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-Gaussian estimation. Starting with Kunchenko's 1972/1973 dissertation applying Volterra series to estimate parameters of random processes, the trajectory is followed through 2006--2026. Kunchenko stochastic polynomials are presented as a coherent family of moment-cumulant procedures: the polynomial maximization method (PMM) for parameter estimation, polynomial criteria for hypothesis testing, and decomposition in spaces with a generating element. The paper details the school's structure: a verified genealogy of 15 defended dissertations, collaborations in Poland, Slovakia, and Germany, and the R package EstemPMM. A recent 2026 paper on Volterra-based signal processing is analyzed, showing how Kunchenko's nonlinear formulation reappears in applied radio engineering. We build a formal bridge between finite Volterra models and generalized Kunchenko polynomials, while separating the MMSE/L2 criterion from PMM: the former is a covariance projection for kernel adaptation, whereas PMM is a parameter-dependent moment procedure. PMM efficiency claims are stated conditionally: gains require that moments exist, the centered correlant matrix is nondegenerate, and the variance reduction coefficient is below one. The concluding research program operationalizes the historical reconstruction into testable statistical and signal-processing tasks.

翻译：本文重构了由尤里·P·昆钦科（1939–2006）创立的科学学派在半个世纪中的演进历程，将其视为非高斯估计的半参数方法论发展。从昆钦科1972/1973年将沃尔泰拉级数应用于随机过程参数估计的学位论文出发，其发展轨迹被追踪至2006–2026年。昆钦科随机多项式被呈现为一个连贯的矩-累积量程序家族：用于参数估计的多项式最大化方法（PMM）、用于假设检验的多项式准则，以及具有生成元空间中的分解。本文详述了该学派的结构：包含15篇已答辩博士论文的经核验谱系、与波兰、斯洛伐克和德国的合作，以及R包EstemPMM。对2026年一篇基于沃尔泰拉级数的信号处理论文进行分析，展示了昆钦科的非线性公式如何在应用无线电工程中重现。我们在有限沃尔泰拉模型与广义昆钦科多项式之间构建了形式化桥梁，同时将MMSE/L2准则与PMM分离：前者是用于核自适应的协方差投影，而PMM则是一种参数依赖的矩程序。PMM的效率声明具有条件性：其增益要求矩存在、中心相关矩阵非退化且方差缩减系数小于1。结论性的研究计划将历史重构转化为可检验的统计与信号处理任务。