How non-normality affects the quadratic discriminant function

The quadratic discriminant function is commonly used for the two group classification problem when the covariance matrices in the two populations are substantially unequal. This procedure is optimal when both populations are multivariate normal with known means and covariance matrices. This study examined the robustness of the QDF to non-normality. Sampling experiments were conducted to estimate expected actual error rates for the QDF when sampling from a variety of non-normal distributions. Results indicated that the QDF was robust to non-normality except when the distributions were highly skewed, in which case relatively large deviations from optimal were observed. In all cases studied the average probabilities of misclassification were relatively stable while the individual population error rates exhibited considerable variability.     

Testing for exponentiality against monotone failure rate average alternatives

We propose a test for exponentiality against the class of non-exponential distributions having monotone failure rate averages. The test statistic, which is a U-statistic and hence asymptotically normally distributed, is much simpler than its competitors yet compares favorably with them in efficiency and power comparisons.     

A note on maximum Z-scores for control charts for individuals

Control chart limits are often constructed retrospectively based on a sequence of individual measurements. It is shown that the usual control chart limits cannot be crossed for small numbers of measurements.     

A Framework for Time Varying Parameter Regression Modeling

A framework for time varying parameter regression models is developed and employed in modeling and forecasting price expectations, using the Livingston data. Alternative model formulations, which include various choices for both the stochastic processes generating the varying parameters and the sets of explanatory variables, are examined and compared by using this framework. These models, some of which have appeared elsewhere and some of which are new, are estimated and used to assess the expectations formation process.     

The Relative Size of Windfall Income and the Permanent Income Hypothesis

A reconciliation is offered for the diverse test results on Friedman's permanent income hypothesis. A large data sample of those receiving windfall income in the Bureau of Labor Statistics' 1972–1973 Consumer Expenditure Survey is divided according to the size of the windfall relative to estimated permanent income. A pattern of a declining marginal propensity to consume windfall income as the relative size of the windfall increases is apparent. These results support the permanent income hypothesis for relatively large windfalls.     

Financial-Firm Production of Monetary Services: A Generalized Symmetric Baroett Variable-Profit-Function Approach

An alternative monetary-production model of financial firms is employed to investigate supply-side monetary aggregation. Financial firms are conceived to produce monetary services as outputs through financial intermediation. A new method for testing the existence of consistent monetary-output aggregates in financial firms' production technology is developed in terms of a multiproduct firm's variable profit function, and the method does not require homotheticity of the aggregator function. We use a generalized symmetric Barnett flexible functional form. That specification satisfies global curvature conditions and retains its flexibility under the null hypothesis of weak separability. Neither of those properties is possessed by other flexible functional forms.     

Beyond the CPI: An Augmented Cost-of-Living Index

This note examines an augmented cost-of-living index (ACOLI) for the purpose of accounting for “augmented consumption” in real-income measures. Well-being includes not only conventional consumer purchases but also goods and services provided by employers, by mandated social regulations, and by tax-financed public goods. Because augmented consumption is often provided in ways that raise prices but not market incomes, deflating with conventional price indexes may understate real income growth. An exploratory application of the ACOLI approach to the United States during the 1960–1997 period suggests that the Consumer Price Index has grown about 19% faster than the ACOLI. This correction would reduce the estimated cost-of-living increase by .47% per year over the last 37 years.     

Correlation in a Bayesian framework

The authors consider the correlation between two arbitrary functions of the data and a parameter when the parameter is regarded as a random variable with given prior distribution. They show how to compute such a correlation and use closed form expressions to assess the dependence between parameters and various classical or robust estimators thereof, as well as between p‐values and posterior probabilities of the null hypothesis in the one‐sided testing problem. Other applications involve the Dirichlet process and stationary Gaussian processes. Using this approach, the authors also derive a general nonparametric upper bound on Bayes risks.