influence measures for the multivariate linear general model through the approach proposed by Muñoz-Pichardo et al. (1995), which is based on the concept of conditional bias. An interesting charasteristic of this approach is that it does not require any distributional hypothesis. Appling the obtained results to the multivariate regression model, we obtain some measures proposed by other authors. Nevertheless, on the results obtained in this paper, we emphasize two aspects. First, they provide a theoretical foundation for measures proposed by other authors for the mul¬tivariate regression model. Second, they can be applied to any linear model that can be formulated as a particular case of the multivariate linear general model. In particular, we carry out an application to the multivariate analysis of covariance.     

Maximum likelihood estimation for the generalized poisson distribution

The generalized Poisson distribution;containing two

parameters and studied by many researchers; describes the distribution of busy periods under a queueing system and has very interesting properties; The probabilities for successive classes depend upon the previous occurrences; The problem of admissible maximum likelihood estimators for for the parameters Is discussed and a necessary and sufficient condition is derived for which unique admissible maximum likelihood estimators exist; The first; order terms in the biases; variances and the covariance of these maximum likelihood estimators are obtained.     

Convergence rates for uniform confidence intervals based on local polynomial regression estimators

We investigate the convergence rates of uniform bias-corrected confidence intervals for a smooth curve using local polynomial regression for both the interior and boundary region. We discuss the cases when the degree of the polynomial is odd and even. The uniform confidence intervals are based on the volume-of-tube formula modified for biased estimators. We empirically show that the proposed uniform confidence intervals attain, at least approximately, nominal coverage. Finally, we investigate the performance of the volume-of-tube based confidence intervals for independent non-Gaussian errors.     

Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields

We investigate the asymptotic behaviour of binned kernel density estimators for dependent and locally non-stationary random fields converging to stationary random fields. We focus on the study of the bias and the asymptotic normality of the estimators. A simulation experiment conducted shows that both the kernel density estimator and the binned kernel density estimator have the same behavior and both estimate accurately the true density when the number of fields increases. We apply our results to the 2002 incidence rates of tuberculosis in the departments of France.     

Transformation and Smoothing in Sample Survey Data

Abstract. We consider model‐based prediction of a finite population total when a monotone transformation of the survey variable makes it appropriate to assume additive, homoscedastic errors. As the transformation to achieve this does not necessarily simultaneously produce an easily parameterized mean function, we assume only that the mean is a smooth function of the auxiliary variable and estimate it non‐parametrically. The back transformation of predictions obtained on the transformed scale introduces bias which we remove using smearing. We obtain an asymptotic expansion for the prediction error which shows that prediction bias is asymptotically negligible and the prediction mean‐squared error (MSE) using a non‐parametric model remains in the same order as when a parametric model is adopted. The expansion also shows the effect of smearing on the prediction MSE and can be used to compute the asymptotic prediction MSE. We propose a model‐based bootstrap estimate of the prediction MSE. The predictor produces competitive results in terms of bias and prediction MSE in a simulation study, and performs well on a population constructed from an Australian farm survey.     

The maximum likelihood estimators of the parameters of the gamma distribution are always positively biased

Several authors have conjectured, on the basis of their numerical work, that the maximum likelihood estimators of the shape and scale parameters of the Gamma distribution are positively biased. It is proved that their conjecture is always true.     

Estimation of the smaller and larger of two exponential location parameters

Assume independent random samples are drawn from two populations which are exponentially distributed with unknown location parameters and a common known scale parameter. We want to estimate the maximum and the minimum of the unknowo location paremeters. In this paper several estimators are proposed which are better than the natural estimations in terms of absolute bias and /or meaqn squared error.     

A Characterization of the Normal Family of Distributions Based on the Bias of the Maximum Likelihood Estimator

This paper characterizes the family of Normal distributions within the class of exponential families of distributions, via the structure of the bias of the maximum likelihood estimator Θ _n of the canonical parameter Θ . More specifically, when E _θ ( Θ n ) – Θ = (1/ n ) Q ( Θ ) + o (1/ n ), the equality Q ( Θ ) = 0 proves to be a property of the Normal distribution only. The same conclusion is obtained for the one-dimensional case bt assuming that Q ( Θ ) is a polynomial of Θ .