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Title: High-Dimensional Structured Covariance Matrix Estimation with Financial Applications
Authors: Mincheva, Martina Zhelcheva
Advisors: Fan, Jianqing
Contributors: Operations Research and Financial Engineering Department
Keywords: covariance
factor models
high dimensional
principal component analysis
Subjects: Statistics
Operations research
Issue Date: 2014
Publisher: Princeton, NJ : Princeton University
Abstract: This thesis deals with high dimensional statistical inference, and more speci- cally with uncovering low dimensional structures in high dimensional systems. It focuses on large covariance and precision matrix estimation under various complexity constraints, such as low rank and conditional sparsity properties. I have also demonstrated their applications in portfolio allocation and risk minimization. My thesis is on high dimensional covariance matrix estimation with a conditional sparsity structure and fast diverging eigenvalues. I consider the high dimensional approximate factor model, in which the number of units grows possibly exponentially fast with the sample size. Classical methods of estimating the covariance matrices in factor models are based on the cross-sectional independence assumption among the idiosyncratic components. This assumption, however, is restrictive in practical applications. For example, returns depend on equity market risks, housing prices depend on economic health. By assuming the error covariance matrix to be sparse, I allow the presence of the cross-sectional correlation, and combine the merits of both the sparsity modeling and the factor structure. In nancial applications, the residual covariance represents idiosyncratic risk that can be diversied away, and so makes a smaller order contribution to portfolio risk, but in practice it can be important. I study the impact of weakly dependent data with strong mixing conditions on estimation, and obtain asymptotically nonsingular estimators for the covariance matrices using various thresholding techniques. It is shown that the estimated covariance matrices are consistent under various norms. Both observable and unobservable factor cases are considered. The uniform rates of convergence for the factor loadings and the unobservable factors are also derived. This approach is simple and optimization free and it uses the data only through the sample covariance matrix.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Operations Research and Financial Engineering

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