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SUMMARY:Dr. Sc. (Technics) Serhii Zabolotnii (ORCID 0000-0003-0242-2234) (
 Cherkasy State Business College)
DTSTART:20261014T140000Z
DTEND:20261014T150000Z
DTSTAMP:20261025T111744Z
UID:AMIS/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AMIS/16/">Se
 cond-Order Least Squares and the Polynomial Maximization Method: An Estima
 ting-Equation Identity and a Higher-Degree Efficiency Reserve</a>\nby Dr. 
 Sc. (Technics) Serhii Zabolotnii (ORCID 0000-0003-0242-2234) (Cherkasy Sta
 te Business College) as part of Asymptotic Methods in Statistics\n\n\nAbst
 ract\nFor linear regression with i.i.d. homoskedastic errors\, optimally w
 eighted second-order least squares (SLS) is the degree-two polynomial maxi
 mization method (PMM) estimating equation: both select the same optimal co
 mbination of the residual e and of e^2 - sigma^2\, share one influence fun
 ction\, and attain the slope variance c_2 g_2 / N\, where g_2 = 1 - gamma_
 3^2 / (2 + gamma_4) depends only on the skewness and kurtosis of the error
  law. The identity is one of estimating equations\, not merely of asymptot
 ic variances: the Kunchenko centered-correlation matrix F_2 is the SLS wei
 ghting operator after a change of variables\, and the design-dependent fac
 tors of the SLS residual cancel in the slope score. The identity stops whe
 re the optimal combination depends on the design\; outside that scope cond
 itional SLS is the more general object. Within the polynomial moment class
 \, degree three holds an efficiency reserve: on four right-skewed laws the
  cubic direction adds between 30% and 50% asymptotic efficiency\, and unde
 r symmetric platykurtic errors it is the only informative direction\, sinc
 e g_2 = 1 there. The reserve belongs to the degree-three span\, which an e
 fficient generalized method of moments estimator also attains\; the PMM no
 rmal system is the low-dimensional route to it\, and the difference is vis
 ible at n <= 200. The talk gives the asymptotic law of the feasible plug-i
 n estimator\, a bootstrap pretest for choosing the degree\, Lean 4 checks 
 of the degree-specific algebra\, simulation evidence\, and a residual-cali
 brated study on drilling innovations from the Utah FORGE 58-32 well.\nPrep
 rint: arXiv:2606.11421\n
LOCATION:https://researchseminars.org/talk/AMIS/16/
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