V. A. Sposito

On the efficiency of using the sample kurtosis in selecting optimal lpestimators

This paper examines the efficiency of thesample kurtosisin obtaining LP estimates as an estimates of central tendency for symmetric distributions. Moreover, guidelines are established for determining an optimal value of P based on the kurtosis of the error distribution.

A computer oriented method for generating test problems for L1 regression

A numerical method for obtaining data (X|y), relative to the linear model , is given. The user is allowed to specify column means for the X matrix, the general order of condition number, the unique L1 solution vector and the deviations of ys about the fitted hyperplane. Implementation of the method requires little more than use of subroutines found in most modern subroutine libraries. Computer generated data of this kind are useful in numerical studies of the operating characteristics of different algorithms.

On the estimation of the variance of the median used in L1 linear inference procedures

Recent results in the literature have considered the distri-bution of the LAV estimator ; i.e, under the criterion of min-izing the sum of absolute deviations. It has been shown that is approximately normally distributed with mean zero and covarianoe matrix where λ2/n is the variance of the median for a sample of size n. Sub-sequent research has shown how the asymptotic results can be used in inference procedures; these procedures are based on λ being known. This paper will consider the estimation of λ as suggested by Cox and Hinkley (1974). In this spirit a Monte Carlo study was conducted using various distributions over various sample sizes. Guidelines for using this estimate of λ in LAV inference proce-dures will also be discussed.

Using an approximate L1 Estimator

This note investigates the efficiency of using near-best or approximate L1 estimators as starting values in L1 linear programming procedures. In particular, it is shown that the total computer time can often be reduced if one first computes the least squares estimator, β, and then adjust y to y - Xβ in Barrodale and Roberts’ improved algorithm.

Modified regularity conditions for nonlinear programming problems over mixed cone domains

In earlier results by Sposito and David, Kuhn—Tucker duality was established over nondegenerate cone domains (not necessarily polyhedral) without differentiability under a certain natural modification of the Slater condition, in addition to the convexity of a certain auxiliary set. This note extends Kuhn—Tucker duality to optimization problems with both nondegenerate and degenerate cone domains. Moreover, under a different condition than presented in earlier results by the author, this note develops Kuhn—Tucker duality for a certain class of nonlinear problems with linear constraints and an arbitrary objective function.

Using the least squares estimator in Chebyshev estimation

This note investigates the advantage of using the least squares estimator as a starting point in Barrodale and Phillips L -algorithm

Useful generalized properties of L1 estimators

Recent results by G. Appa and C. Smith, as well as I. Barrodale and F. D. K. Roberts, underscore several properties exhibited for fitting a linear model to a set of observation points under the criterion of least sum of absolute deviations(commonly denoted as the L1 criterion). This paper will generalize these properties to the non-full rank case and relax in a natural way some assumptions given by Appa and Smith.