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Register a new userOn Integral Theorems: Monte Carlo Estimators and Optimal Functions
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Added by
Nhat Ho
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals theorem. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The integral theorems provide natural estimators of density functions via Monte Carlo integration. Assessments of the quality of the density estimators can be used to obtain optimal cyclic functions which minimize square integrals. Our proof techniques rely on a variational approach in ordinary differential equations and the Cauchy residue theorem in complex analysis.
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