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- Genre: Doctoral Dissertation
Description
One necessary condition for the two-pass risk premium estimator to be consistent and asymptotically normal is that the rank of the beta matrix in a proposed linear asset pricing model is full column. I first investigate the asymptotic properties of the risk premium estimators and the related t-test and Wald test statistics when the full rank condition fails. I show that the beta risk of useless factors or multiple proxy factors for a true factor are priced more often than they should be at the nominal size in the asset pricing models omitting some true factors. While under the null hypothesis that the risk premiums of the true factors are equal to zero, the beta risk of the true factors are priced less often than the nominal size. The simulation results are consistent with the theoretical findings. Hence, the factor selection in a proposed factor model should not be made solely based on their estimated risk premiums. In response to this problem, I propose an alternative estimation of the underlying factor structure. Specifically, I propose to use the linear combination of factors weighted by the eigenvectors of the inner product of estimated beta matrix. I further propose a new method to estimate the rank of the beta matrix in a factor model. For this method, the idiosyncratic components of asset returns are allowed to be correlated both over different cross-sectional units and over different time periods. The estimator I propose is easy to use because it is computed with the eigenvalues of the inner product of an estimated beta matrix. Simulation results show that the proposed method works well even in small samples. The analysis of US individual stock returns suggests that there are six common risk factors in US individual stock returns among the thirteen factor candidates used. The analysis of portfolio returns reveals that the estimated number of common factors changes depending on how the portfolios are constructed. The number of risk sources found from the analysis of portfolio returns is generally smaller than the number found in individual stock returns.
ContributorsWang, Na (Author) / Ahn, Seung C. (Thesis advisor) / Kallberg, Jarl G. (Committee member) / Liu, Crocker H. (Committee member) / Arizona State University (Publisher)
Created2011
Description
This work is concerned with how best to reconstruct images from limited angle tomographic measurements. An introduction to tomography and to limited angle tomography will be provided and a brief overview of the many fields to which this work may contribute is given.
The traditional tomographic image reconstruction approach involves Fourier domain representations. The classic Filtered Back Projection algorithm will be discussed and used for comparison throughout the work. Bayesian statistics and information entropy considerations will be described. The Maximum Entropy reconstruction method will be derived and its performance in limited angular measurement scenarios will be examined.
Many new approaches become available once the reconstruction problem is placed within an algebraic form of Ax=b in which the measurement geometry and instrument response are defined as the matrix A, the measured object as the column vector x, and the resulting measurements by b. It is straightforward to invert A. However, for the limited angle measurement scenarios of interest in this work, the inversion is highly underconstrained and has an infinite number of possible solutions x consistent with the measurements b in a high dimensional space.
The algebraic formulation leads to the need for high performing regularization approaches which add constraints based on prior information of what is being measured. These are constraints beyond the measurement matrix A added with the goal of selecting the best image from this vast uncertainty space. It is well established within this work that developing satisfactory regularization techniques is all but impossible except for the simplest pathological cases. There is a need to capture the "character" of the objects being measured.
The novel result of this effort will be in developing a reconstruction approach that will match whatever reconstruction approach has proven best for the types of objects being measured given full angular coverage. However, when confronted with limited angle tomographic situations or early in a series of measurements, the approach will rely on a prior understanding of the "character" of the objects measured. This understanding will be learned by a parallel Deep Neural Network from examples.
The traditional tomographic image reconstruction approach involves Fourier domain representations. The classic Filtered Back Projection algorithm will be discussed and used for comparison throughout the work. Bayesian statistics and information entropy considerations will be described. The Maximum Entropy reconstruction method will be derived and its performance in limited angular measurement scenarios will be examined.
Many new approaches become available once the reconstruction problem is placed within an algebraic form of Ax=b in which the measurement geometry and instrument response are defined as the matrix A, the measured object as the column vector x, and the resulting measurements by b. It is straightforward to invert A. However, for the limited angle measurement scenarios of interest in this work, the inversion is highly underconstrained and has an infinite number of possible solutions x consistent with the measurements b in a high dimensional space.
The algebraic formulation leads to the need for high performing regularization approaches which add constraints based on prior information of what is being measured. These are constraints beyond the measurement matrix A added with the goal of selecting the best image from this vast uncertainty space. It is well established within this work that developing satisfactory regularization techniques is all but impossible except for the simplest pathological cases. There is a need to capture the "character" of the objects being measured.
The novel result of this effort will be in developing a reconstruction approach that will match whatever reconstruction approach has proven best for the types of objects being measured given full angular coverage. However, when confronted with limited angle tomographic situations or early in a series of measurements, the approach will rely on a prior understanding of the "character" of the objects measured. This understanding will be learned by a parallel Deep Neural Network from examples.
ContributorsDallmann, Nicholas A. (Author) / Tsakalis, Konstantinos (Thesis advisor) / Hardgrove, Craig (Committee member) / Rodriguez, Armando (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2020