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Exact Computation of Non-Gaussian Mismatch Penalties in Wiener-Hermite Cross-Correlation Identification
Serhii Zabolotnii
Wiener-Hermite cross-correlation identification represents a polynomial response in the Hermite basis. Under Gaussian excitation the basis is orthogonal and a diagonal rule recover…
A Closed-Form Skew Penalty for Volterra Cross-Correlation Identification under Non-Gaussian Input
Serhii Zabolotnii
The monomial parameterization of finite-memory Volterra identification is ill-conditioned under non-Gaussian input, and the Wiener--Hermite expansion removes this ill-conditioning…
Parametrically Adaptive Transition Polynomial: a Signed-Parity Continuous-alpha Extension of Kunchenko Stochastic Polynomials
Serhii Zabolotnii
Kunchenko's method of polynomial maximization provides a semiparametric apparatus for parameter estimation under non-Gaussian errors, but its classical power basis relies on finite…
Moment-Free Kunchenko Stochastic Polynomials via Empirical Characteristic Function
Serhii Zabolotnii
We give a characteristic-function formulation of Kunchenko's stochastic-polynomial construction for settings in which raw moments may fail to exist. In the finite-variance trigonom…
Second-Order Least Squares as a Special Case of the Polynomial Maximization Method
Serhii Zabolotnii
For linear regression with i.i.d. homoskedastic errors, optimally weighted second-order least squares (SLS) is the degree-two polynomial maximization method (PMM) estimating equati…
A Transferability Criterion for Null-Optimized Variance Reduction in Cumulant-Based Error-Independence Testing
Serhii Zabolotnii
Control-variate and polynomial-maximization (PMM) estimators are optimized at a single fixed distribution, yet they are increasingly proposed to strengthen hypothesis tests, which…
Efficient frequentist fractional polynomials for skewed dose-response and survival data: a variance-reducing alternative to OLS-FP
Serhii Zabolotnii
Fractional polynomials (FP) are a standard tool for modelling nonlinear dose-response and covariate effects, implemented in the widely used mfp package. The conventional FP fit est…
Matched generating elements in maximum entropy density reconstruction
Serhii Zabolotnii
Moment-constrained maximum entropy (MaxEnt) reconstructs a density as an exponential family whose sufficient statistics are chosen constraint functions. We study this choice separa…
Variance-Reduced Manifold Sampling via Polynomial-Maximization Density Estimation
Serhii Zabolotnii
Uniform sampling on implicitly defined manifolds is a core primitive in motion planning, constrained simulation, and probabilistic machine learning. MASEM addresses this problem by…
From Volterra Series to Kunchenko Stochastic Polynomials: Half a Century of Non-Gaussian Estimation Methodology
Serhii Zabolotnii
This paper reconstructs the half-century evolution of the scientific school founded by Yuriy P. Kunchenko (1939--2006) as the development of a semiparametric methodology for non-Ga…
EstemPMM: Polynomial Maximization Method for Non-Gaussian Regression and Time Series in R
Serhii Zabolotnii
We describe the R package EstemPMM, which implements the Polynomial Maximization Method (PMM) for parameter estimation under non-Gaussian errors. PMM exploits higher-order cumulant…
Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection
Serhii Zabolotnii
Generalized stochastic approximation replaces the log-likelihood ratio of a sequential change-point problem by an affine function of a fixed feature dictionary, whose coefficients…
Applying the Polynomial Maximization Method to Estimate ARIMA Models with Asymmetric Non-Gaussian Innovations
Serhii Zabolotnii
Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distri…