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This dissertation focuses on issues related to fitting an optimal variance-covariance structure in multilevel linear modeling framework with two Monte Carlo simulation studies. In the first study, the author evaluated the performance of common fit statistics such as Likelihood Ratio Test (LRT), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) and a new proposed method, standardized root mean square residual (SRMR), for selecting the correct within-subject covariance structure. Results from the simulated data suggested SRMR had the best performance in selecting the optimal covariance structure. A pharmaceutical example was also used to evaluate the performance of these fit statistics empirically. The LRT failed to decide which is a better model because LRT can only be used for nested models. SRMR, on the other hand, had congruent result as AIC and BIC and chose ARMA(1,1) as the optimal variance-covariance structure. In the second study, the author adopted a first-order autoregressive structure as the true within-subject V-C structure with variability in the intercept and slope (estimating [tau]00 and [tau]11 only) and investigated the consequence of misspecifying different levels/types of the V-C matrices simultaneously on the estimation and test of significance for the growth/fixed-effect and random-effect parameters, considering the size of the autoregressive parameter, magnitude of the fixed effect parameters, number of cases, and number of waves. The result of the simulation study showed that the commonly-used identity within-subject structure with unstructured between-subject matrix performed equally well as the true model in the evaluation of the criterion variables. On the other hand, other misspecified conditions, such as Under G & Over R conditions and Generally misspecified G & R conditions had biased standard error estimates for the fixed effect and lead to inflated Type I error rate or lowered statistical power. The two studies bridged the gap between the theory and practical application in the current literature. More research can be done to test the effectiveness of proposed SRMR in searching for the optimal V-C structure under different conditions and evaluate the impact of different types/levels of misspecification with various specifications of the within- and between- level V-C structures simultaneously.

MV is the traditional method to treat international portfolio selection problems, which bases its theory on the assumption of Normal Distribution. However, during economy recession the portfolio return turns out to be a fat tail distribution. Therefore, in this sense, we explore Roy’s SF criterion and apply the extreme theory to the historical data. We demonstrate how such portfolios would perform during the Asian Crisis, IT Bubble Bust and the Financial Crisis separately. We also compare the SF portfolio’s performance to the MV portfolio’s performance, therefore to check, SF and MV portfolio, which will outperform during bust and boom of the economy. The Asian Crisis was marked with great currency devaluation and lower currency return on equity. The Dot.Com Bubble Busts was known for its sharp plummet in the stock market, while, the Financial Crisis was known as the large falls in the US stock market and elsewhere. They are the extreme events of the world capital markets, which in some way contribute to the non-normal distribution. Simulated results over the 1997-2010 period which include six busts and booms: the Asian Crisis, period after Asian Crisis, IT Bubble Bust, period after IT Bubble Bust, The Financial Crisis and period after The Financial Crisis, indicate that SF portfolio outperforms MV portfolio during most of the times, this result is especially obvious for Indonesian and Thailand.

Parametric uncertainty is one of many possible causes of divergence for the Kalman filter. Frequently, state estimation errors caused by imperfect model parameters are reduced by including the uncertain parameters as states (i.e., augmenting the state vector). For many situations, this not only improves the state estimates, but also improves the accuracy and precision of the parameters themselves. Unfortunately, not all filters benefit from this augmentation due to computational restrictions or because the parameters are poorly observable. A parameter with low observability (e.g., a set of high order gravity coefficients, a set of camera offsets, lens calibration controls, etc.) may not acquire enough measurements along a particular trajectory to improve the parameter's accuracy, which can cause detrimental effects in the performance of the augmented filter. The problem is then how to reduce the dimension of the augmented state vector while minimizing information loss. This dissertation explored possible implementations of reduced-order filters which decrease computational loads while also minimizing state estimation errors. A theoretically rigorous approach using the ?consider" methodology was taken at discrete time intervals were explored for linear systems. The continuous dynamics, discretely measured (continuous-discrete) model was also expanded for use with nonlinear systems. Additional techniques for reduced-order filtering are presented including the use of additive process noise, an alternative consider derivation, and the minimum variance reduced-order filter. Multiple simulation examples are provided to help explain critical concepts. Finally, two hardware applications are also included to show the validity of the theory for real world applications. It was shown that the minimum variance consider Kalman filter (MVCKF) is the best reduced-order filter to date both theoretically and through hardware and software applications. The consider method of estimation provides a compromise between ignoring parameter error and completely accounting for it in a probabilistic sense. Based on multiple measures of optimality, the consider filtering framework can be used to account for parameter error without directly estimating any or all of the parameters. Furthermore, by accounting for the parameter error, the consider approach provides a rigorous path to improve state estimation through the reduction of both state estimation error and with a consistent variance estimate. While using the augmented state vector to estimate both states and parameters may further improve those estimates, the consider estimation framework is an attractive alternative for complex and computationally intensive systems, and provides a well justified path for parameter order reduction.

