This dissertation concerns the use of logistic regression when certain standard model assumptions are violated. Chapters I and II study the problem of estimating regression parameters when covariates are subject to measurement error. The latter chapters study robust methods applicable to logistic regression. To facilitate study of the errors-in-variables problem a small measurement error asymptotic theory is developed. This allows comparison of certain estimators which have appeared in the literature and also suggests new estimators which are shown to have better asymptotic properties. A small Monte-Carlo study confirms the superiority of the new estimators in certain settings. In the course of studying the asymptotic behavior of the various estimators interesting use is made of some random convex analysis. To deal with the problem of messy data, i.e. outliers and extreme covariables, several bounded influence estimators are proposed. The optimality properties of these estimators are studied in Chapter III. Asymptotic theory for the robust procedures is given in Chapter IV. Finally, Chapter V concludes the thesis with an application of these methods to two sets of data.

The application of artificial neural networks (ANNs) for prognostic and diagnostic classification in clinical medicine has become very popular. Some indications might be derived from a recent "mini-series" in the Lancet 7,23,30,94 with three more or less enthusiastic review articles and an additional commentary expressing at least some scepticism. In this paper, the essentials of feed-forward neural networks and their statistical counterparts (e.g. logistic regression models) are reviewed. We point to serious problems of ANNs as the fitting of implausible functions to describe the probability of class membership and the underestimation of misclassification probabilities. In applications of ANNs to survival data many suggested procedures result in predicted survival probabilities which are not necessarily monotone functions of time and lack a proper incorporation of censored observations. Finally, the results of a search in the medical literature from 1991 to 1995 on applications of A...

regression

The blood beryllium lymphocyte proliferation test (BeLPT) is a modification of the standard lymphocyte proliferation test that is used to identify persons who may have chronic beryllium disease. A major problem in the interpretation of BeLPT test results is outlying data values among the replicate well counts ( ß 7%). A log-linear regression model is used to describe the expected well counts for each set of Be exposure conditions, and the variance of the well counts is proportional to the square of the expected count. Two outlier resistant regression methods are used to estimate stimulation indices (SIs) and the coefficient of variation. The first approach uses least absolute values (LAV) on the log of the well counts as a method for estimation; the second approach uses a resistant regression version of maximum quasi-likelihood estimation. A major advantage of these resistant methods is that they make it unnecessary to identify and delete outliers. These two new methods for the statist...

Logistic regression models have been used in political science for estimating ideal points of legislators and Supreme Court justices. These models present estimation and identifiability challenges, such as improper variance estimates, scale and translation invariance, reflection invariance, and issues with outliers. We address these issues using Bayesian hierarchical modeling, linear transformations, informative regression predictors, and explicit modeling for outliers. In addition, we explore new ways to usefully display inferences and check model fit. 1

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supported by the National Science Foundation. The work of Carroll has been supported by the Air Force Office of Scientific Research. The authors wish to thank two referees for their helpful and thought provoking comments which improved the clarity of presentation. Iu this paper we study robust estimation in general models for the dependence of a response y on an explanatory vector z. We extend previous work on bounded influence estimators in linear regression. Second we construct optimal bounded influence estimators for generalized linear models. We consider the class ofestimators defined by an estimating equation with a conditionally unbiased score flwction given the desgin. The resulting estimators are said to be conditionally Fisherconsistent. Ordinary least squares in linear regression has this property as does the Mallows type bounde.d influence estimator. The Schweppe class does not have a conditionally unbiased score function if the errors are asymmetric. For generalized linear models, the optimal conditionally Fisher-consistent estimators are computationally simpler than the unconditional ones proposed by Stefanski, Carroll and Ruppert (1986) because the centering constant can be given in explicit form. The optimal score function contains an unknown auxiliary nuisance matrix B. In contrast to the

In a non–life insurance business an insurer often needs to build up a reserve to able to meet his or her future obligations arising from incurred but not reported completely claims. To forecast these claims reserves, a simple but generally accepted algorithm is the classical chain-ladder method. Recent research essentially focused on the underlying model for the claims reserves to come to appropriate bounds for the estimates of future claims reserves. Our research concentrates on scenarios with outlying data. On closer examination it is demonstrated that the forecasts for future claims reserves are very dependent on outlying observations. The paper focuses on two approaches to robustify the chain-ladder method: the first method detects and adjusts the outlying values, whereas the second method is based on a robust generalized linear model technique. In this way insurers will be able to find a reserve that is similar to the reserve they would have found if the data contained no outliers. Because the robust method flags the outliers, it is possible to examine these observations for further examination. For obtaining the corresponding standard errors the bootstrapping technique is applied. The robust chain-ladder method is applied to several run-off triangles with and without outliers, showing its excellent performance.

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