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.

Asymptotic Methods in Statistics

Series comments: Abstract: In ensemble-based probabilistic weather forecasting, it is often necessary to verify multidimensional predictions using verification scores. Such multidimensional quantities can be, for example, values of a weather variable taken at different locations, a set of several weather quantities, or simply the two-dimensional wind vector. Assuming multivariate normality of the forecasts, we determine the dependence of two different verification measures on the ensemble size and provide their sample size-adjusted fair versions. We demonstrate the usefulness of the application of fair scores using real weather forecasts and simulation studies, also examining their robustness with respect to deviations from normality.