TIME-VARYING PARAMETER ESTIMATION AS EXPLORATION*

A sequential time-variation method is utilized in an attempt to detect changes over time in the effectiveness of market communication for an ethical drug. Sudden changes are indicated at three different points in time, and two of these are confirmed by subsequent analysis and information. Gradual changes are also indicated, but these are not confirmed by market information or statistical analysis.     

Estimating the Geographic Extent of Part-Time Labor Markets: U.S. Army Reserves*

Local labor market supportability is becoming an increasingly important issue for the United States Army Reserves. As military bases close and Reserve units are consolidated at fewer Reserve centers, the appropriate reassignments of units to Reserve centers require accurate measures of the ability of local labor markets to support such consolidations. A two-stage random effect model is applied to evaluate the geographical extent of the labor market for Army Reserve centers. In the first stage model, a lognormal distribution is used to describe the commuting distance behavior of the Reserve center members. In the second stage model, we estimate the mean of log transformed commute distance as a function of regional characteristics of the Reserve center. An iterative weighted stepwise selection method is used to find a set of characteristics that adequately predict variation of the mean commute distance over Reserve centers. The resulting model is used as inputs to location and market assessment models to assist the marketing decisions of the Army Recruiting Command.     

Minimizing Misclassifications in Linear Discriminant Analysis*

A procedure is developed for determining two-group linear discriminant classifiers that misclassify the fewest number of observations in the training sample. An experimental study confirms the value of this approach.     

Concepts,Theory, and Techniques ON THE USE OF THE GEOMETRIC MEAN IN LONG-TERM INVESTMENT

Application of the geometric mean to holding-period returns is discussed from a statistical theory standpoint. The population geometric mean is considered a parameter of the probability distribution of returns its relationship to moments of the distribution is discussed. The sample geometric mean and its relation to sample moments is assessed through its sampling distribution it is viewed as an estimator of the population geometric mean. For application to long-term investment where a geometric mean is maximized, the distributional properties of the geometric mean should be used. The terms statistic, approximation, and parameter are differentiated.     

Neural Networks: A New Tool for Predicting Thrift Failures*

A neural network model that processes input data consisting of financial ratios is developed to predict the financial health of thrift institutions. The network's ability to discriminate between healthy and failed institutions is compared to a traditional statistical model. The differences and similarities in the two modelling approaches are discussed. The neural network, which uses the same financial data, requires fewer assumptions, achieves a higher degree of prediction accuracy, and is more robust.     

Note on Second-Order Polynomial Regression Models

Polynomial regression models have applications in the social sciences and in business research. Unfortunately, such models have a high degree of multicollinearity that creates problems with the statistical assessment of the model. In fact, the collinearity may be so severe that it could lead to an incorrect conclusion that some of the terms in the model are not statistically significant and should therefore be omitted from the model. This note provides a simple transformation to achieve orthogonality in polynomial models between the linear and quadratic terms, thereby eliminating the collinearity problem. It also shows that the same procedure does not achieve orthogonality for higher-order terms. An example data set is analyzed to show the benefits of such a procedure.     

Predicting the Winner's Curse

If quantity uncertainty exists in a first price auction that specifies a fixed bid, a participant must answer two questions when evaluating a candidate bid: “What are my chances of winning?” and “What is the effect of the winner's curse on my quantity estimate?” The winner's curse is the tendency of the winner of a first-price sealed-bid auction to be the bidder that most overvalues the items being offered. When value uncertainty is due to quantity uncertainty, the winner's curse implies that the bidder that most overestimates the quantity tends to win. Thus, if there is quantity uncertainty, a participant must adjust its bid for this tendency to overestimate quantities. This paper presents an empirical method to answer the above questions by estimating a predictive distribution of the highest competing bid and the quantity bias caused by the winner's curse. The method is developed for timber auctions but is general to auctions where a fixed bid is called for and there is uncertainty in the mix and quantities of items being offered. An example that uses data from timber auctions is used to demonstrate the method.     

MULTIVARIATE NORMALITY AND A BOND RATING DECISION MODEL*

An assumption of multivariate normality for a decision model is validated in this paper. Measurements for the independent variables of a bond rating model were taken from a sample of municipal bonds. Three methods for examining both univariate and multivariate normality (including normal probability plots) are described and applied to the bond data. The results imply, after applying normalizing transformations to four of the variables, that the data reasonably approximate multivariate normality, thereby validating a distributional requirement of the discriminant-analysis-based decision model. The methods described in the paper may also be used by others interested in examining multivariate normality assumptions of decision models.     

Multiple Attribute Decision Making with Inexact Value-Function Assessment

A major issue in value-function assessment is the possibility of receiving an indefinite response from a decision maker to a question about preferences. The conventional treatment requires a single, definite response from the decision maker. This approach either assumes that response error is zero or accepts the final solution as only approximate, without knowing how approximate it might be. In this paper we examine the issue of indefinite responses, define it more precisely, and present a method for incorporating it into decision making. The method is adaptive in that it is iterative and interactive with the decision maker who, at each iteration, is provided with information regarding the potential advantage of answering more trade-off questions and/or answering questions more carefully to reduce response error. In contrast to other approaches that “force” rationality and decisiveness, we work with irrationality and indecisiveness on the part of the decision maker. The method is demonstrated for the case of concave, increasing value functions.     

Notes and Communications RESOLVING CERTAIN DIFFICULTIES AND IMPROVING THE CLASSIFICATION POWER OF LP DISCRIMINANT ANALYSIS FORMULATIONS

In certain settings, difficulties arise that limit the effectiveness of LP formulations for the discriminant problem. Explanations and possible remedies have been offered, but these have had only limited success. We provide a simple way to overcome these problems based on an appropriate use and interpretation of normalizations. In addition, we demonstrate a normalization that is invariant under all translations of the problem data, providing a stability property not shared by previous approaches. Finally, we discuss the possibility of using more general models to improve discrimination.