Evaluation of An Approximation of Quadratic Form with Unknown Covariance Matrix
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
This thesis studies the performance of two approximations of distribution of quadratic form by using moment matching method with covariance matrix unknown. One of the approximations uses the sample covariance matrix, referred to as the plug-in approximation, as plug-in estimator in the moments. The second, modified, approximation estimates the moments, composed of the traces involving the unknowing covariance matrix, directly, by using unbiased and consistent estimators of the said traces. The entire investigation is carried out, first under normality, and then the robustness of the approximation under normality is evaluated. For robustness, two typical non-normal distributions, viz., exponential and uniform, are considered. Further, the closeness of the approximation methods are assessed by using different criteria including tail probability estimation and formal Kolmogorov-Simrnov test criteria. It is observed that the modified approximation, in general, outperforms the plug-in approximation, in particular, under non-normality and also when d increases for any fixed n, where d ≤ n.
Place, publisher, year, edition, pages
2013. , 35 p.
Plug-in Estimator, Modified Estimator, Kolmogorov-Simrnov Test, Monte Carlo Simulation, Covariance Structure
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-208227OAI: oai:DiVA.org:uu-208227DiVA: diva2:651372
Master Programme in Statistics
2013-05-29, F332, Kyrkogårdsgatan 10, Uppsala, 13:15 (English)
Rauf, Amad, Senior lecturer
Fan, Yang-Wallentin, Professor