Design optimality plays a central role in the area of statistical experimental design. In general, problems in design optimality are composed of two vital, but separable, components. One of these is determining conditions under which a design is optimal (such as criterion bounds, values of design parameters, or special structure in the information matrix). The other is construction of designs satisfying those conditions. Most papers deal with either optimality conditions, or design construction in accordance with desired combinatorial properties, but not both. This dissertation determines optimal designs for three treatments in the one-way and multi-way heterogeneity settings, first proving optimality through a series of bounding arguments, then applying combinatorial techniques for their construction. Among the results established are optimality with respect to the well known E and A criteria. A- and E-optimal block designs and row-column designs with three treatments are found, for any parameter set. E-optimal hyperrectangles with three treatments are also found, for any parameter set. Systems of distinct representatives theory is used for the construction of optimal designs. Efficiencies relative to optimal criterion values are used to determine robustness of block designs against loss of a small number of blocks. Nonisomorphic bal anced incomplete block designs are ranked based on their robustness. A complete list of most robust BIBDs for v ≤ 10, r ≤ 15 is compiled. / Ph. D.

This paper, a review of the literature on word order typology, examines in detail a body of work (Comrie 1989; Comrie, Dryer, Gil, Haspelmath 2005; Dryer 1988, 1991, 1992, 2007; Greenberg 1966; Hawkins 1983; Lehmann 1973; Vennemann 1974) that made a major contribution to linguistics by introducing the subfield of typology and the study of word order across the world’s languages from a typological perspective. Greenberg’s (1966) seminal paper advanced an understanding of cross-linguistic tendencies that had been unknown at the time and which are still being investigated today, especially his three-way typology based on the relative position of V with respect to S and O. Lehmann (1973) and Vennemann (1974) pushed the VO/OV distinction which led to a reanalysis and diminishing of the role of S as an organizing parameter. Two theories, Vennemann’s Head-Dependent Theory and Hawkins’ Cross-Category Harmony, account for many attested correlation pairs, but neither is as strong as Dryer’s Branching Direction Theory in terms of explanatory adequacy, elegance, and adherence to observed cross-linguistic tendencies. As far as theoretical approaches, we note that generative grammar with its focus on single-language study cannot provide an account of the variations in the world’s languages, while the typological approach comes closer to describing universals of language based on empirical data. Finally, I present the idea that investigations of word order from a typological perspective can be successfully undertaken using a functionalist approach within the framework of Optimality Theory. / text

Optimal strategies under worst-case scenarios have been studied in Bernard et al. [2013a]. Bernard et al. utilize copulas to construct cost-efficient strategies with a predefined dependence structure in the tail between the payoff and the market. In their study they show that such strategies with state-dependent copula constraints dominate traditional diversification strategies in terms of the provided protection in the states of market downturns. We derive similar strategies, however using correlation constraints instead of copula constraints in the tail. We found that for an investor seeking negative dependence with the market, it is cheaper to construct a strategy with conditional correlation constraint in the tail. However, the constructed strategies with conditional correlation constraints do not provide sufficient protection in bad states of the economy. Therefore, when analyzing a strategy, negative correlation with the market in the tail is not a sufficient indicator for the protection level in the event of a market crisis.

Thesis (Ph.D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [163]-171).

Optimal design problems aim at selecting design points optimally with respect to certain statistical criteria. The research of this thesis focuses on optimal design problems with respect to A-, D- and E-optimal criteria, which minimize the trace, determinant and largest eigenvalue of the information matrix, respectively. Semide nite programming (SDP) is concerned with optimizing a linear objective function subject to a linear matrix being positive semide nite. Two powerful MATLAB add-ons, SeDuMi and CVX, have been developed to solve SDP problems e ciently. In this paper, we show in detail how to formulate A- and E-optimal design problems as SDP problems and solve them by SeDuMi and CVX. This technique can be used to construct approximate A-optimal and E-optimal designs for all linear and non-linear models with discrete design spaces. The results can also provide guidance to nd optimal designs on continuous design spaces. For one variable polynomial regression models, we solve the A- and E- optimal designs on the continuous design space by using a two-stage procedure. In the rst stage we nd the optimal moments by casting it as an SDP problem and in the second stage we extract the optimal designs from the optimal moments obtained from the rst stage. Unlike E- and A-optimal design problems, the objective function of D-optimal design problem is nonlinear. So D-optimal design problems cannot be reformulated as an SDP. However, it can be cast as a convex problem and solved by an interior point method. In this thesis we give details on how to use the interior point method to solve D-optimal design problems. Finally several numerical examples for A-, D-, and E-optimal designs along with the MATLAB codes are presented. / Graduate

This thesis focuses on the construction of optimum designs for the estimation of the variance components in multistage variability models. Variance components are the model parameters that represent the different sources of variability that affect the response of a system. A general and highly detailed way to define the linear mixed effects model is proposed. The extension considers the explicit definition of all the elements needed to construct a model. One key aspect of this formulation is that the random part is stated as a functional that individually determines the form of the design matrices for each random regressor, which gives significant flexibility. Further, the model is strictly divided into the treatment structure and the variability structure. This allows separate definitions of each structure but using the single rationale of combining, with little restrictions, simple design arrangements called factor layouts. To provide flexibility for considering different models, methodology to find and select optimum designs for variance components is presented using MLE and REML estimators and an alternative method known as the dispersion-mean model. Different forms of information matrices for variance components were obtained. This was mainly done for the cases when the information matrix is a function of the ratios of variances. Closed form expressions for balanced designs for random models with 3-stage variability structure, in crossed and nested layouts were found. The nested case was obtained when the information matrix is a function of the variance components. A general expression for the information matrix for the ratios using REML is presented. An approach to using unbalanced models, which requires the use of general formulae, is discussed. Additionally, D-optimality and A-optimality criteria of design optimality are restated for the case of variance components, and a specific version of pseudo-Bayesian criteria is introduced. Algorithms to construct optimum designs for the variance components based on the aforementioned methodologies were defined. These algorithms have been implemented in the R language. The results are communicated using a simple, but highly informative, graphical approach not seen before in this context. The proposed plots convey enough details for the experimenter to make an informed decision about the design to use in practice. An industrial internship allowed some the results herein to be put into practice, although no new research outcomes originated. Nonetheless, this is evidence of the potential for applications. Equally valuable is the experience of providing statistical advice and reporting conclusions to a non statistical audience.

