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A number of efficient computer codes are available for the simple linear L 1 regression problem. However, a number of these codes can be made more efficient by utilizing the least squares solution. In fact, a couple of available computer programs already do so. We report the results of a computational study comparing several openly available computer programs for solving the simple linear L 1 regression problem with and without computing and utilizing a least squares solution.

Finding Groups in Data: An Introduction to Cluster Analysis. By L. Kaufman and P. J. Rousseeuw. ISBN 0 471 87876 6. Wiley, New York, 1990. xiv + 342 pp. £39.30.

The stltdetltized bivnhte range, R s , it1 a sample from a circrdur normal distribution is espressed as the maximum of a set of F variables. Using a method employed by pearson and Chandra Sekar [7], the exact upper tail distribution for small samples is given. The same procedure provides over-approximations to the percentage points of R s , for larger sample sizes. Methods for obtaining the full distribution are discrussed. The use of the statistic in testitrg for homogeneity is considered.

A brief review and bibliography of least absolute values (LAV) estimation is given. This paper serves to introduce the other articles in this special issue on the computational aspects of LAV estimation.

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 y's 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.

Two techniques for detecting inaccuracies in least absolute values (LAV) regression computations are presented and discussed. Examples of the use of the methods are given. The techniques are shown to apply to the more general case of M-estimation.

When the disturbances in regression models do not have normal distributions, the usual F-test for coincidence of regressions is not appropriate. We propose a simple robust test for coincidence of regressions and by means of a simulation study compare its performance with that of the usual F-test for models with errors having distributions from the family of symmetric stable distributions.

This section is devoted to the publication of computer Algorithms for statistical applications. It is intended for listings of usable computer programs, together with descriptions of their use, and for comments on previously published algorithms. Ordinarily the program published will be in FORTRAN (ANSI 1966 or 1977). In the case of longer programs, only the description and comment statements from the program will be published in this Section., Machine. readable copies of any program published or described in this Section can be obtained from the author(s). A statement of the algorithm policy and guidelines for submission can be found in the first issue each year of the Simulation and Computation Journal. Changes do occur periodically, and it is advisable to check the first Simulation and Computation Journal for the current year.