## 概率密度函数的非参数估计及R语言图形展示

Title Nonparametric estimation of probability density function  and R language graphics display
Abstract
On the basis of probability theory and mathematical statistics and multivariate statistical analysis, this topic is to estimate the probability density function using sample data under the condition of random variables with unknown distribution.This paper introduces several common methods of nonparametric density estimation,such as histogram density estimation, kernel density estimation, the k-nearest neighbour estimation etc. It also discusses the optimal bandwidth selection principles by minimizing mean square error. On the basis of those,we search for the service life of the lighting samples as the actual data, estimate the probability density function, and use MATLAB to display the estimated graphics.After verification,the histogram density estimation results are not smooth and slow convergence.K-nearest neighbor estimation is more suitable for classification problems.Kernel density estimation can solve the problem faced by the histogram,and the result is more ideal.At last,the two-dimensional case is discussed and a set of 2D dates are estimated.

Keywords  nonparametric density estimation    bandwidth  histogram density estimation    kernel density estimation    the k-nearest neighbour estimation

1  引言    1
1.1  研究现状    1
1.2  背景知识    2
2  非参数密度估计方法    4
2.1  直方图密度估计    4
2.2  核密度估计    7
2.3   k-近邻估计    12
3  数据集的选取及图形展示    15
3.1  数据集的选取    15
3.2  直方图密度估计结果    15
3.3  核密度估计结果    17
4  二维密度函数估计    23
4.1  二维直方图估计法    23
4.2  二维核密度估计法    23
4.3  实例分析    25

1  引言

------分隔线----------------------------