Design optimality for treatment comparison experiments has been intensively studied by numerous researchers, employing a variety of statistically sound criteria. Their general formulation is based on the idea that optimality functions of the treatment information matrix are invariant to treatment permutation. This implies equal interest in all treatments. In practice, however, there are many experiments where not all treatments are equally important. When selecting a design for such an experiment, it would be better to weight the information gathered on different treatments according to their relative importance and/or interest. This dissertation develops a general theory of weighted design optimality, with special attention to the block design problem. Among others, this study develops and justifies weighted versions of the popular A, E and MV optimality criteria. These are based on the weighted information matrix, also introduced here. Sufficient conditions are derived for block designs to be weighted A, E and MV-optimal for situations where treatments fall into two groups according to two distinct levels of interest, these being important special cases of the "2-weight optimality" problem. Particularly, optimal designs are developed for experiments where one of the treatments is a control. The concept of efficiency balance is also studied in this dissertation. One view of efficiency balance and its generalizations is that unequal treatment replications are chosen to reflect unequal treatment interest. It is revealed that efficiency balance is closely related to the weighted-E approach to design selection. Functions of the canonical efficiency factors may be interpreted as weighted optimality criteria for comparison of designs with the same replication numbers. / Ph. D.

Assimilation and coarticulation both involve extending the duration of some property or feature. The similarities between these phenomena can be seen by comparing Basque vowel raising with vowel -to -vowel coarticulation in a language like English. In Basque the low vowel /a/ is raised to [el following a high vowel. This gives rise to alternations in the form of the definite suffix, /-a/ (de Rijk 1970): (1) sagar –a; 'apple (def.)'; mutil-e 'boy (def.)'. In an English sequence containing a low vowel preceded by a high vowel, like [-ilæ-] in 'relapse', the high vowel also conditions raising of the low vowel. But in spite of the parallels between these cases, standard analyses regard Basque vowel raising as phonological whereas the English vowel raising is regarded as non-phonological, being attributed to a phonetic process of coarticulation. In this paper, we will argue that this distinction is untenable. We will see that coarticulation can affect the distribution of contrasts, and therefore must be specified in the phonology. This opens up the possibility of giving a unified analysis of assimilation and coarticulation. Analyzing coarticulation as phonological implies that phonological representations contain far more phonetic detail than is usually assumed to be the case. Vowel-to-vowel coarticulation involves fine degrees of partial assimilation in that vowels assimilate only partially in quality, and the effects may extend through only part of the duration of a segment (e.g. Ohman 1966). This conclusion thus flies in the face of the standard assumption that the richness of phonological representations should be severely restricted in order to avoid over-predicting the range of possible phonological contrasts. So before we turn to evidence that coarticulation is phonological, we will lay the groundwork by examining the arguments for limiting the detail in phonological representations and show that they are based on very questionable assumptions.

This paper presents an analysis of vowel harmony in Yawelmani and its interaction with vowel epenthesis and lowering, within the non -derivational, constraint -based model of Optimal Domains Theory (ODT). Kisseberth's (1969) analysis of the Yawelmani system, formulated within classical generative phonology, demonstrates an opaque rule interaction among the rules governing vocalic phonology, and was taken as an important piece of evidence for the notion of rule ordering in generative theory. The challenge in providing a non -derivational analysis of Yawelmani lies in accounting for conditions on vowel harmony which factor in phonological structure that is "inserted" in surface form, as well as structure that is "deleted" from underlying form. This paper presents a restricted means of bringing together information from underlying and surface representations in a theoretical framework that eschews intermediate representations, through the use of abstract (ie., unrealized) feature-domain structure. We discuss problems that arise under an alternative approach in which individual constraints are able to freely inspect structure at both underlying and surface levels of representation.

The neutralization of the laryngeal features of a consonant that is not directly followed by a vowel is a common process cross -linguistically. Laryngeal neutralization in this position has a clear phonetic cause: laryngeal features are not salient unless they are immediately followed by a vowel. Since laryngeal neutralization has a phonetic cause, it seems reasonable to characterize it directly in phonetic terms, without positing any additional layer of phonological abstraction. However, a phonetic explanation is not sufficient to account for all cases of laryngeal neutralization. For example, in Korean, laryngeal neutralization occurs in a nonneutralizing phonetic environment; in Nisgha, laryngeal neutralization occurs only in the reduplicant, although the phonetic environment for neutralization is found in both the reduplicant and the base. Although phonetics is the major factor leading to the development of these types of restrictions on laryngeal features, I argue that a phonetic account is not adequate for all such restrictions. Abstract phonological constraints and representations are necessary. Hence, two types of neutralization are possible: (i) phonetic neutralization, which results directly from the lack of saliency of cues and occurs in every instance of the neutralizing environment; and (ii) abstract phonological neutralization, which may occur where the neutralizing environment is absent (as will be demonstrated for Korean), and may fail to occur in every instance of the neutralizing environment (as will be demonstrated for Nisgha).