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Philippa Foot’s account of natural normativity relies on functions. For Foot, having a function is what distinguishes those traits that can serve as the basis for the evaluation of an organism from those traits that cannot. For example, Foot asserts that a blue-headed tit that lacks the blue spot on its head is merely unusual but a peacock that lacks a brightly colored tail is defective because while the blue spot does not have a function, the brightly colored tail does. Problematically, it is not immediately clear just how Foot understands functions. I argue that Foot’s account of functions requires a distinction between functions and accidents. In Foot’s schema, functions appear similar to contributions to the achievement of ends: in the case of non-human organisms, functional traits contribute to survival and reproduction, while human beings are sui generis in that our ends are not exhausted by survival and reproduction. However, a trait’s contributing to these ends is not sufficient grounds for that trait to have a function. Only those traits that contribute in the right way count as having a functional role and can consequently serve as the basis for evaluations of the organism. Borrowing Reid Blackman’s example, a deer that evades predators through camouflage rather than swiftness is uncharacteristic and not naturally good in Foot’s schema. In such cases, the trait in question makes only an accidental contribution to an end. Furthermore, I argue that in order to maintain a function/accident distinction, Foot must understand functions in terms of kinds. These kinds entail three things for any organism that instantiates the kind: some work or end achieved by the organism, a characteristic story of how that work is achieved, and some sort of purposiveness to the characteristic achievement of that work. In the case of the deer above, its work is survival and reproduction, the story of how it achieves those ends includes eating leaves and avoiding predators through swiftness, and the achievement of survival and reproduction in this way is purposive because it answers to the capacity of living things to be a beneficiary. On one hand, my account of Foot’s natural goodness solves numerous problems in the interpretation of her work. It explains why natural goodness is unique to living things as opposed to entities that admit of similarly structured evaluations by looking at the purposiveness involved in these evaluations. Additionally, my interpretation counters the objection that Foot’s treatment of nature appears ignorant of pertinent empirical scientific evidence. In evaluating organisms as members of kinds, presumably an organism might belong to multiple kinds. Consequently, we can understand and evaluate an organism both as a member of a biological kind whose work is genetic promulgation and as a member of its neo-Aristotelian species whose work, at least in the case of non-human organisms, is survival and reproduction. Seen in this way, the relevant concern is not “how can Foot’s account of organisms avoid the charge of being scientifically uninformed?” but “why should the natural goodness of an organism be evaluated with respect to one kind instead of another?” Some neo-Aristotelians have endeavored to address this difficulty through the following commitments: that the neo-Aristotelian understanding of an organism is special because it is a self-interpretation, that these interpretations do not compete with one another, or that the natural sciences must presuppose a neo-Aristotelian understanding of species in order to have a notion of life. Rather than adopting any of these approaches, I contend that by understanding Foot through this three-part model we can understand the evaluation of an organism as a member of the neo-Aristotelian species as primary in a way that the biological account is not. On the other hand, my interpretation entails epistemological problems for Foot. We seem unable to distinguish accidental contributions to the work of an organism from functional contributions in a well-informed way, and the sui generis nature of human work makes it difficult to establish what counts as a contribution to its achievement. In light of these difficulties, the prospect of our having knowledge of the kinds on which her account depends seems dim. / Philosophy

The Empirical Likelihood method (ELM) was introduced by A. B. Owen to test hypotheses in the early 1990s. It's a nonparametric method and uses the data directly to do statistical tests and to compute confidence intervals/regions. Because of its distribution free property and generality, it has been studied extensively and employed widely in statistical topics. There are many classical test statistics such as the Cramer-von Mises (CM) test statistic, the Anderson-Darling test statistic, and the Watson test statistic, to name a few. However, none is universally most powerful. This thesis is dedicated to extending the ELM to several interesting statistical topics in hypothesis tests. First of all, we focus on testing the fit of distributions. Based on the CM test, we propose a novel Jackknife Empirical Likelihood test via estimating equations in testing the goodness-of-fit. The proposed new test allows one to add more relevant constraints so as to improve the power. Also, this idea can be generalized to other classical test statistics. Second, when aiming at testing the error distributions generated from a statistical model (e.g., the regression model), we introduce the Jackknife Empirical Likelihood idea to the regression model, and further compute the confidence regions with the merits of distribution free limiting chi-square property. Third, the ELM based on some weighted score equations are proposed for constructing confidence intervals for the coefficient in the simple bilinear model. The effectiveness of all presented methods are demonstrated by some extensive simulation studies.

