This article examines methods to efficiently estimate the mean response in a linear model with an unknown error distribution under the assumption that the responses are missing at random. We show how the asymptotic variance is affected by the estimator of the regression parameter and by the imputation method. To estimate the regression parameter the Ordinary Least Squares method is efficient only if the error distribution happens to be normal. If the errors are not normal, then we propose a One Step Improvement estimator or a Maximum Empirical Likelihood estimator to estimate the parameter efficiently. In order to investigate the impact that imputation has on estimation of the mean response, we compare the Listwise Deletion method and the Propensity Score method (which do not use imputation at all), and two imputation methods. We show that Listwise Deletion and the Propensity Score method are inefficient. Partial Imputation, where only the missing responses are imputed, is compared to Full Imputation, where both missing and non-missing responses are imputed. Our results show that in general Full Imputation is better than Partial Imputation. However, when the regression parameter is estimated very poorly, then Partial Imputation will outperform Full Imputation. The efficient estimator for the mean response is the Full Imputation estimator that uses an efficient estimator of the parameter.

Two-colour microarrays are a popular tool for measuring relative gene expression between RNA populations for thousands of genes simultaneously. This thesis develops methods for assessing the quality and variability of data from such experiments and for incorporating these assessments into algorithms for discovering differential expression. The variability of microarray data depends not only on the quality of the arrays, but also on how they are processed and normalised. The intimate relationship between variability of expression log-ratios and the method used for background correcting the expression values is specifically explored. The performance of different estimators of the background level and various model-based processing methods, including a novel normal-exponential convolution model are compared in search of a ‘best’ alternative. The results indicate that the choice of method should be guided by the specific question of interest; the model-based methods give gene expression measures with low bias, and do very well at choosing differentially expressed genes, while subtracting low background estimates, or not background correcting the data produces low variance estimates which are the most biased, however perform best at choosing DE genes. All of these alternatives give better results than those obtained by the standard approach of subtracting high local background estimates from the foreground signal, which is not recommended. (For complete abstract open document)

The forex market is a complex, evolving, and a non-linear dynamical system, and its forecast is difficult due to high data intensity, noise/outliers, unstructured data and high degree of uncertainty. However, the exchange rate of a currency is often found surprisingly similar to the history or the variation of an alternative currency, which implies that correlation knowledge is valuable for forex market trend analysis. In this research, we propose a computational correlation analysis for the intelligent correlation extraction from all available economic data. The proposed correlation is a synthesis of channel and weighted Pearson's correlation, where the channel correlation traces the trend similarity of time series, and the weighted Pearson's correlation filters noise in correlation extraction. In the forex market analysis, we consider 3 particular aspects of correlation knowledge: (1) historical correlation, correlation to previous market data; (2) cross-currency correlation, correlation to relevant currencies, and (3) macro correlation, correlation to macroeconomic variables. While evaluating the validity of extracted correlation knowledge, we conduct a comparison of Support Vector Regression (SVR) against the correlation aided SVR (cSVR) for forex time series prediction, where correlation in addition to the observed forex time series data is used for the training of SVR. The experiments are carried out on 5 futures contracts (NZD/AUD, NZD/EUD, NZD/GBP, NZD/JPY and NZD/USD) within the period from January 2007 to December 2008. The comparison results show that the proposed correlation is computationally significant for forex market analysis in that the cSVR is performing consistently better than purely SVR on all 5 contracts exchange rate prediction, in terms of error functions MSE, RMSE, NMSE, MAE and MAPE. However, the cSVR prediction is found occasionally differing significantly from the actual price, which suggests that despite the significance of the proposed correlation, how to use correlation knowledge for market trend analysis remains a very challenging difficulty that prevents in practice further understanding of the forex market. In addition, the selection of macroeconomic factors and the determination of time period for analysis are two computationally essential points worth addressing further for future forex market correlation analysis.

The forex market is a complex, evolving, and a non-linear dynamical system, and its forecast is difficult due to high data intensity, noise/outliers, unstructured data and high degree of uncertainty. However, the exchange rate of a currency is often found surprisingly similar to the history or the variation of an alternative currency, which implies that correlation knowledge is valuable for forex market trend analysis. In this research, we propose a computational correlation analysis for the intelligent correlation extraction from all available economic data. The proposed correlation is a synthesis of channel and weighted Pearson's correlation, where the channel correlation traces the trend similarity of time series, and the weighted Pearson's correlation filters noise in correlation extraction. In the forex market analysis, we consider 3 particular aspects of correlation knowledge: (1) historical correlation, correlation to previous market data; (2) cross-currency correlation, correlation to relevant currencies, and (3) macro correlation, correlation to macroeconomic variables. While evaluating the validity of extracted correlation knowledge, we conduct a comparison of Support Vector Regression (SVR) against the correlation aided SVR (cSVR) for forex time series prediction, where correlation in addition to the observed forex time series data is used for the training of SVR. The experiments are carried out on 5 futures contracts (NZD/AUD, NZD/EUD, NZD/GBP, NZD/JPY and NZD/USD) within the period from January 2007 to December 2008. The comparison results show that the proposed correlation is computationally significant for forex market analysis in that the cSVR is performing consistently better than purely SVR on all 5 contracts exchange rate prediction, in terms of error functions MSE, RMSE, NMSE, MAE and MAPE. However, the cSVR prediction is found occasionally differing significantly from the actual price, which suggests that despite the significance of the proposed correlation, how to use correlation knowledge for market trend analysis remains a very challenging difficulty that prevents in practice further understanding of the forex market. In addition, the selection of macroeconomic factors and the determination of time period for analysis are two computationally essential points worth addressing further for future forex market correlation analysis.

Thesis (M.S.)--Georgia State University, 2007. / Title from file title page. Yichuan Zhao, committee chair; Yu-Sheng Hsu , Xu Zhang, Yuanhui Xiao , committee members. Electronic text (54 p.) : digital, PDF file. Description based on contents viewed Feb. 25, 2008. Includes bibliographical references (p. 30-32).

Thesis (Ph.D.)--Murdoch University, 2005. / Thesis submitted to the Division of Science and Engineering. Bibliography: leaves 206-214.

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 103-113) Also available in print.

Thesis (Ph.D.)--York University, 2006. Graduate Programme in Economics. / Typescript. Includes bibliographical references (leaves 137-141). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR19821

Thesis (Ph.D.)--Victoria University of Wellington, 2009. / Includes bibliographical references.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 82-86). Also available via the Internet.