An approximation of logarithmic functions in the regression setting

We consider a method of moments approach for dealing with censoring at zero for data expressed in levels when researchers would like to take logarithms. A Box–Cox transformation is employed. We explore this approach in the context of linear regression where both dependent and independent variables are censored. We contrast this method to two others, (1) dropping records of data containing censored values and (2) assuming normality for censored observations and the residuals in the model. Across the methods considered, where researchers are interested primarily in the slope parameter, estimation bias is consistently reduced using the method of moments approach.     

GMM tests for the Katz family of distributions

Generalized method of moments (GMM) is used to develop tests for discriminating discrete distributions among the two-parameter family of Katz distributions. Relationships involving moments are exploited to obtain identifying and over-identifying restrictions. The asymptotic relative efficiencies of tests based on GMM are analyzed using the local power approach and the approximate Bahadur efficiency. The paper also gives results of Monte Carlo experiments designed to check the validity of the theoretical findings and to shed light on the small sample properties of the proposed tests. Extensions of the results to compound Poisson alternative hypotheses are discussed.     

Almost Consistent Estimation of Panel Probit Models with “Small” Fixed Effects

We propose four different GMM estimators that allow almost consistent estimation of the structural parameters of panel probit models with fixed effects for the case of small Tand large N. The moments used are derived for each period from a first order approximation of the mean of the dependent variable conditional on explanatory variables and on the fixed effect. The estimators differ w.r.t. the choice of instruments and whether they use trimming to reduce the bias or not. In a Monte Carlo study, we compare these estimators with pooled probit and conditional logit estimators for different data generating processes. The results show that the proposed estimators outperform these competitors in several situations.     

Expected sample moments of concomitants of selected order statistics

In this paper, the task of determining expected values of sample moments, where the sample members have been selected based on noisy information, is considered. This task is a recurring problem in the theory of evolution strategies. Exact expressions for expected values of sums of products of concomitants of selected order statistics are derived. Then, using Edgeworth and Cornish-Fisher approximations, explicit results that depend on coefficients that can be determined numerically are obtained. While the results are exact only for normal populations, it is shown experimentally that including skewness and kurtosis in the calculations can yield greatly improved results for other distributions.     

A relation for the covariances of order statistics from n independent and non-identically distributed random variables

We derive a simple relation satisfied by the covariances of order statistics in the i.i.d. case and then generalize it to the case when the variables are independent and non-identically distributed. This relation could be employed successfully either to check the calculations or to reduce the amount of direct computations involved in evaluating the covariances of order statistics from an outlier model.     

Tests for generalized exponential laws based on the empirical Mellin transform

Recently, many standard families of distributions have been generalized by exponentiating their cumulative distribution function (CDF). In this paper, test statistics are constructed based on CDF–transformed observations and the corresponding moments of arbitrary positive order. Simulation results for generalized exponential distributions show that the proposed test compares well with standard methods based on the empirical distribution function.     

A procedure for testing the equality of k dependent correlation coefficients

A procedure is proposed for testing the equality of k dependent correlation coefficients. The procedure is simulated utilizing Monte Carlo techniques; and, a method for post hoc probing is also suggested.     

Modeling censored data using modified lambda family

In the present article we propose the modified lambda family (MLF) which is the Freimer, Mudholkar, Kollia, and Lin (FMKL) parametrization of generalized lambda distribution (GLD) as a model for censored data. The expressions for probability weighted moments of MLF are derived and used to estimate the parameters of the distribution. We modified the estimation technique using probability weighted moments. It is shown that the distribution provides reasonable fit to a real censored data.     

Comparison between method of moments and entropy regularization algorithm applied to parameter estimation for mixed-Weibull distribution

Mixed-Weibull distribution has been used to model a wide range of failure data sets, and in many practical situations the number of components in a mixture model is unknown. Thus, the parameter estimation of a mixed-Weibull distribution is considered and the important issue of how to determine the number of components is discussed. Two approaches are proposed to solve this problem. One is the method of moments and the other is a regularization type of fuzzy clustering algorithm. Finally, numerical examples and two real data sets are given to illustrate the features of the proposed approaches.     

The exact properties of the lawless and wang operational ridge regression estimator in a misspecified regression equation

The exact properties of the Lawless and Wang Operational Ridge Regression estimator are derived in the context of a misspecified regression equation.