In many areas of research, such as within medical statistics, biology and geostatistics, problems arise requiring the analysis of angular (or directional) data. Many possess experimental design problems and require analysis of variance techniques for suitable analysis of the angular data. These techniques have been developed for very limited cases and the sensitivity of such techniques to the violation of assumptions made, and their possible extension to larger experimental models, has yet to be investigated. The general aim of this project is therefore to develop suitable experimental design models and analysis of variance type techniques for the analysis of directional data. Initially a generalised linear modelling approach is used to derive parameter estimates for one-way classification designs leading to maximum likelihood methods. This approach however, when applied to larger experimental designs is shown to be intractable due to optimization problems. The limited analysis of variance techniques presently available for angular data are reviewed and extended to take account of the possible addition of further factors within an experimental design. These are shown to breakdown under varying conditions and question basic underlying assumptions regarding the components within the original approach. A new analysis of variance approach is developed which possesses many desirable properties held in standard 'linear' statistical analysis of variance. Finally several data sets are analysed to support the validity of the new techniques.

The purpose of this study is to determine boundary conditions associated with the number of treatment groups (K), the common treatment group sample size (n), and an index of the extent to which the assumption of equality of treatment population variances is violated (Q) with regard to user confidence in application of the one-way analysis of variance F-test for determining equality of treatment population means. The study concludes that the analysis of variance F-test is robust when the number of treatment groups is less than seven and when the extreme ratio of variances is less than 1:5, but when the violation of the assumption is more severe or the number of treatment groups is seven or more, serious discrepancies between actual and nominal significance levels occur. It was also concluded that for seven treatment groups confidence in the application of the analysis of variance should be limited to the values of Q and n so that n is greater than or equal to 10 In (1/2)Q. For nine treatment groups, it was concluded that confidence be limited to those values of Q and n so that n is greater than or equal to (-2/3) + 12 ln (1/2)Q. No definitive boundary could be developed for analyses with five treatment groups.

國立大學校院校務基金政策從民國八十四開始試辦，至今已推行多年，但本研究發現目前尚無研究探討各校校務基金決算書上所列示之差異原因。由於國立大學預算是學校承諾未來計畫之工作，而決算是實際執行之結果，兩者差異除了一些無法控制因素外，若詳細檢討差異可以回饋給學校及主管機關未來在執行計畫或活動時能夠加以修改或改善。本研究分析公立大學96年至99年44所學校預算數、決算數差異情況，並彙整各校院對於預、決算數差異之原因，嘗試透過標準成本制與差異分析法之應用，詳細探討造成各校於預、決算數差異之因素，使差異分析能具體提供資訊給學校作為未來預算編製及成本控制管理之參考運用。 本研究發現儘管各校在國立大學校務基金決算書中，有列示預、決算差異及在備註說明其差異之理由，但說明都相當簡略除非原因明顯，否則甚難瞭解。研究發現教學研究及訓輔成本、管理費用與總務費用的用人費用皆有高估之傾向，主要是因為教、職員預算員額編列高估所致，同時透過差異分析亦顯示，即便有數量上之有利差異，仍有價格上之不利差異，代表相關之人事成本也偏高。教學研究及訓輔成本與管理費用與總務費用之折舊、折耗及攤銷在預算編列時嚴重低估。學生公費及獎勵金之靜態預算不利差異是由於平均每單位學生成本決算數較預算數高，而部分學校也是因為數量之不利差異；而靜態預算有利差異則主要是由於價格之有利差異所造成。大部分學校在研究發展費用中，其靜態預算不利差異係因價格上不利差異，即便大部分學校也具有數量上之有利差異。在學雜費收入淨額部分，靜態預算有利差異大部分係由數量之有利差異所造成；而造成學雜費收入淨額靜態預算不利差異除了數量上的不利差異外，大部分的學校是因為價格上的不利差異。本研究建議預算差異說明部分應明確界定差異金額與％需強制說明原因，並考慮編列「彈性預算」及差異分析方式增加價格差異及數量差異部分。 / Public universities have adopted public university fund instead of government fund since 1995. However, no research tries to analyze the reasons of the variance between the budget and the actual accounts of public universities. Since the budget of a public university is a commitment for the future plans and the actual account is the school’s executed result. The variance between them, except some uncontrollable factors, not only can provide some feedback but also can provide for improvement of the future plans, if the analysis had been analyzed effectively. Therefore, this study attempts to apply variance analysis of the standard cost and analyzes the variance between budget and final account of 44 public universities from 2007 to 2011. The proposed variance analysis approach is expected to substantially provide some useful information for public universities for the budget preparation and cost control and management. This study reveals that many universities indeed listed and explained the variance, but most of the explanations are quite rough. However, based on schools’ variance analysis it is very difficult to understand why and how the variances stand for, unless the reason is quite obviously. The study founds that the employees’ payrolls of teaching and research, training and consulting expenses, and general and administration expenses are overestimated due to overestimate the number of teachers and staffs. Variance analysis indicates that even a favorable variance on quantity, the price variance is still unfavorable, which means that the average personnel expenses are higher than the budget. The depreciation expenses of teaching and research and general and administration expenses are underestimated for all schools. Most school has an unfavorable static budget variance on student grant mainly due to higher actual average cost per student than the budget, and some schools due to unfavorable quantity variance. Most of schools’ unfavorable research and development expenses are caused by unfavorable price variance, although most of them have favorable quantity variances. The net revenue on tuition and fees, the favorable static budget variance is mainly due to favorable quantity variance and the unfavorable variance of net revenue on tuition and fees results from price variance. The research suggests that Ministry of Education should establish a standard amount or percentage of variance and requires public universities to explain when variance is higher than the standard. The public universities should prepare the “flexible budget” and apply the the price variance and quantity variance to variance analysis.

