A closed-form orthogonality condition K0^T mu_a,H1 = 0 determines unbiased transfer of null-optimized variance reduction to the alternative; application to the Wiedermann-Shi cumulant test shows a second-order PMM correction is inconsistent under the alternative due to nonzero auxiliary means.
Parametrically Adaptive Transition Polynomial: a Signed-Parity Continuous-alpha Extension of Kunchenko Stochastic Polynomials
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abstract
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 higher-order integer moments. This paper introduces the Parametrically Adaptive Transition Polynomial (PATP), a signed-parity fractional-power family controlled by a continuous parameter alpha in [0,1]. The quadratic exponent map p_i(alpha) connects the fractal regime p_i(0)=1/i, the degenerate linear point p_i(1/2)=1, and the signed-parity integer-power regime p_i(1)=i. For the degree-S=2 case we derive a closed-form variance-reduction coefficient g_2(alpha) in terms of signed and absolute fractional moments, identify the singular behavior at alpha=1/2, and state the moment and regularity conditions under which the formula is meaningful. The construction should be read as a Form-B PATP analogue within Kunchenko's generalized apparatus, not as an exact recovery of the canonical even-power PMM basis at alpha=1. Numerical illustrations on canonical distributions are used to examine the finite-sample behavior of the signed-parity estimator and to mark the boundary of applicability for extremely heavy-tailed cases such as Cauchy.
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stat.ME 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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