Kernel density estimates are boundary effects when estimating the boundary regions.

Based on the univariate kernel density estimation,A predictive model of value-at-risk can be built.By weighting the kernel density estimates coefficients of variation, predictive models for different values-at-risk can be built.

The problem of solving the distribution density function of a random variable from a given set of sample points is one of the basic problems of probability statistics.Solutions to this problem includeparametric estimation and non-parametric estimation.Parameter estimation can be further divided into parametric regression analysis and parametric discriminant analysis.In parametric regression analysis, one assumes that the data distribution conforms to a particular property, such as linear, differentiable linear or exponential property, etc.Then find a specific solution in the family of objective functions, i.e., determine the unknown parameters in the regression model.In parametric discriminant analysis, one needs to assume that the randomly valued data samples on which the discriminant is based obey a specific distribution in each of the possible classes. Experience and theory illustrate that there is often a large gap between such basic assumptions of parametric models and actual physical models, and these methods do not always achieve satisfactory results. Due to these shortcomings, Rosenblatt and Parzen proposed nonparametric estimation methods, namely kernel density estimation methods.

Since the kernel density estimation method does not use a priori knowledge about the data distribution and does not attach any assumptions to the data distribution, it is a method to study the characteristics of the data distribution from the data sample itself, and therefore, it is highly valued in both statistical theory and application fields. Since the kernel density estimation method does not use a priori knowledge about the data distribution and does not attach any assumptions to the data distribution, it is a method to study the characteristics of the data distribution from the data sample itself, and is therefore highly valued in both theoretical and applied fields of statistics.