A method of robust nonparametric estimations of wind velocity functionals and their confidence intervals is suggested in the report that allows the estimations to be adapted depending on the initial functional distribution and outliers. It is shown that standard methods of data processing lead to considerable shift of location and low efficiency of the estimations in comparison with the nonparametric estimations of the weighed maximum likelihood method.
Since the late 70s, Doppler sodars have been widely used to study the statistical characteristics of wind velocity field in the atmospheric boundary layer and to analyze their dynamics. However, the distribution functions of the wind velocity components are asymmetric with the presence of outliers, which significantly reduces the efficiency of application of the classical parametric methods of statistics. In the report, an algorithm is suggested for nonparametric robust estimations of the first four moments of wind velocity components and their confidence intervals from minisodar measurements in the atmospheric boundary layer.
The application of robust methods of statistics to processing of data of minisodar measurements of vertical profiles of three wind velocity components at altitudes 5–200 m is considered in the report. The statistical characteristics of three wind velocity components obtained using nonparametric methods based on the weighted maximum likelihood method and classical methods are analyzed. Results of minisodar data processing showed that the standard methods of processing lead to considerable bias and low efficiency of estimations in comparison with the nonparametric WMLM estimations.
In the report the spatiotemporal dynamics of three components of wind velocity vector retrieved from Doppler minisodar measurements in the atmospheric boundary layer is analyzed. Robust nonparametric methods of data processing based on the weighed maximum likelihood method (WMLM) are used for analysis. It is demonstrated that the efficiency (mean square error, MSE) of the adaptive estimates of the parameters of wind velocity components measured by the sodar based on the WMLM is much higher that the efficiency of the classical parametric estimates based on the LSM.
In this report the identification problem of laser and acoustic sounding of the atmosphere is considered in the presence of outliers in experimental data. The efficiency of estimates of the regression by the weighed method of maximum likelihood is investigated. Expressions for the efficiency of estimates are derived. It is demonstrated that the estimates of the regression by the weighed maximum likelihood method are more efficient in comparison with a number of well-known robust estimates for the examined outlier distributions, both symmetric and asymmetric.
The problem of testing the hypothesis H<sub>0</sub>: θ = θ<sub>0</sub> against the alternative hypothesis H<sub>1</sub>:θ<sub>l</sub>=θ<sub>0</sub>+▵(√N)<sup>-1</sup> is examined for the Shurygin noise model, where θ =T(Fθ) is an unknown parameter. In the present report, a class of
criteria robust in the sense of the significance value and power density function is considered for parametric and
nonparametric problem formulation on statistics of the form S<sub>N</sub>=√N((θ<sub>N</sub>-θ)/(√V(θ<sub>N</sub>))), where V(θ<sub>N</sub>) is the θ<sub>N</sub> variance and
θ<sub>N</sub> =T(F<sub>N</sub>) is the robust parametric or nonparametric estimate of the parameter θ =T(Fθ) obtained by the weighted
maximum likelihood method.
An analysis of the radicalness criteria and robust estimation algorithms allows us to conclude that all these estimates can
be derived based on the weighted maximum likelihood method (WMLM) with the estimation function of the form (see manuscript for formula). In the present study, robust estimates of shifts and scales are synthesized in the class of Student's global supermodels and approximately normal distributions depending on the radicalness parameter <i>l</i>. Algorithms of adaptive robust estimates are suggested. They allow estimates to be adapted to distribution types and local deviations.
In the present study, a class of nonparametric robust estimates of the shift and scale parameters (μ, S) of the form (please see manuscript for formula) is synthesized by the weighted maximum likelihood method based on parametric density estimates, where (see manuscript for formula) are the Walsh half-sums, K(u) is the kernel function, and W(u) is the weighting function: (see formula in manuscript.) The radicalness parameter <i>I</i> determines the weighting functions W(z<sub>ij</sub>) executing the process of soft truncation of the estimates depending on <i>a priori </i>information on outliers: the estimates converge to maximum likelihood estimates (MLE) at <i>l</i> = 1 and to radical estimates at <i>l</i> = 0.5. The adaptive estimates converge to radical ones. They belong to the class of nonparametric estimates of implicit parameters, and their
study is performed based on the generalized M-estimates.