Bias Adjustment Minimizing the Asymptotic Mean Square Error

A method of bias adjustment which minimizes the asymptotic mean square error is presented for an estimator typically given by maximum likelihood. Generally, this adjustment includes unknown population values. However, in some examples, the adjustment can be done without population values. In the case of a logit, a reasonable fixed value for the adjustment is found, which gives the asymptotic mean square error smaller than those of the asymptotically unbiased estimator and the maximum likelihood estimator. The weighted-score method, which yields directly the estimator with the minimized asymptotic mean square error, is also given.     

Some improved estimators for a measures of dispersion of an inverse gaussian distribution

In this paper some improved estimators for the measure of dispersion of an inverse Gaussian distribution have been obtained. If some guessed value of λ is available in the form of a point esitmate λ₀ the shrikage technique has been applied and an estimator has been proposed which has smaller mean squared error than the usual estimator. Since the shrinkage estimator has better performance if the guessed value is in the vicinity of the true value, a shrinkage testimator has also been proposed and compared with the usual estimator.     

The conditional MLE in the two-parameter geometric distribution and its competitors

The conditional maximum likelihood estimator of the shape parameter in the two-parameter geometric distribution is introduced and explored. The estimator is compared with the unconditional maximum likelihood estimator and the uniformly minimum variance unbiased estimator.     

On the generalized negative binomial distribution

The generalized negative binomial distribution (GNBD) was defined and studied by Jain and Consul (1971). The GNBD model has been found useful in many fields such as random walk, queuing theory, branching processes and polymerization reaction in chemistry. In this paper, four methods by which the GNBD model gets generated are discussed. The different methods of estimating the model parameters are provided. By using the bias property, we found that the truncated version of GNBD model provides a better parameter estimates than the GNBD model when fitted to data sets from the GNBD model.     

Finite Sample Properties of the Two-Step Empirical Likelihood Estimator

ABSTRACT

We investigate the finite sample properties of two-step empirical likelihood (EL) estimators. These estimators are shown to have the same third-order bias properties as EL itself. The Monte Carlo study provides evidence that (i) higher order asymptotics fails to provide a good approximation in the sense that the bias of the two-step EL estimators can be substantial and sensitive to the number of moment restrictions and (ii) the two-step EL estimators may have heavy tails.     

Asymptotic cumulants of the estimator of the canonical parameter in the exponential family

Asymptotic cumulants of the maximum likelihood estimator of the canonical parameter in the exponential family are obtained up to the fourth order with the added higher-order asymptotic variance. In the case of a scalar parameter, the corresponding results with and without studentization are given. These results are also obtained for the estimators by the weighted score, especially for those using the Jeffreys prior. The asymptotic cumulants are used for reducing bias and mean square error to improve a point estimator and for interval estimation to have higher-order accuracy. It is shown that the kurtosis to squared skewness ratio of the sufficient statistic plays a fundamental role.     

On Testing Sample Selection Bias Under the Multicollinearity Problem

ABSTRACT

This paper reviews and extends the literature on the finite sample behavior of tests for sample selection bias. Monte Carlo results show that, when the “multicollinearity problem” identified by Nawata (1993 Nawata , K. ( 1993 ). A note on the estimation of models with sample-selection biases . Economics Letters 42 : 15 – 24 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) is severe, (i) the t-test based on the Heckman–Greene variance estimator can be unreliable, (ii) the Likelihood Ratio test remains powerful, and (iii) nonnormality can be interpreted as severe sample selection bias by Maximum Likelihood methods, leading to negative Wald statistics. We also confirm previous findings (Leung and Yu, 1996 Leung , S. F. , Yu , S. ( 1996 ). On the choice between sample selection and two-part models . Journal of Econometrics 72 : 197 – 229 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) that the standard regression-based t-test (Heckman, 1979 Heckman , J. J. ( 1979 ). Sample selection bias as a specification error . Econometrica 47 : 153 – 161 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) and the asymptotically efficient Lagrange Multiplier test (Melino, 1982 Melino , A. ( 1982 ). Testing for sample selection bias . Review of Economic Studies 49 : 151 – 153 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]), are robust to nonnormality but have very little power.     

Estimating Long and Short Run Effects in Static Panel Models

Abstract

This paper assesses the biases of four different estimators with respect to the short run and the long run parameters if a static panel model is used, although the data generating process is a dynamic error components model. We analytically derive the associated biases and provide a discussion of the determinants thereof. Our analytical and numerical results as well as Monte Carlo simulations illustrate that the asymptotic bias of both the within and the between parameter with respect to the short run and long run impact can be substantial, depending on the memory of the data generating process, the length of the time series and the importance of the cross-sectional variation in the explanatory variables.     

Bootstrap variance and bias estimation in linear models

Let θ be a nonlinear function of the regression parameters and θ be its estimator based on the least-squares method. This paper studies the bootstrap estimators of the variance and bias of θ. The bootstrap estimators are shown to be consistent and asymptotically unbiased under some conditions. Asymptotic orders of the mean squared errors of the bootstrap estimators are also obtained. The bootstrap and the classical linearization method are compared in a simulation study. Discussions about when to use the bootstrap are given.     

A Note on Derived Means of Scaled Data

Details are given of the procedures for calculating derived means of square-root and log transformed variables from un-subdivided and layered samples. A method for determining approximate confidence limits of the derived means is also described. The temporal distribution of nematodes in grass herbage is given as an example to illustrate the procedures used.