Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a class of estimators, consistent simultanously for both a semiparametric distribution and a distinct parametric distribution, is proposed. These efficient estimators are robust to both gross errors and departures from parametric assumptions, making them ideal for estimating the mean and central moments of common unimodal distributions. This article also illuminates the understanding of the common nature of probability distributions and the measures of them.

In descriptive statistics, U -statistics arise naturally in producing minimum-variance unbiased estimators. In 1984, Serfling considered the distribution formed by evaluating the kernel of the U -statistics and proposed generalized L-statistics which includes Hodges-Lehamnn estimator and Bickel-Lehmann spread as special cases. However, the structures of the kernel distributions remain unclear. In 1954, Hodges and Lehmann demonstrated that if X and Y are independently sampled from the same unimodal distribution, X − Y will exhibit symmetrical unimodality with its peak centered at zero. Building upon this foundational work, the current study delves into the structure of the kernel distribution. It is shown that the kth central moment kernel distributions (k > 2) derived from a unimodal distribution exhibit location invariance and is also nearly unimodal with the mode and median close to zero. This article provides an approach to study the general structure of kernel distributions.

Timely and accurate information on tree species is crucial for the sustainable management of natural resources, forest inventory, biodiversity detection, and carbon stock calculation. The advancement of remote sensing technology and artificial intelligence has facilitated the acquisition and analysis of remote sensing data, resulting in more precise and effective classification of tree species. Multimodal remote sensing data and deep learning seem to be the current tree species classification research mainstream, whether or not. The current review on the remote sensing data and deep learning tree species classification methods perspectives to analyze the unimodal and multimodal remote sensing data and classification methods in this realm is missing. To bridge the gap, we search for major trends in the remote sensing data and tree species classification methods, provide a detailed overview of classic deep learning-based methods for tree species classification, and discuss the limitations.