Many studies of k-class estimators have investigated their distributional properties (see Kadane [4], pp. 723-724 for a useful summary). Here we are concerned with the mathematical analysis of the k-class formulae rather than with their statistical analysis. Other work in this field includes Theil [10], pp. 233-237, Maeshiro [7], Oi [8] and Kadiyala [5]. In this paper we examine how the k-class estimator varies with k. We derive an expression from which the main features of the graph of a k-class estimator may be obtained and show that, except in a subspace of measure zero, the parameter estimates and their asymptotic standard errors become infinite for some value k1 that is common to the parameters of an equation whilst their ratios (the t-ratios) tend to zero.

and where tl, 2, ... , n-k is a set of independent standard normal variates. The significance points of dM, dL, and du may be evaluated by the methods of Imhof [3] and Pan [8]. Savin and White [9] have noted that Koerts and Abrahamse's [5, pp. 159-160] FORTRAN implementation of Imhof's procedure fails to converge when the significance point is near A1. This defect is easily remedied by replacing Imhof's lower bound for the inverse of the truncation error by