When studying detection systems, parameters associated with the Receiver Operating Characteristic (ROC) curve are often estimated to assess system performance. In some applied settings it is often not possible to test the detection system with large numbers of stimuli. The resulting small sample statistics many have undesirable properties. The characteristics of these small sample ROC estimators were examined in a Monte Carlo simulation. Three popular ROC parameters were chosen for study. One of the parameters was a single parameter index of system performance, Area under the ROC curve. The other parameters, ROC intercept and slope, were considered as a pair. ROC intercept and slope were varied along with sample size and points on the certainty rating scale to form a four way factorial design. Several types of estimators were examined. For the parameter, Area under the curve, Maximum Likelihood (ML), three types of Least Squares (LS), and Distribution Free (DF) estimators were considered. Except for the DF estimator, the same estimators were considered for the parameters, intercept and slope. These estimators were compared with respect to three characteristics: bias, efficiency, and consistency. For Area under the curve, the ML estimator was the least biased. The DF estimator was the most efficient, and all the estimators except the DF estimator appeared to be consistent. For intercept and slope the LS estimator that minimized vertical error of the points from the ROC curve (line) was the least biased for both estimators. This LS estimator was also the most efficient. This estimator along with the ML estimator also appeared to be the most consistent. The other two estimators had no significant trend toward consistency. These results along with other findings, illustrate that different estimators may be "best" for different sample sizes and for different parameters. Therefore, researchers should carefully consider the characteristics of ROC estimators before using them as indices of system performance.

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published_or_final_version / Statistics / Master / Master of Philosophy

This thesis documents dental maturation in a mid C18, early C19 population where age at death is known (N=63, age range birth and 5.4 years). Emphasis is placed on the mineralization of individual deciduous and certain permanent teeth. In the first part of this thesis, the literature on dental maturation is reviewed with special reference to radiographic studies of populations, methodology and statistical analysis. Quantitative data on developing teeth, population differences and age estimation are also reviewed. In the second part of the thesis the Spitalfields material is described and used to investigate the accuracy of five types of age estimating methods that make use of the developing dentition. It emerges that the atlas method of Schour and Massler (1941) predicted age best. The third part of the thesis documents dental development in the Spitalfields Collection. New data for human deciduous anterior teeth and early stages of permanent anterior teeth are presented. In this study, few permanent anterior tooth crowns were complete before 5 years of age, contrary to published data from radiographic studies. Alveolar eruption of deciduous teeth and measurements of tooth length and weight are presented and discussed in context with published standards. The fourth part of this thesis is a preliminary investigation of cranial and postcranial development in this population. The fifth part is an appendix of data.

My dissertation includes three essays that examine or relax classical restrictive assumptions used in econometrics estimation methods. The first chapter proposes methods for examining how a response variable is influenced by a covariate. Rather than focusing on the conditional mean I consider a test of whether a covariate has an effect on the entire conditional distribution of the response variable given the covariate and other conditioning variables. This type of analysis is useful in situations where the econometrician or policy maker is interested in knowing whether a variable or policy would improve the distribution of the response outcomes in a stochastic dominance sense. The response variable is assumed to be continuous, while both discrete and continuous covariate cases are considered. I derive the asymptotic distribution of the test statistics and show that they have simple known asymptotic distributions under the null by using and extending conditional empirical process results given by Horvath and Yandell (1988). Monte Carlo experiments are conducted, and the tests are shown to have good small sample behavior. The tests are applied to a study on father's labor supply. The second chapter is based on previous joint work with Jason Abrevaya. It considers estimation of censored panel-data models with individual-specific slope heterogeneity. The slope heterogeneity may be random (random-slopes model) or related to covariates (correlated-random-slopes model). Maximum likelihood and censored least-absolute deviations estimators are proposed for both models. Specification tests are provided to test the slope-heterogeneity models against nested alternatives. The proposed estimators and tests are used for an empirical study of Dutch household portfolio choice. Strong evidence of correlated random slopes for the age variables is found, indicating that the age profile of portfolio adjustment varies significantly with other household characteristics. The third chapter proposes specification tests in models with endogenous covariates. In empirical studies, econometricians often have little information on the functional form of the structural model, regardless of whether covariates in model are exogenous or endogenous. In this chapter, I propose tests for restricted structural model specifications with endogenous covariates against the fully nonparametric alternative. The restricted model specifications include the nonparametric specification with a restricted set of covariates, the semiparametric single index specification and the parametric linear specification. Test statistics are “leave-one-out” type kernel U-statistic as used in Fan and Lee (1996). They are constructed using the idea of the control function approach. Monte Carlo results are provided and tests are shown to have reasonable small sample behavior. / text

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