Date of Award

Spring 1-1-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Sergei Kuznetsov

Second Advisor

Janos Englander

Third Advisor

Judith Packer

Fourth Advisor

Martin Walter

Fifth Advisor

Jem Corcoran

Abstract

This thesis extends work on finding optimal estimates of Pt, both in the case where P is a scalar, and when P is a matrix. In the scalar case, we present a formula for minimum variance unbiased estimates of Pt, given k independent observations of the scalar P. We discuss the generalization to the matrix case, and compare the new estimate to the unbiased estimate presented by Kuznetsov and Orlov. We compare the estimates in terms of variance and computation. This comparison is done both theoretically and computationally.

B1_original_eqn_t12_neatened.nb (72 kB)
Mathematica code

B2_fixed_t_verification_neat.nb (15 kB)
Mathematica code

B3_fixed_t_variance_formula_new_s2_final.nb (10 kB)
Mathematica code

B4_fixed_t_variance_efficiency.nb (8 kB)
Mathematica code

B5_fixed_t_variance_efficiency_rec.nb (13 kB)
Mathematica code

B7_check_matrix_timing.nb (20 kB)
Mathematica code

B8_check_matrix_k3t6_efficiency.nb (26 kB)
Mathematica code

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