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1986 Applied Stochastic Models and Data Analysis
This paper compares three different linear procedures for classification: the normal one, the canonical one and a distribution‐free one recently described by Heuchenne. The study is mainly conducted using a simulation which makes it possible to compute the probabilities of correct allocation of the three methods in 3888 different cases. The normal rule looks slightly better than Heuchenne's, which looks clearly better than the canonical one. Finally, inference on Heuchenne's method is examined and conditions under which this method is optimal are given.
Atkinson, S. E.; Crocker, T. D.; Williams, D. H.
1986 Applied Stochastic Models and Data Analysis
Recently, Pirkle et al. used a sample of 40–59 year old white males from the second cycle of the U.S. National Health and Nutrition Survey (NHANES II) to estimate the association between blood pressure and blood lead concentration. They found that, on average, a 1 μg/dl increase in blood lead increased diastolic blood pressure by about 4.5 per cent and systolic blood pressure by about 6.5 per cent. We use Bayesian diagnostics to enquire into the statistical robustness of some dimensions of their results. In particular, we ask whether the results they report are sensitive to specification uncertainty and are intolerant to measurement error. We conclude the possibility to be remote that the introduction or the omission of other covariates will significantly alter the estimated influence of blood lead upon either the diastolic blood pressures or the systolic blood pressures of the adult white males in their sample. Similarly, our analysis demonstrates that other covariates are likely to affect the estimated influence of blood lead concentration only if they are quite poorly measured.
1986 Applied Stochastic Models and Data Analysis
In this paper we obtain identities for some stopped Markov chains. These identities give a unified approach to many problems in optimal stopping of a Markovian sequence, extinction probability of a Markovian branching process and martingale theory.
1986 Applied Stochastic Models and Data Analysis
The aim of this paper is to add results to the everlasting attempt to find appropriate models for the description and analysis of choice behaviour. As stochastic generalizations within choice models which allow estimation and testing in a straightforward way should be of great interest, probabilistic ideal point and vector approaches are used to handle inter‐ and intra‐individual irregularities in paired comparisons preference data. For choice behaviour analysis maximum likelihood estimates of the model parameters are computed and possibilities of testing various model variants by means of log‐likelihood ratio tests are discussed. The proposed models offer information to decide whether an ideal point or a vector approach is more appropriate for the description of the pairwise choice data. Examples of data sets known from previous research in choice behaviour are used for the comparison and for the demonstration of the merits of the proposed procedures.
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