## 1 Introduction
They can be divided into different classes: parametric (when \(F(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), and \(H(\zeta)\) are parameterized to within unknown parameters \(\stackrel{{\rightarrow}}{{\theta}}\)), semiparametric (when \(F(\zeta,\stackrel{{\rightarrow}}{{\theta}})\) and \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\) are parameterized, and the form of \(H(\zeta)\) is unknown), and semi-nonparametric (when the forms of \(F(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), and \(H(\zeta)\) are unknown) problems of robust statistics [6]. As to the prior distribution \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), from physical considerations, most researchers think that it belongs to the class of symmetric normal-type distributions with light or medium tails [1; 2; 3]. The dynamics of the atmosphere in the ABL depends on many significant and not always measurable parameters. In this regard, the distribution \(F(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), representing a mixture of the distributions \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\) and \(H(\zeta)\), should be referred to the nonparametric class. Traditionally, this class of problems is of great interest to scientists and has a century-old solution history [20; 21]. Typical robust problems belong to the class of semiparametric statistics, provided that the fraction \(\varepsilon\) and the distribution of the outliers \(H(\zeta)\) are unknown. In this case, the problem arises: how many sample observations, and from which side, should be trimmed to ensure the stability of the solutions obtained [12; 17; 20; 21]. For example, symmetric trimming provides unbiased estimates for the symmetric distributions \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\) and eliminates remote outliers [12; 17], but the application of these procedures for asymmetric internal outliers leads to biased and ineffective estimates [6]. The semi-nonparametric problems for the unknown forms of \(F(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\), and \(H(\zeta)\) were not considered within the framework of robust statistics [6; 12]. This is due to the fact that, for the unknown forms of the distributions \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\) and \(H(\zeta)\), the formal problem arises in the assessment of their differences. On the other hand, it should be noted that although the forms of distributions of the majority of observations \(G(\zeta,\stackrel{{\rightarrow}}{{\theta}})\) and outliers \(H(\zeta)\) are unknown, researchers usually implicitly use some additional prior information concerning these distributions (their semi-nonparametric forms) to distinguish them. For example, the information on the class of distributions \(H(\zeta)\) with external (internal) symmetric (asymmetric) outliers, and on the normal symmetric distributions \(G(\zeta,\overrightarrow{\theta})\) with light or medium tails, is often implicitly implied and allows symmetric trimming to be performed at a level of \(2\sigma\). The wind outliers, including wind gusts, are investigated using the skewness and kurtosis of their distributions [17; 18]. This additional information on the distributions should be normalized and taken into account [22; 23] to synthesize robust semi-nonparametric algorithms [12]. Hence, to estimate the kinetic wind energy components in the ABL from inhomogeneous data samples with the distribution \(F(\zeta,\overrightarrow{\theta})\), effective robust algorithms for the processing of experimental data with different levels of prior uncertainty should be developed. In the present work, new robust parametric, semiparametric, and semi-nonparametric algorithms of the weighted maximum likelihood method are used to process experimental data with different levels of a priori statistical uncertainty to estimate the kinetic wind energy components in the ABL.