The Use of OLUMV Estimators in Inference Robustness Studies of the Location Parameter of a Class of Symmetric Distributions

Abstract Coefficients for computing ordered linear unbiased minimum variance (OLUMV) estimators of the location and scale parameters have been obtained for selected members of a class of symmetric power distributions which includes the normal, double exponential, and as a limiting case, the rectangular. Two examples are given illustrating how these coefficients may be used to study the sensitivity of inferences concerning location parameters to departure from normality. The first example involves a single location parameter while the second extends the method to linear contrasts of several location parameters. Other uses of the coefficients are indicated, and a comparison of the efficiencies of the OLUMV estimators with several commonly used estimators of location is given.

[1]  H. Scheffé.  The Analysis of Variance , 1960 .

[2]  G. C. Tiao,et al.  A note on criterion robustness and inference robustness , 1964 .

[3]  F. N. David,et al.  The Advanced Theory of Statistics. Vol II. Inference and Relationship , 1962 .

[4]  Zakkula Govindarajulu.  Best Linear Estimates under Symmetric Censoring of the Parameters of a Double Exponential Population , 1966 .

[5]  R. Geary.  The Distribution of “Student'S” Ratio for Non‐Normal Samples , 1936 .

[6]  Allan Birnbaum,et al.  Optimal Robustness: A General Method, with Applications to Linear Estimators of Location , 1967 .

[7]  A. George Carlton.  Estimating the Parameters of a Rectangular Distribution , 1946 .

[8]  A. E. Sarhan,et al.  Contributions to order statistics , 1964 .

[9]  G. C. Tiao,et al.  A Further Look at Robustness via Bayes's Theorem , 1962 .

[10]  Arnold Zellner,et al.  BAYESIAN ANALYSIS OF THE REGRESSION MODEL WITH AUTOCORRELATED ERRORS. , 1964 .

[11]  A. Gayen.  The distribution of the variance ratio in random samples of any size drawn from non-normal universes. , 1950, Biometrika.

[12]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[13]  G. C. Tiao,et al.  Bayesian analysis of random-effect models in the analysis of variance II. Effect of autocorrelated erros , 1966 .

[14]  M. Kendall,et al.  The Advanced Theory of Statistics: Vol. I—Distribution Theory , 1959 .

[15]  D. Teichroew.  Tables of Expected Values of Order Statistics and Products of Order Statistics for Samples of Size Twenty and Less from the Normal Distribution , 1956 .

[16]  E. H. Lloyd.  LEAST-SQUARES ESTIMATION OF LOCATION AND SCALE PARAMETERS USING ORDER STATISTICS , 1952 .

[17]  Z. Govindarajulu.  On Moments of Order Statistics and Quasi-ranges from Normal Populations , 1963 .

[18]  R. A. Fisher,et al.  Design of Experiments , 1936 .

[19]  S. L. Andersen,et al.  Permutation Theory in the Derivation of Robust Criteria and the Study of Departures from Assumption , 1955 .

[20]  G. C. Tiao,et al.  A Bayesian approach to the importance of assumptions applied to the comparison of variances , 1964 .