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This thesis explores the association between a response variable and various regressors in dairy cattle breeding data using the various survival models in general and the partially linear single index survival model (PLSISM) in particular. In this study calf survival data and culling data were used. The calf survival data contains the following information: survival time, birth weight, weaning weight, calving ease score, average daily gain, number of disease incidences and serum total protein content. The culling data include, survival time, herd size variation, production level (milk, fat and protein), type of supervision, body condition score and age at first calving. Both data sets contain herd, year and season of calving and were analyzed using the various survival models. The Weibull model, however, was used for detailed analyses of the data sets. The nonparametric vector of PLSISM includes body weight, total serum protein and average daily gain for calf survival data and age at first calving, fat production and body condition core for culling data. The parametric vector of PLSISM consists of the rest of the covariates. The results show that the estimates of the parametric component are similar in the two models (Weibull and PLSISM). However, the estimates of the nonparametric component differ from parametric analysis. This difference may be attributed largely to the nonlinearity of the estimated function indicating the standard linear survival model does not adequately describe the underlying association between the response variable and the various covariates in this study. This is the first implementation and application of this complex model, PLSISM, with large real censored data.

This thesis examines a series of problems with the goal of better understanding the fundamental dilemma of whether to invest effort in obtaining information that may lead to better opportunities in the future versus exploiting immediately available opportunities. In particular this work investigates how this dilemma is affected by competition in an evolutionary setting. To achieve this requires both the use of evolutionary game theory, and Markov decision procesess or stochastic dynamic programming. This thesis grows directly out of earlier work on the Social Learning Strategies Tournament. Although I cast the problem in the biological setting of optimal foraging theory, where it fills an obvious gap, this fundamental dilemma should also be of some interest to economists, operations researchers, as well as those working in ecology, evolution and behaviour. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-01-31 19:55:25.11

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Thesis (Ph.D.)--Syracuse University, 2008. / "Publication number: AAT 3323082."

Thesis (M.S.)--University of Michigan, 1959.

This dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved that for any finite poset P, the dimension of P is at most half of the number of points in P. We develop some new inequalities for the dimension of finite posets. These inequalities are then used to bound dimension in terms of the maximum size of matchings. We prove that if the dimension of P is d and d is at least 3, then there is a matching of size d in the comparability graph of P, and a matching of size d in the incomparability graph of P. The bounds in above theorems are best possible, and either result has Hiraguchi's theorem as an immediate corollary. In the second component, we focus on an extremal graph theory problem whose solution relied on the construction of a special kind of posets. In 1959, Paul Erdos, in a landmark paper, proved the existence of graphs with arbitrarily large girth and arbitrarily large chromatic number using probabilistic method. In a 1991 paper of Kriz and Nesetril, they introduced a new graph parameter eye(G). They show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most three. Answering a question of Kriz and Nesetril, we were able to strengthen their results and show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most two. The last component is about random posets--the poset version of the Erdos-Renyi random graphs. In 1991, Erdos, Kierstead and Trotter (EKT) investigated random height 2 posets and obtained several upper and lower bounds on the dimension of the random posets. Motivated by some extremal problems involving conditions which force a poset to contain a large standard example, we were compelled to revisit this subject. Our sharpened analysis allows us to conclude that as p approaches 1, the expected value of dimension first increases and then decreases, a subtlety not identified in EKT. Along the way, we establish connections with classical topics in analysis as well as with latin rectangles. Also, using structural insights drawn from this research, we are able to make progress on the motivating extremal problem with an application of the asymmetric form of the Lovasz Local Lemma.