The work of Kramer and Bradley on the use of factorials in incomplete block designs bas been extended to permit both the intra-block and combined intra- and inter-block analyses of factorials in balanced and partially balanced incomplete block designs. In particular, we have obtained a combined intra- and inter-block analysis for factorials in balanced incomplete block designs, group divisible designs, and Latin Square types of partially balanced, incomplete block designs. For the class of Latin Square sub-type L₃ designs both the intra-block and combined intra- and inter-block analyses have been developed. In general, factorial treatment combinations were assigned to the association schemes by permitting the rows of the association schemes to represent the levels of one factor and the columns to represent the levels of a second factor. The extension to multifactor factorials was then carried out by sub-dividing the levels of the basic two-factor factorial, the levels in the sub-divisions representing the levels of the multi-factor factorials. Estimators for the factorial effects have been obtained along with their variances and covariances. Sums of squares in terms of the factorial estimators have been derived and can be used to carry out tests of significance. These sums of squares were shown, for the combined intra- and inter-block analyses, to be independently distributed as χ²-variates with the appropriate numbers of degrees of freedom. Suitable sums of squares for tests of significance are not possible in general for Latin Square sub-type L₃ designs. In situations such as these, we can only consider contrasts among the estimators and use their variances to perform tests of significance. However, for the special cases of factorials in the 4 x 4 Latin Square sub-type L₃ design, a complete analysis yielding the adjusted sums of squares for the factorial effects is possible if the factorial treatments are applied to the association scheme in a different manner. Single-degree-of-freedom contrasts are obtained in much the usual way as for factorials in complete block designs. The method of incorporating a fractional replicate of a factorial into incomplete block designs is also considered. Numerical examples have been worked in detail for a group divisible design and a Latin Square sub-type L₂ design. The procedure for analyzing a Latin Square sub-type L₃ design is also discussed. / Ph. D.

Cyclic designs are incomplete block designs consisting of sets of blocks where in each set successive blocks are obtained in a cyclic manner from the first block of the set. It is convenient to label the objects (treatments) by the integers 0, 1, …, n-. Then if for a particular set the first block consists of, say, the objects 0, h, i, j, then the second block would contain 1, h+1, i+1, j+1. The remaining blocks in the set are obtained similarly, with reduction modulo n whenever an object label exceeds n-1. A cyclic design consists of such sets or combinations of sets, and will be said to be of size (n, k, r) if the block size is k and the object occurs r times. Cyclic designs are a subclass of partially balanced incomplete block (PBIS) designs. In this dissertation all non-isomorphic designs for combinations of n, k, and r are enumerated, and their efficiencies computed. Non-isomorphic designs are those which are not derivable from any other by a relabeling or permutation of the object labels. A method of analysis is presented which utilizes the cyclic property of the designs. The efficiencies are compared with those of two-associate class PBIB designs and a discussion on the utility of the designs is also given. / Ph. D.

We take a critical view of the standard approach to finance and growth. The mapping between the theory and empirics is shown to be poorly understood, and this is traced to deficiencies in our understanding of the microeconomics at play. By looking at both primary and secondary historical evidence we argue that issues of aggregation are critical, and that spatial factors are also prevalent. Further, we suggest that these disaggregated elements can change over the course of an industrial revolution. A model in the spirit of standard finance and growth theories is extended to consider these further effects, and we calibrate the model to data on historical growth paths. In order to advance our understanding of the microeconomic factors that cause the observed phenomena in the finance-growth nexus, we develop a general equilibrium theory of financial intermediation in which exchange costs are endogenously determined by technologies, endowments and preferences. We suggest that incomplete contracts might be central to these phenomena. We link this framework to an understanding of power and political economy in a setting with heterogeneous agents. We develop these results numerically, showing a number of interesting interactions between markets, exchange costs and institutions in economies with different levels of wealth. The model of endogenous exchange costs can be thought of in terms of the findings coming out of our historical analysis. We outline in some detail the further steps that need to be taken before we can speak of the microfoundations of finance and growth with any confidence. First, a fully dynamic model of markets and coalitions must be embedded within a story of economic growth that can match the dynamic observations. Second, we must develop our conception of incomplete contracting and the link with institutions and political economy. The thesis thus opens a number of interesting avenues for future research.

The main objective of this project is to develop a "black-box" multigrid preconditioner for the iterative solution of finite element discretisations of the convection-diffusion equation with dominant convection. This equation can be considered a stand alone scalar problem or as part of a more complex system of partial differential equations, such as the Navier-Stokes equations. The project will focus on the stand alone scalar problem. Multigrid is considered an optimal preconditioner for scalar elliptic problems. This strategy can also be used for convection-diffusion problems, however an appropriate robust smoother needs to be developed to achieve mesh-independent convergence. The focus of the thesis is on the development of such a smoother. In this context a novel smoother is developed referred to as truncated incomplete factorisation (tILU) smoother. In terms of computational complexity and memory requirements, the smoother is considerably less expensive than the standard ILU(0) smoother. At the same time, it exhibits the same robustness as ILU(0) with respect to the problem and discretisation parameters. The new smoother significantly outperforms the standard damped Jacobi smoother and is a competitor to the Gauss-Seidel smoother (and in a number of important cases tILU outperforms the Gauss-Seidel smoother). The new smoother depends on a single parameter (the truncation ratio). The project obtains a default value for this parameter and demonstrated the robust performance of the smoother on a broad range of problems. Therefore, the new smoothing method can be regarded as "black-box". Furthermore, the new smoother does not require any particular ordering of the nodes, which is a prerequisite for many robust smoothers developed for convection-dominated convection-diffusion problems. To test the effectiveness of the preconditioning methodology, we consider a number of model problems (in both 2D and 3D) including uniform and complex (recirculating) convection fields discretised by uniform, stretched and adaptively refined grids. The new multigrid preconditioner within block preconditioning of the Navier-Stokes equations was also tested. The numerical results gained during the investigation confirm that tILU is a scalable, robust smoother for both geometric and algebraic multigrid. Also, comprehensive tests show that the tILU smoother is a competitive method.