A test for independence and identical distribution of functional observations is proposed in this thesis. To reduce dimension, curves are projected on the most important functional principal components. Then a test statistic based on lagged cross--covariances of the resulting vectors is constructed. We show that this dimension reduction step introduces asymptotically negligible terms, i.e. the projections behave asymptotically as iid vector--valued observations. A complete asymptotic theory based on correlations of random matrices, functional principal component expansions, and Hilbert space techniques is developed. The test statistic has chi-square asymptotic null distribution. Two inferential tests for error correlation in the functional linear model are put forward. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distributions are chi--squared with known numbers of degrees of freedom (different for the two forms). A test for detecting a change point in the mean of functional observations is developed. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution. A comprehensive asymptotic theory for the estimation of a change--point in the mean function of functional observations is developed. The procedures developed in this thesis can be readily computed using the R package fda. All theoretical insights obtained in this thesis are confirmed by simulations and illustrated by real life-data examples.

Exponential Random Graph Models (ERGMs) have been developed for fitting social network data on both static and dynamic levels. However, the lack of large sample asymptotic properties makes it inadequate in assessing the goodness-of-fit of these ERGMs. Simulation-based goodness-of-fit plots were proposed by Hunter et al (2006), comparing the structured statistics of observed network with those of corresponding simulated networks. In this research, we propose an improved approach to assess the goodness of fit of ERGMs. Our method is shown to improve the existing graphical techniques. We also propose a simulation based test statistic with which the model comparison can be easily achieved. / Biostatistics

The ability to regulate emotions is thought to influence the development of positive peer relations in early childhood. By effectively regulating fear and anger in peer settings, social interactions tend to unfold in a smooth and successful manner, leading children to become socially competent over time. Fear regulation, however, is especially difficult for children who were highly reactive and frequently expressed negative affect as infants. These children, often referred to as having an inhibited temperament, are likely to become distressed by novel stimuli and show a high degree of vigilance and anxious behaviors as toddlers. After toddlerhood, research has shown that some of these children handle novel, social situations in a competent manner, whereas others continue along the pathway of inhibition and become socially reticent. Socially reticent children often engage in hovering behavior and stay on the outskirts of the peer group, which can have negative consequences for the development of positive peer relations. One factor that influences inhibited toddlers to follow one pathway versus another seems to be whether they have learned to effectively regulate emotions. The acquisition of emotion regulation strategies is a complex process, but parents usually have the most proximal influence during early childhood. Therefore, in order to learn more about promoting socially competent behavior, it is important to understand how parents are socializing emotion regulation in toddlerhood. Using data from a larger longitudinal study, the current study examined how the socialization of emotion regulation at age three influenced social engagement at age four among behaviorally inhibited toddlers. It was hypothesized that sensitive maternal socialization of emotion regulation strategies would predict higher levels of engagement in future peer social interactions.

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

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In a meta-analysis of articles employing clustering methods, we find that little attention is paid to remaining within-cluster heterogeneity and that average values are relatively high. We suggest addressing this potentially problematic "dark side" of cluster analysis by providing two coefficients as standard information in any cluster analysis findings: a goodness-of-fit measure and a measure which relates explained variation of analysed empirical data to explained variation of simulated random data. The second coefficient is referred to as the Index of Clustering Appropriateness (ICA). Finally, we develop a classification scheme depicting acceptable levels of remaining within-cluster heterogeneity. (authors' abstract)