In contrast to the studies of constant or time-varying correlations between stock and bond returns, in this thesis, I explore the regime-dependent correlations between stock and bond returns. Specifically, I start with a comprehensive asset pricing model, i.e., a regime-switching multifactor model, and then investigate the regime-dependent correlations between stock and bond returns. Based on the BIC, the number of regimes in the regime-switching model is optimally determined to be two. For the two regimes, the directions of the regime-dependent correlations appear to be significantly different. Also, the magnitudes of the regime-dependent correlations are substantially larger in these two regimes than the correlation in the single regime. With my findings in the regime-dependent correlations, I then examine the performance of portfolio strategies. Throughout the in-sample and out-of-sample tests, I find that the two portfolio strategies, regime inferred portfolio and probability implied portfolio, can outperform the benchmark, S&P 500.

Thesis (Ph. D.)--University of Florida, 1981. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 108-109).

<p> In this thesis a systematic and short method for computing the expected values of mean squares has been developed. One chapter is devoted to the theory of regression analysis by the method of least squares using matrix notation and a proof is given that the method of least squares leads to an absolute minimum, a result which the author has not found in the literature. For two-way classifications the results have been developed for proportional frequencies, a subject which again has been neglected in the literature except for the Type II model. Finally, the methods for computing the expected values of the mean squares are applied to nested classifications and Latin square designs.</p> / Thesis / Master of Arts (MA)

Um importante problema enfrentado por engenheiros é a busca por soluções ótimas para problemas com um grande número de soluções possíveis. Neste trabalho, estudamos métodos otimização probabilísticos baseados em algoritmos genéticos, propostos inicialmente para o estudo de sistemas biológicos. Propomos algumas alterações do método de otimização por algoritmos genéticos tradicional, utilizando técnicas estatísticas de planejamento experimental, que resultaram em uma melhoria da convergência, percebida, não só na velocidade de convergência, como no número de possibilidades de soluções diferentes analisadas. Como resultado, é proposto um algoritmo que cobre o domínio de atuação dos métodos por algoritmos genéticos e do método por gradientes, permitindo uma melhor sintonização do otimizador com o problema. / A important problem faced by engineers is the search of optimal solutions for problems with a great number of possible solutions. Throughout this work, it is studied stochastic optimizers based on genetic algorithms, applied initially to the study of biological systems. Some alterations on the traditional genetic algorithms based optimizer are proposed through the use of experiment design techniques, which resulted in a improvement of the convergence that can be perceived, not only in the convergence speed, but on the number of solutions analyzed as well. As a consequence, a algorithm is proposed, covering both the traditional genetic algorithms based optimizer and the gradient method domains, allowing a better tuning of the optimizer to the problem.

