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Statistical decision techniques are developed for loan screening that provide a guide as to how long nonpaying defaulted loans of various types should be pursued by adjusters or collectors before they are completely dropped as uncollectible. A mathematical model yields the optimum pursuit duration and maximum expected net profit for each type of delinquent loan considered and which, if followed, will maximize the over-all net profit of a loan adjustment or collection department. The application of these rules by simulation to a random sample of defaulted loans indicates a potential increase in net profit of approximately 33 per cent.

A new concept of unbiasedness (density unbiasedness) for point estimates is introduced and the "best" density unbiased point estimate for the mean of any normal distribution is proved to be the ordinary sample mean $\bar{x} = \sum^n_{i = 1} x_i/n$. Under certain conditions on the form of the characteristic function of a family of probability density functions involving an unknown location parameter, $\bar{x}$ is shown to be a density unbiased point estimate of the location parameter.

Forty-five third graders from two schools were presented with different patterns of digits and letters tachistoscopically at ½-sec. exposure and reported the symbols in the order identified. Consistent patterns of reading the symbols appeared for many Ss, five of which were identified. The remaining Ss changed patterns from one exposure to the next. The distribution of patterns in relation to reading-achievement scores by schools revealed inter-school differences, but no one pattern consistently identified better readers or distinguished between reading comprehension and word recognition. Ss' reactions to the task suggested anxiety as a possible cause for the shifts from one pattern to another by many Ss.

Let#!, . . ., xn deno te s (not necessarily independent) observed values of a random variable f, which is distributed over a space S according to a distribution Pz(x, 0i, . . ., 0S). I t is assumed that Pz(x, 0i, . . ., 0S) is completely specified except for the s unknown parameters 0U . . ., 0S. These parameters may be represented by a point 6=(d1, . . ., 0S) in the s-dimensional Euclidean parameter space 12. Also X—(xi, . . ., xn) is a point in the n-dimensional Euclidean sample space, M. We shall assume that Pz(x, 0) is absolutely continuous, that is, £ possesses an integrable probability density function g^x, 0). Let p(X, 6)=p(x1, . . ., xn, 0) denote the joint probability density function of the observations at XeM. A statistical point estimate of a parameter 0*. which ranges over a subset co* of one-dimensional Euclidean space, is a function ft{X) of the sample values that takes on values in ut. Let W\fi(X), 0] be a nonnegative measurable function denned for all 0e& and XeM. W[fi(X), .0] is a weight function that represents the relative seriousness of taking ft(X) as the value of 0* for any particular sample point X. The function