Conditional Best Linear Invariant Estimation of the Location and Scale Parameters of the Cauchy Distribution by the Use of Order Statistics
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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Linear coefficients which can be applied to sample data from a Cauchy distribution to obtain estimates of the location and scale parameters are developed and tabled. Several previous works have presented such tables for nearly best linear unbiased estimation and best linear unbiased estimation of the parameters. The estimates developed in the paper are best in the sense that they possess minimum mean square error. By using exact values of the means, variances, and covariances of the Cauchy standardized order statistics and minimizing the mean square error functions, matrix equations are developed and solved to obtain the required coefficients.
- Statistics and Probability