Optimum Spacings, ABLUE and Tests of Hypothesis in Simple Linear Model with Extreme-Value Errors

 

A.K.Md.E. Saleh, K.M. Hassanein and E.F. Brown (1994). Optimum Spacings, ABLUE and Tests of Hypothesis in Simple Linear Model with Extreme-Value Errors. Journal of Statistical Research, Vol. 28, No. 1-2, pp.  53-63.

 

Abstract

Consider the simple linear model y_j= \theta_0 + \theta_1 x_j +\sigma z_j , j=1,\ldots,n where z_1,\ldots,z_n are i.i.d.r.v. with the pdf exp(z - e^z), -\infty < z < \infty. This paper considers the joint estimation and test of hypothesis of (\theta_0, \theta_1,\sigma)' based on a few selected "regression quantiles". The question of optimum spacings is addressed and it is shown that they are independent of the design matrix. Tables of optimum spacings, coefficients of the ABLUE of (\theta_0, \theta_1,\sigma)' along with some asymptotic relative efficiencies are provided in Table 1-4.

 

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