In statistical inference one of the most important properties that an estimator of an unknown parameter can possess is the property of sufficiency. The use of sufficient statistics has been prescribed in the past and their use today plays an ever increasing role in modern statistical inference. Because of the utmost importance of sufficient statistics, it is the goal of this thesis to study the various aspects of sufficiency in connection with the estimation of parameters.This study utilizes a blend of a geometric and an analytic approach to sufficiency. This is done to show the power of each and to demonstrate how the two approaches complement each other and combine to give better insight into the concept of sufficiency.In this thesis the author also establishes some new and important results on sufficiency and minimal sufficiency. These results, taken as a whole, constitute a unified presentation of some of the most important aspects of sufficiency and non-sufficiency.

No description available.

No description available.

No description available.

No description available.

No description available.

This thesis addresses the technical and linguistic aspects of discourse-level processing in phrase-based statistical machine translation (SMT). Connected texts can have complex text-level linguistic dependencies across sentences that must be preserved in translation. However, the models and algorithms of SMT are pervaded by locality assumptions. In a standard SMT setup, no model has more complex dependencies than an n-gram model. The popular stack decoding algorithm exploits this fact to implement efficient search with a dynamic programming technique. This is a serious technical obstacle to discourse-level modelling in SMT. From a technical viewpoint, the main contribution of our work is the development of a document-level decoder based on stochastic local search that translates a complete document as a single unit. The decoder starts with an initial translation of the document, created randomly or by running a stack decoder, and refines it with a sequence of elementary operations. After each step, the current translation is scored by a set of feature models with access to the full document context and its translation. We demonstrate the viability of this decoding approach for different document-level models. From a linguistic viewpoint, we focus on the problem of translating pronominal anaphora. After investigating the properties and challenges of the pronoun translation task both theoretically and by studying corpus data, a neural network model for cross-lingual pronoun prediction is presented. This network jointly performs anaphora resolution and pronoun prediction and is trained on bilingual corpus data only, with no need for manual coreference annotations. The network is then integrated as a feature model in the document-level SMT decoder and tested in an English–French SMT system. We show that the pronoun prediction network model more adequately represents discourse-level dependencies for less frequent pronouns than a simpler maximum entropy baseline with separate coreference resolution. By creating a framework for experimenting with discourse-level features in SMT, this work contributes to a long-term perspective that strives for more thorough modelling of complex linguistic phenomena in translation. Our results on pronoun translation shed new light on a challenging, but essential problem in machine translation that is as yet unsolved.

No description available.

A well known theorem of Hurwitz states that any plane point-lattice, which has no points in the interior of the star-shaped domain |xy| ≤ 1, must have the area of its fundamental parallelogram ≥√5. In this thesis a generelization of plane point-lattices, with respect to the star-shaped domain |xy| ≤ 1, is given and it is shown that the average area ≥√5.

The main theme of this dissertation deals with the impact and consequences of non-normal distribution on the process capability index Cpm. In this thesis, much work has been done in this area including the properties of C^pm, the estimate of Cpm, under normality, its sensitivity to non-normality and also the relationship of Cpm to squared error loss. Related to Cpm is the unifying measure of process capability index Cpw. Several properties of C^pw are investigated. Much of the controversy surrounding the Cp index involves 6[sigma] in the denominator. It carries particular physical meaning when the process characteristic is normally distributed. A new index Cpo is proposed which is based on the difference between two order statistics. The sampling distribution of C^po is obtained for those cases where the process characteristic is uniform, exponential and normal distributions. The behavior of C^p, when n = 2, under non-normal situations such as uniform and exponential distributions is also investigated as a special case of C^po. Another major issue addressed in this dissertation is the Inverted Probability Loss Functions (IPLFs). It is a modified loss function found by inverting a probability density function which was first invented by my supervisor Dr. F.A. Spiring in 1993. The first loss function I studied is the inverted beta loss function (IBLF). I have found certain interesting properties that this class of loss function possesses such as the shape, the loss function and its associated risk function of the IBLF are scale invariant under linear transformation. Finally, I have investigated a few more IPLFs satisfying the usual loss function properties and developed some theorems in this portion of the study.