Constrained Non-Parametric Density Estimation with Applications in Dynamical Model Construction and Safety Verification

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Esmaeil Zadeh Soudijani, Saleh | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50941 (01)
University: Sharif University of Technology
Department: Industrial Engineering
Advisor(s): Mahlooji, Hashem
Abstract:
In this thesis we study non-parametric estimation of constrained bivariate probability density functions and discuss its applications in model construction of dynamical systems and their safety verification. In many industrial applications, it is essential to obtain an estimator for density functions that satisfy particular constraints. If additional information about distribution of a random variable is known in form of moment constraints, the kernel density estimator can be obtained by replacing uniform weights with the generalized empirical likelihood estimators.Our results indicate that the constructed kernel density estimator provides an improved approximation. Moreover, due to the systematic use of moment constraints in the construction of density estimator, it results in a reduction in mean integrated square error (MISE) of the estimation.We also discuss how the results of this thesis can be used for construction of a discrete-time stochastic dynamical model as a conditional stochastic kernel, which is then utilized for safety verification of the system
Keywords:
Non-Parametric Estimation ; Verification ; Dynamical Systems ; Non-Parametric Density Estimator ; Safety System Verification ; Kernel Density Estimate

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