The impact on banks' portfolio under BIS amendment to the capital accord of 1996 and reserve requirement.

Um importante problema enfrentado por engenheiros é a busca por soluções ótimas para problemas com um grande número de soluções possíveis. Neste trabalho, estudamos métodos otimização probabilísticos baseados em algoritmos genéticos, propostos inicialmente para o estudo de sistemas biológicos. Propomos algumas alterações do método de otimização por algoritmos genéticos tradicional, utilizando técnicas estatísticas de planejamento experimental, que resultaram em uma melhoria da convergência, percebida, não só na velocidade de convergência, como no número de possibilidades de soluções diferentes analisadas. Como resultado, é proposto um algoritmo que cobre o domínio de atuação dos métodos por algoritmos genéticos e do método por gradientes, permitindo uma melhor sintonização do otimizador com o problema. / A important problem faced by engineers is the search of optimal solutions for problems with a great number of possible solutions. Throughout this work, it is studied stochastic optimizers based on genetic algorithms, applied initially to the study of biological systems. Some alterations on the traditional genetic algorithms based optimizer are proposed through the use of experiment design techniques, which resulted in a improvement of the convergence that can be perceived, not only in the convergence speed, but on the number of solutions analyzed as well. As a consequence, a algorithm is proposed, covering both the traditional genetic algorithms based optimizer and the gradient method domains, allowing a better tuning of the optimizer to the problem.

Copy number variation, causing by the genome rearrangement, generally refers to the copy numbers increased or decreased of large genome segments whose lengths are more than 1kb. Such copy number variations mainly appeared as the sub-microscopic level of deletion and duplication. Copy number variation is an important component of genome structural variation, and is one of pathogenic factors of human diseases. Next generation sequencing technology is a popular CNV detection method and it has been widely used in various fields of life science research. It possesses the advantages of high throughput and low cost. By tailoring NGS technology, it is plausible to sequence individual cells. Such single cell sequencing can reveal the gene expression status and genomic variation profile of a single-cell. Single cell sequencing is promising in the study of tumor, developmental biology, neuroscience and other fields. However, there are two challenging problems encountered in CNV detection for NGS data. The first one is that since single-cell sequencing requires a special genome amplification step to accumulate enough samples, a large number of bias is introduced, making the calling of copy number variants rather challenging. The performances of many popular copy number calling methods, designed for bulk sequencings, are not consistent and cannot be applied on single-cell sequenced data directly. The second one is to simultaneously analyze genome data for multiple samples, thus achieving assembling and subgrouping similar cells accurately and efficiently. The high level of noises in single-cell-sequencing data negatively affects the reliability of sequence reads and leads to inaccurate patterns of variations. To handle the problem of reliably finding CNVs in NGS data, in this thesis, we firstly establish a workflow for analyzing NGS and single-cell sequencing data. The CNVs identification is formulated as a quadratic optimization problem with both constraints of sparsity and smoothness. Tailored from alternating direction minimization (ADM) framework, an efficient numerical solution is designed accordingly. The proposed model was tested extensively to demonstrate its superior performances. It is shown that the proposed approach can successfully reconstruct CNVs especially somatic copy number alteration patterns from raw data. By comparing with existing counterparts, it achieved superior or comparable performances in detection of the CNVs. To tackle this issue of recovering the hidden blocks within multiple single-cell DNA-sequencing samples, we present an permutation based model to rearrange the samples such that similar ones are positioned adjacently. The permutation is guided by the total variational (TV) norm of the recovered copy number profiles, and is continued until the TV-norm is minimized when similar samples are stacked together to reveal block patterns. Accordingly, an efficient numerical scheme for finding this permutation is designed, tailored from the alternating direction method of multipliers. Application of this method to both simulated and real data demonstrates its ability to recover the hidden structures of single-cell DNA sequences.