TR Multivariate Conditional Median Estimation

An affine equivariant version of the nonparametric spatial conditional median (SCM) is constructed, using an adaptive transformation–retransformation (TR) procedure. The relative performance of SCM estimates, computed with and without applying the TR-procedure, are compared through simulations. Also included is the vector of coordinate conditional, kernel-based medians (VCCMs). The methodology is illustrated via an empirical data set. The simulations indicate that the TR-SCM estimator is more efficient than the SCM estimator for data generated from asymmetric contaminated trivariate normals. However, when the dimension of the covariates increases the efficiency of the TR-SCM estimator decreases. The TR-VCCM- and VCCM estimators lack efficiency, and consequently should not be used in practice.     

A Note on the Distribution of Linear Functions of Two Ordered Correlated Normal Random Variables

We consider the problem of finding the distribution of linear functions of two ordered correlated normal random variables. We derive some distributional properties for these linear statistics and briefly discuss the use of them in location estimation. The connection of the subject with the skew normal distribution is also noted.     

Inferences on the Coefficients of Variation in a Multivariate Normal Population

In this article, the problem of testing the equality of coefficients of variation in a multivariate normal population is considered, and an asymptotic approach and a generalized p-value approach based on the concepts of generalized test variable are proposed. Monte Carlo simulation studies show that the proposed generalized p-value test has good empirical sizes, and it is better than the asymptotic approach. In addition, the problem of hypothesis testing and confidence interval for the common coefficient variation of a multivariate normal population are considered, and a generalized p-value and a generalized confidence interval are proposed. Using Monte Carlo simulation, we find that the coverage probabilities and expected lengths of this generalized confidence interval are satisfactory, and the empirical sizes of the generalized p-value are close to nominal level. We illustrate our approaches using a real data.     

Parametric inference in a perturbed gamma degradation process

Abstract

We consider a degradation model which is the sum of two independent processes: an homogeneous gamma process and a Brownian motion. This model is called perturbed gamma process. Based on independent copies of the perturbed gamma process observed at irregular instants we propose to estimate the unknown parameters of the model using the moment method. Some general conditions allow to derive the asymptotic behavior of the estimators. We also show that these general conditions are fulfilled for some specific observation schemes. Finally, we illustrate our method by a numerical study and an application to a real data set.     

Impacts of auxiliary information on outliers in regression

Iheil and Goldberger (1961) and Theil (1963) founded the mixed regression approach, Their mixed regression estimator is essentially a large class of estimators that includes ridge, generalized ridge and shrinkage estimators, Properties of these estimators when data contain outliers have not been examined extensively. The present investigation shows that the mixed regression estimator, when observationsare subject to shift in means and variances, is uniformly superior, in terms of squared bias and variance, to the least squares estimator.     

On some generalized wishart expectations

In a recent paper Muirhead (1986) derived certain useful identities involving expectations taken with respect to the Wishart distribution. This note generalizes the above results by taking expectations with respect to a generalized version of the Wishart distribution, considered by Sutradhar and Ali (1989), based on a multivariate tdistribution.     

How fair can employers be?

In this article we examine three concepts of fairness in employment decisions. Two of these concepts are widely known in the literature as “Fairness 1”and “Fairness 2”. The third concept, which we refer to as “Fairness 0”, is defined and introduced here. Fairness 0 applies to the hiring stage, whereas Fairness 1 and Fairness 2 apply to the placement or promotion stages of employment. Our results have important policy implications. We show that the three concepts of fairness can only rarely be achieved simultaneously.     

Some properties of,and relationships among,several uncorrelated and homoscedastic residual vectors

In this paper we examine the properties of four types of residual vectors, arising from fitting a linear regression model to a set of data by least squares. The four types of residuals are (i) the Stepwise residuals (Hedayat and Robson, 1970), (ii) the Recursive residuals (Brown, Durbin, and Evans, 1975), (iii) the Sequentially Adjusted residuals (to be defined herein), and (iv) the BLUS residuals (Theil, 1965, 1971). We also study the relationships among the four residual vectors. It is found that, for any given sequence of observations, (i) the first three sets of residuals are identical, (ii) each of the first three sets, being identical, is a member of Thei’rs (1965, 1971) family of residuals; specifically, they are Linear Unbiased with a Scalar covariance matrix (LUS) but not Best Linear Unbiased with a Scalar covariance matrix (BLUS). We find the explicit form of the transformation matrix and show that the first three sets of residual vectors can be written as an orthogonal transformation of the BLUS residual vector. These and other properties may prove to be useful in the statistical analysis of residuals.     

Additional approximations to the distribution of a structural coefficient estimator for the case of two included endogenous variables

Four new approximations t o the exact distribution of the two-stage l e a s t squares estimator of astructuralcoefficient for

the case of two included endogeneous variables are introduced and compared with the others in the literatur e . Two of the new approximations are based on the Pearson distribution and are found to be adequate throughout the parameter space. A normal approximation using exact moments and an approximation based on the saddlepoint method (Holly and Phillips,1979) are found to be

poor for a wide range of parameter values.     

A method for estimating lorenz curves

This paper proposes a new method for estimating the parameters of Lorenz Curves (LC’s) and fitting LC’s to observed data. The method is very general. It is applicable to any family of LC’s as long as it is given in closed form which is often the case in practice. The method can also be applied to either the LC or to its associated distribution. The estimators are easy to compute as they are obtained one at a time by solving only one equation in one unknown and in many cases the solutions are given in closed-forms. An additional advantage, that is not shared with the currently used method of estimation, is that the method is invariant as to the specification of which variable is written as a function of the other in the LC form. The method is applied to the most commonly suggested LC’s families. An example of real-life data is used to illustrate the methodology. A simulation study is performed to study the properties of the proposed estimators and to compare them with existing ones. The results seem to indicate that the proposed estimators have good properties and they often perform much better than the existing ones.