High-order extensions of the Double Chain Markov Model

The Double Chain Markov Model is a fully Markovian model for the representation of time-series in random environments. In this article, we show that it can handle transitions of high-order between both a set of observations and a set of hidden states. In order to reduce the number of parameters, each transition matrix can be replaced by a Mixture Transition Distribution model. We provide a complete derivation of the algorithms needed to compute the model. Three applications, the analysis of a sequence of DNA, the song of the wood pewee, and the behavior of young monkeys show that this model is of great interest for the representation of data that can be decomposed into a finite set of patterns.     

Approximating M/G/1 Waiting Time Tail Probabilities

Abstract

We propose a new approximation formula for the waiting time tail probability of the M/G/1 queue with FIFO discipline and unlimited waiting space. The aim is to address the difficulty of obtaining good estimates when the tail probability has non-exponential asymptotics. We show that the waiting time tail probability can be expressed in terms of the waiting time tail probability of a notional M/G/1 queue with truncated service time distribution plus the tail probability of an extreme order statistic. The Cramér–Lundberg approximation is applied to approximate the tail probability of the notional queue. In essence, our technique extends the applicability of the Cramér–Lundberg approximation to cases where the standard Lundberg condition does not hold. We propose a simple moment-based technique for estimating the parameters of the approximation; numerical results demonstrate that our approximation can yield very good estimates over the whole range of the argument.     

On the sample breakdown robustness of some nonparametric tests

In this paper, relying on the sample breakdown points, we investigate the sample breakdown properties of some nonparametric tests. It is shown that the sample breakdown points of the sign test asymptotically dominate those of the Wilcoxon test for one–sided hypotheses, However, the different conclusion is derived in the case of testing some shrinking neighborhood hypotheses. The breakdown behaviors of the Kolmogorov test and X²–test are also explored. These studies unify or refine some existing breakdown analyses of tests.     

Non–zero inflated modified power series distributions

In this paper, we study the class of inflated modified power series distributions (IMPSD) where inflation occurs at any of the support points. This class include among other the generalized Poisson, the generalized negative binomial, the generalized logarithmic series and the lost games distributions. We give expressions for the moments, factorial moments and central moments of the IMPSD. The maximum likelihood estimation of the parameters of the IMPSD and the variance – covariance matrix of the estimators is obtained. We derive these estimators and their information matrices for mentioned above particular members of IMPSD class. The second part of this paper deals with the distribution of sum of independent and identically distributed random variables taking values s, s+1. s + 2, …, s ≥ 0, with modified power series distributions inflated at the point s.     

Reverse Regression and Employment Discrimination

The importance of interval forecasts is reviewed. Several general approaches to calculating such forecasts are described and compared. They include the use of theoretical formulas based on a fitted probability model (with or without a correction for parameter uncertainty), various “approximate” formulas (which should be avoided), and empirically based, simulation, and resampling procedures. The latter are useful when theoretical formulas are not available or there are doubts about some model assumptions. The distinction between a forecasting method and a forecasting model is expounded. For large groups of series, a forecasting method may be chosen in a fairly ad hoc way. With appropriate checks, it may be possible to base interval forecasts on the model for which the method is optimal. It is certainly unsound to use a model for which the method is not optimal, but, strangely, this is sometimes done. Some general comments are made as to why prediction intervals tend to be too narrow in practice to encompass the required proportion of future observations. An example demonstrates the overriding importance of careful model specification. In particular, when data are “nearly nonstationary,” the difference between fitting a stationary and a nonstationary model is critical.     

Primal and Dual Capacity Utilization: An Application to Productivity Measurement in the U.S. Automobile Industry

Capacity utilization measures have traditionally been constructed as indexes of actual, as compared to “potential,” output. This potential or capacity output (Y*) can be represented within an economic model of the firm as the tangency between the short- and long-run average cost curves. Economic theoretical measures of capacity utilization (CU) can then be characterized as Y/Y* where Y is the realized level of output. These quantity or primal CU measures allow for economic interpretation; they provide explicit inference as to how changes in exogenous variables affect CU. Additional information for analyzing deviations from capacity production can be obtained by assessing the “dual” cost of the gap.

In this article the definitions and representations of primal-output and dual-cost CU measures are formalized within a dynamic model of a monopolistic firm. As an illustration of this approach to characterizing CU measures, a model is estimated for the U.S. automobile industry, 1959–1980, and primal and dual CU indexes are constructed. Application of these indexes to adjustment-of-productivity measures for “disequilibrium” is then carried out, using the dual-cost measure.     

The Effects of Detrending in Granger Causality Tests

Nonstationary time series are frequently detrended in empirical investigations by regressing the series on time or a function of time. The effects of the detrending on the tests for causal relationships in the sense of Granger are investigated using quarterly U.S. data. The causal relationships between nominal or real GNP and M1, inferred from the Granger–Sims tests, are shown to depend very much on, among other factors, whether or not series are detrended. Detrending tends to remove or weaken causal relationships, and conversely, failure to detrend tends to introduce or enhance causal relationships. The study suggests that we need a more robust test or a better definition of causality.     

Comment: The Future of Administrative Records in the Economic Programs of the Census Bureau

Using recently developed statistical tools for analyzing cointegrated 1(2) data, this article models money, income, prices, and interest rates in Denmark. The final model describes the dynamic adjustment to short-run changes of the process, to deviations from long-run steady states, and to several political interventions. It provides new insights about the effects of the liberalization of trade and capital in a small open European economy.     

Covariate classification by post–stratification

The plug–in Anderson's covariate classification statistic is constructed on the basis of an initially unclassified training sample by means of posty–stratification. The asymptotic efficiency relative to the discriminant based on an initially classified training sample is evaluated for the case where a covariate is present. Effect of post–stratification is examined.     

Cross-Validated Assessments of Test Scoring Models

On a multiple choice test in which each item has r alternative options, a given number c of which are correct, various scoring models have been proposed. In one case the test-taker is allowed to choose any size solution subset and he/she is graded according to whether the subset is small and according to how many correct answers the subset contains. In a second case the test-taker is allowed to select only solution subsets of a prespecified maximum size and is graded as above. The first case is analogous to the situation where the test-taker is given a set of r options with each question; each question calls for a solution which consists of selecting that subset of the r responses which he/she believes to be correct. In the second case, when the prespecified solution subset is restricted to be of size at most one, the resulting scoring model corresponds to the usual model, referred to below as standard. The number c of correct options per item is usually known to the test-taker in this case.

Scoring models are evaluated according to how well they correctly identify the total scores of the individuals in the class of test-takers. Loss functions are constructed which penalize scoring models resulting in student scores which are not associated with the students true (or average) total score on the exam. Scoring models are compared on the basis of cross-validated assessments of the loss incurred by using each of the given models. It is shown that in many cases the assessment of the loss for scoring models which allow students the opportunity to choose more than one option for each question are smaller than the assessment of the loss for the standard scoring model.