Roger C. Pfaffenberger

A comparison of quantile estimators

Ten nonparametric estimators of quantiles are compared in small samples by Monte Carlo simulation methods. The estimators are compared by using properties such as mean square error and mean absolute deviation. Nine distributions are used for the comparisons and include long-tailed distributions (e.g., Laplace), short-tailed distributions (e.g., uniform), and skewed distributions (e.g., exponential)

Bootstrapping in least absolute value regression: an application to hypothesis testing

A Monte Carlo simulation is used to study the performance of hypothesis tests for regression coefficients when least absolute value regression methods are used. In small samples, the results of the simulation suggest that using the bootstrap method to compute standard errors will provide improved test performance

A stochastic dominance analysis of ranked voting systems with scoring

Abstract Selection procedures and elections often use a ranked voting system combined with a set of point values assigned to the various ranks. The winner is the one with the highest total points. However, the choice of the set of point values tends to be arbitrary. Stochastic dominance will be used to define a partial ordering of candidates in this situation. This shows the effect of choosing different point values and, in particular, determines all possible orderings of the candidates. Examples from sports competitions will be used.

Tests of linear hypotheses and LAV estimation: a Monte Carlo comparison

A Monte Carlo simulation is used to study the performance of the Wald, likelihood ratio and Lagrange multiplier tests for regression coefficients when least absolute value regression is used. The simulation results provide support for use of the Lagrange multiplier test, especially when certain computational advantages are considered.

A further comparison of tests of hypotheses in LAV regression

Abstract This study compares five alternate test procedures for the significance of coefficients in LAV regression. The WALD and LR tests using the SECI estimator of λ proposed by McKean and Schrader (Commun. Statist. - Simulation Comput. 13 (1984) p. 751–773) were examined as well as versions of these tests using bootstrap estimates of λ (BWALD and BLR) and the LM test. There is some evidence that the empirical level of significance for the LM test more nearly conforms to the expected level (5% used in study) than the observed levels do for the other tests. The two tests that appear to perform best in the experiment are the LR test using the SECI estimator of λ and the LM test. The bootstrap version of the LR test is computationally more expensive and appears to be no better (and perhaps worse in terms of the empirical size) than the traditional version. The WALD test appears inferior in the computations in either its traditional or bootstrap versions.

Computational Algorithms for Calculating Least Absolute Value and Chebyshev Estimates for Multiple Regression

SYNOPTIC ABSTRACTLeast absolute value (LAV) and Chebyshev estimation are two possible alternatives to least squares estimation in multiple regression models. This paper reviews the historical development of these two alternatives with special attention placed on the development of algorithms for producing LAV and Chebyshev estimates of the regression parameters. Recent algorithmic improvements are reviewed, sources for obtaining computer programs are identified and recommendations are made for the most efficient algorithm for specific cases. In the final section suggestions for future research are made for the development and refinement of computational algorithms and inference procedures.

Efficiency of Ordinary Least Squares for Linear Models with Autocorrelation

Abstract This article provides a reconsideration of Kramers (1980) results on least squares estimation in linear models with autocorrelated errors. Kramers results are shown to be dependent on his measure of efficiency and to understate the advantages of correcting for autocorrelation.

Estimation of error probabilities in stochastic dominance

The process of using data to infer the existence of stochastic dominance is subject to sampling error. Kroll and Levy (1980), among others, have presented simulation results for several normal and lognormal distributions which show high error probabilities for a wide range of parameter values. This paper continues this line of research and uses simulation to estimate error probabilities. Distributions considered are a pair of normals and a pair of lognormals. Analysis of these distributions is made computationally feasible through theoretical results which reduce the number of parameters of the pair of distributions from four to two.

On the Estimation Risk in First-Order Stochastic Dominance: A Note

By using order statistics, the authors develop formulas for calculating the proba? bilities of committing a Type I or a Type II error. However, these formulas are based on n-dimensional integrals with very complex limits of integration. As a consequence, these formulas cannot be evaluated analytically except for very simple cases (e.g., the uniform distribution of returns). Rather than attempting to assess the integrals numerically, the authors use Monte Carlo simulation tech? niques to estimate the Type I and the Type II error probabilities. The purpose of this note is to point out that there are well-known analytical results for the Type I error probability for both the equal1 and the unequal sample size cases for firstorder stochastic dominance (FSD) when it is assumed that both options have been sampled from the same population of returns.

Small sample properties of estimators in the autocorrelated error model: a review and some additional simulations

This paper provides a review of the literature concerning estimation in time series regression with first-order autocorrelated disturbances. Some additional simulation results confirm that the Cochrane-Orcutt estimator should not be used to correct for autocorrelation whether the explanatory variable is trended or not. Preferred estimators include a Bayesian estimator, full maximum likelihood and the iterative Prais-Winsten estimator.