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

As a large number of single nucleotide polymorphisms (SNPs) and microsatellite markers are available, high resolution mapping employing multiple markers or multiple allele markers is an important step to identify quantitative trait locus (QTL) of complex human disease. For many complex diseases, quantitative phenotype values contain more information than dichotomous traits do. Much research has been done on conducting high resolution mapping using information of linkage and linkage disequilibrium. The most commonly employed approaches for mapping QTL are pedigree-based linkage analysis and population-based association analysis. As one of the methods dealing with multiple alleles markers, mixed models are developed to work out family-based association study with the information of transmitted allele and nontransmitted allele from one parent to offspring. For multiple markers, variance component models are proposed to perform association study and linkage analysis simultaneously. Linkage analysis provides suggestive linkage based on a broad chromosome region and is robust to population admixtures. One the other hand, allelic association due to linkage disequilibrium (LD) usually operates over very short genetic distance, but is affected by population stratification. Combining both approaches plays a synergistic role in overcoming their limitations and in increasing the efficiency and effectiveness of gene mapping.

In the study of sound identification, land animals such as birds and bats have been well investigated, and so are their habitats. On the other hand, sound making creatures in the ocean are much less researched. In this research, the stress calls of three Holocentridaes, Neoniphon sammara, Myripristis murdjan, and Sargocentron spinosissimum, who are commonly found in coral reefs, were recorded in water tank for analysis of sound characteristics. The averaged characteristic parameters of single pulse among three is around 410 Hz for the peak frequency, 100 Hz for the bandwidth, 0.07 dB/Hz for the slope, and duration of 0.05 s. As for the impulse train, averaged peak frequency is 415 Hz, 55 Hz for the bandwidth, 0.07 dB/Hz for the slope, and duration of 0.5 s. These parameters were first checked by the Kolmogorov-Smirnov Test to identify if each parameter follows normal distribution; the slopes of ascending and descending frequency and the total duration are not in normal distribution. The three parameters were later transferred so as to concentrate variances. Next, analysis of variance was applied on all characteristics to extract the significant parameters (including non transferred and transferred data), which were then tested by Stepwise Discriminat and Back-propagation Network. The identification rate of for single pulse with and without data transfer is 63% and 82% while pulse train is 57% and 73%. Both identification rates were raised up approximately 20% due to the data transfer. Both methods provide an reliable tool for marine sound identification, and the whole process of the study may be applied to another biological identification.

Taiwan is the country which relies on foreign trade and the value of import and export markets accounts for eighty percent of the Gross Net Product¡]GNP¡^. It is obvious that the feature of economic system in island highly depends on the existence of foreign trade. Therefore, exchange rate is considered as one of the major indexes for Taiwan¡¦s economic activities. Federal Reserve System¡]FED¡^has constantly begun to lower the interest rate for thirteen times since 2001, and this would influence the trends of the interest rate of the whole world. Also, it seems that reducing the interest rate promotes the low interest which leads to a more prosperous economy in Taiwan society than before. It is clear, thus, that the interest is regarded as a major variable in economic system. The stock market of Taiwan has shifted from bear market to bullish one since 2002 and it would have developed the bullish market for almost ten years. According to this phenomenon, the issue of how to evaluate the trend of the stock index has been becoming important for Taiwanese investors to explore the stock market. This study is based on the observation of the relationships between the stock index and the two rates, exchange and interest rates. It is hoping, by doing so, that investors can obtain sufficient information and successfully estimate different aspects of investing trends in the stock market in Taiwan.

The Dynamic Conditional Correlation (DCC) model proposed by Engle (2002) has become one of the most popular models for the analysis of multivariate financial time series. Yet, the impact of temporal aggregation on the DCC estimates has not yet been rigorously investigated. This thesis examines the changes of DCC estimates when the intraday returns are aggregated from 5-minutes to 270-minutes returns using Taiwanese eight industry index returns from Jan. 2, 2004 to Dec. 31, 2006. Our empirical analysis finds that dynamic correlation coefficients between the 8 industry index returns are all positive and time-varying. Further, Electronic and Building indices seem to have high correlation with other industry indices whereas plastics has a lower correlation with others. What is more important, all return series have higher conditional correlation for lower frequencies. In other words, temporary aggregation will increase the conditional correlation. This thesis also seeks to categorize the loan accounts of small- and medium-scale corporations according to their respective business sectors and calculate the monthly returns and standard deviation of the bank loans according to the groups of sample of credit records from each sector, with the purpose of establishing the efficient frontier of the loan combinations of the banks and estimation the dynamic conditional correlation to discover the optimal crediting policy. It is expected that the discussion using the model presented in the thesis may provide the basis for financial institutions as they establish their respective crediting policies.

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