Simulation-Based Insights and Novel Criteria for Linear Regression Modeling

statistics theorydata analysis, statistics and probability

Audience: researchers in the topic

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Comments: Abstract: We study asymptotic behavior of the averaged integrals of a Lévy-driven linear process weighted by a complex exponent of polynomials with real coefficients. Such functionals naturally arise in the problems relating to nonlinear regression analysis and signal processing, specifically in the estimation of parameters of frequency-modulated signals. Under some conditions on the Lévy process and kernel defining the linear process, we get a uniform strong law of large numbers for this weighted process. More precisely, it is shown that the considered integrals converge a.s. to zero uniformly over all the values of the real coefficients of the polynomials of fixed order. The result obtained is then used to prove strong consistency of LSE for the parameters of linearly-modulated trigonometric signal (chirp signal) observed against the background of shot noise described above.

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Asymptotic Methods in Statistics

Series comments: One can find video files and slides of talks at the seminar on Asymptotic Methods in Statistics here: www.youtube.com/@SeminarforAsymptoticMethods

A link to a slide is below the description of the video, namely shorturl.at/jUAhL and shorturl.at/6wjUA shorturl.at/rdpqs

Alas the links do not work in one click: you should emphasize them with a mouse and select, e.g., "Go to shorturl.at/rdpqs".

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