Date of Graduation
Statler College of Engineering and Mineral Resources
Lane Department of Computer Science and Electrical Engineering
Krzysztof Chris Ciesielski
James E Harner
In this research, we propose formulas for recovering the regression function based on the product moments as well as recovering the distributions and derivative function in some indirect models. The upper bounds for the uniform rate of approximations are also derived. For regression functions two cases where the support of underlying functions is bounded and unbounded from above are studied. Based on the proposed approximations, new types of nonparametric estimates of the cumulative distribution, the density functions and the derivative functions in multiplicative-censoring model, as well as the approximations of conditional variance, are constructed. The suggested approach is also applied in the demixing problem and the constrained deconvolution problem, as well as for recovery of a distribution for unknown finite support. The absolute and mean squared errors of corresponding estimates are investigated as well. A simulation study justifies the consistency of the proposed estimates.
Garai, Broti, "Recovery of the Regression Functions and Distributions in some Incomplete Models" (2016). Graduate Theses, Dissertations, and Problem Reports. 5648.