An analysis of constrained robust regression estimators

Multicollinearity and nonnormal errors are problems often encountered in the application of linear regression. Estimators are proposed for dealing with the simultaneous occurrence of both multicollinearity and nonnormality. These estimators are developed by combining biased estimation techniques with certain robust criteria. An iteratively reweighted least-squares procedure is used to compute the estimates. The performance of the combined estimators is studied empirically through Monte Carlo experiments structured according to factorial designs. With respect to a mean-squared-error criterion, the combined estimators are superior to ordinary least-squares, pure biased estimators, and pure robust estimators when multicollinearity and nonnormality are present. The loss in efficiency for the combined estimators relative to least squares is small when these problems do not occur. Some guidelines for the use of these combined estimators are given.     

Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.     

A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

A class of inventory models with customer impatience

Classical inventory models generally assume either no backlogging of demands or unlimited backlogging. This paper treats the case wherein backlogged customers are willing to wait for a random period of time for service. A broad class of such models is discussed, with a more complete analysis performed on a simple subclass. Steady state equations are derived and solved assuming exponentially distributed interarrival times of customers, order delivery lead times, and customer patience.     

Determining optimal growth paths in logistics operations

This paper considers a logistics system modelled as a transportation problem with a linear cost structure and lower bounds on supply from each origin and to each destination. We provide an algorithm for obtaining the growth path of such a system, i. e., determining the optimum shipment patterns and supply levels from origins and to destinations, when the total volume handled in the system is increased. Extensions of the procedure for the case when the costs of supplying are convex and piecewise linear and for solving transportation problems that are not in “standard form” are discussed. A procedure is provided for determining optimal plant capacities when the market requirements have prespecified growth rates. A goal programming growth model where the minimum requirements are treated as goals rather than as absolute requirements is also formulated.     

Some estimates of reliability using interference theory

According to “interference theory” of reliability, a component fails if the maximum stress exceeds the component's strength. Assuming that both these quantities are random and their distributions are normal, we obtain in this paper some point and interval estimates of reliability when the stress distribution is known and a few observations exist on component strengths.     

Optimal interdiction of a supply network

Under certain conditions, the re-supply capability of a combatant force may be limited by the characteristics of the transportation network over which supplies must flow. Interdiction by an opposing force may be used to reduce the capacity of that network. The effects of such efforts vary for differing missions and targets. With only a limited total budget available, the interdictor must decide which targets to hit, and with how much effort. An algorithm is presented for determining the optimum interdiction plan for minimizing network flow capacity when the minimum capacity on an arc is positive and the cost of interdiction is a linear function of arc capacity reduction.