A large literature has related the failure of interest rate parity in the foreign exchange market to the existence of a time-varying risk premium. Nevertheless, most modern open economy DSGE models imply a (near) perfect interest rate parity condition. This paper presents a stylized two-country incomplete-markets model in which countries have strong precautionary motives because they face international liquidity constraints, the presence of which successfully generates a time-varying risk premium: the country that has accumulated debt after experiencing relative worse times has stronger precautionary motives and its asset carries a risk premium. (author's abstract) / Series: Department of Economics Working Paper Series

The concomitance of prosperity and poverty come as an enigma in today's world.As some people in this world benefit greatly from advanced technologies andglobalization, others are still suffering heavily from poverty. One noticeable fact is thatalmost all developing countries have their own distinguished "poor area". Such poorareas seem to persist regardless of robust economic growth enjoyed by the overalleconomy.By decomposing the developing country into two regions, one rich coastal regionand one poor inland region, this research establishes a new classical general equilibrium3X2 Ricardian model to investigate how trade liberalization will affect the participationin the division of labor by poor individuals in the inland region in a developing countryand their associated welfare change under different trading conditions.Our model of division of labor on poverty delineates the interdependentrelationship between individuals in the poor inland region, the rich coastal region and thedeveloped country. Market integration plays a very important role in suchinterdependency. Low transaction efficiency is the bottle-neck constraint on the poorinland region's integration into international division of labor through international trade.Thus, it is critical for the poor inland region to improve the market transaction efficiencyin order to enjoy gains from trade.Our marginal and inframarginal analysis show that as an important part of tradeliberalization policy, tariff reduction may not always be a good policy choice for thedeveloping country to alleviate the poverty. Whether tariff reduction makes the inlandregion better off depends on the initial general equilibrium market structure and thedeveloping country's power of influencing its terms of trade. If the developing country islarge enough to determine the terms of trade in international trade with the developedcountry, the developing country may increase the welfare level of the poor inland regionby increasing its tariff rate. But the developed country will oppose it because the tariffrate increase in the developing country will hurt its welfare. Trade negotiation is thennecessary to determine the final tariff rate and the share of gains of trade to each countryand region.

Symmetric generalized eigenvalue problems arise in many physical applications and frequently only a few of the eigenpairs are of interest. Typically, the problems are large and sparse, and therefore traditional methods such as the QZ algorithm may not be considered. Moreover, it may be impractical to apply shift-and-invert Lanczos, a favored method for problems of this type, due to difficulties in applying the inverse of the shifted matrix. With these difficulties in mind, Golub and Ye developed an inverse free Krylov subspace algorithm for the symmetric generalized eigenvalue problem. This method does not rely on shift-and-invert transformations for convergence acceleration, but rather a preconditioner is used. The algorithm suffers, however, in the presence of multiple or clustered eigenvalues. Also, it is only applicable to the location of extreme eigenvalues. In this work, we extend the method of Golub and Ye by developing a block generalization of their algorithm which enjoys considerably faster convergence than the usual method in the presence of multiplicities and clusters. Preconditioning techniques for the problems are discussed at length, and some insight is given into how these preconditioners accelerate the method. Finally we discuss a transformation which can be applied so that the algorithm extracts interior eigenvalues. A preconditioner based on a QR factorization with respect to the B-1 inner product is developed and applied in locating interior eigenvalues.

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In this thesis, we follow the incomplete contract model developed by Freixas and Rochet (1997). They model the decision of a bank regulator for continuing the sound bank or restructuring the failing bank as a game between bank equity owners, the bank manager, and the regulator under the incomplete contract framework. In this essay, we apply this incomplete contract model to Taiwan empirical data. After using several kinds of financial ratios as our indicators, we select nine ratios to process our empirical examination. And we find that: there are two banks appeared in the “ex-post efficient interference” segment except two ratios and also another two banks shown in the “ex-post efficient passivity” segment except one ratio. / In this thesis, we follow the incomplete contract model developed by Freixas and Rochet (1997). They model the decision of a bank regulator for continuing the sound bank or restructuring the failing bank as a game between bank equity owners, the bank manager, and the regulator under the incomplete contract framework. In this essay, we apply this incomplete contract model to Taiwan empirical data. After using several kinds of financial ratios as our indicators, we select nine ratios to process our empirical examination. And we find that: there are two banks appeared in the “ex-post efficient interference” segment except two ratios and also another two banks shown in the “ex-post efficient passivity” segment except one ratio.

Atkinson 及 Riani 應用前進搜尋演算法來處理百牡利資料中所包含的多重離群值(2001）。在這篇論文中，我們沿用相同的想法來處理在不完整資料下一般線性模型中的多重離群值。這個演算法藉由先填補資料中遺漏的部分，再利用前進搜尋演算法來確認資料中的離群值。我們所提出的方法可以解決處理多重離群值時常會遇到的遮蓋效應。我們應用了一些真實資料來說明這個演算法並得到令人滿意結果。 / Atkinson and Riani (2001) apply the forward search algorithm to deal with the problem of the detection of multiple outliers in binomial data. In this thesis, we extend the similar idea to identify multiple outliers for the generalized linear models when part of data are missing. The algorithm starts with imputation method to fill-in the missing observations in the data, and then use the forward search algorithm to confirm outliers. The proposed method can overcome the masking effect, which commonly occurs when multiple outliers exit in the data. Real data are used to illustrate the procedure, and satisfactory results are obtained.