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.     

Inequalities involving the lifetime of series and parallel systems

Let {Xⁱ} be independent HNBUE (Harmonic New Better Than Used in Expectation) random variables and let {Yⁱ} be independent exponential random variables such that E{Xⁱ}=E{Yⁱ} It is shown that \documentclass{article}\pagestyle{empty}\begin{document}$ E\left[{u\left({\mathop {\min \,X_i}\limits_{l \le i \le n}} \right)} \right] \ge E\left[{u\left({\mathop {\min \,Y_i}\limits_{l \le i \le n}} \right)} \right] $\end{document} for all increasing and concave u. This generalizes a result of Kubat. When comparing two series systems with components of equal cost, one with lifetimes {Xⁱ} and the other with lifetimes {Yⁱ}, it is shown that a risk-averse decision-maker will prefer the HNBUE system. Similar results are obtained for parallel systems.     

A note on a paper by houston and huffman

This paper calls attention to an experimental design which enhances the efficiency of the technique described by B. F. Houston and R. A. Huffman [3]. This alternative design is a modification of the simplex lattice design developed by Scheffé [6] for the mixture problem. While not possessing the optimal statistical properties of the central composite design proposed in [3], such as minimum bias and minimum variance, this modified design is optimum with respect to the number of design points employed; hence, it is the minimum cost design. Further, the design proposed in this note is excellent for use in multiple-block experimentation, which is very often required with constrained systems.     

An optimum t-test for the scale parameter of an extreme-value distribution

A Student's t-test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H₁: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.     

Optimal location of public facilities

Location of both public and private facilities has become an important consideration in today's society. Progress in solution of location problems has been impeded by difficulty of the fixed charge problem and the lack of an efficient algorithm for large problems. In this paper a method is developed for solving large-scale public location problems. An implicit enumeration scheme with an imbedded transportation algorithm forms the basis of the solution technique.     

On the theory of semi-infinite programming and a generalization of the kuhn-tucker saddle point theorem for arbitrary convex functions

We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations. We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.     

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.     

A solution for queues with instantaneous jockeying and other customer selection rules

This paper presents a general solution for the M/M/r queue with instantaneous jockeying and r > 1 servers. The solution is obtained in matrices in closed form without recourse to the generating function arguments usually used. The solution requires the inversion of two (Z^r?1) × (2^r?1) matrices. The method proposed is extended to allow different queue selection preferences of arriving customers, balking of arrivals, jockeying preference rules, and queue dependent selection along with jockeying. To illustrate the results, a problem previously published is studied to show how known results are obtained from the proposed general solution.     

Minimum-cost flows in convex-cost networks

An algorithm is given for solving minimum-cost flow problems where the shipping cost over an arc is a convex function of the number of units shipped along that arc. This provides a unified way of looking at many seemingly unrelated problems in different areas. In particular, it is shown how problems associated with electrical networks, with increasing the capacity of a network under a fixed budget, with Laplace equations, and with the Max-Flow Min-Cut Theorem may all be formulated into minimum-cost flow problems in convex-cost networks.