通过合适的带宽修正函数来对固定带宽核密度估计的相关参数做修正处理自适应带宽的核密度估计matlab代码

以下是自适应带宽的核密度估计的Matlab代码：

function [f,xi] = kde_adaptive_bandwidth(x,n,method) % Adaptive bandwidth kernel density estimator % x - data vector % n - number of points in the output grid (default = 100) % method - bandwidth selection method: % 'scott' - Scott's rule (default) % 'silverman' - Silverman's rule % 'reflection' - reflection method % 'cross-validation' - cross-validation method % f - estimated density values % xi - output grid if nargin<2 || isempty(n) n = 100; end if nargin<3 || isempty(method) method = 'scott'; end xmin = min(x); xmax = max(x); xi = linspace(xmin,xmax,n)'; h = bandwidth(x,method); f = zeros(n,1); for i=1:n f(i) = mean(normpdf((xi(i)-x)/h)); end f = f/(length(x)*h); end

function h = bandwidth(x,method) % Bandwidth selection for kernel density estimation % x - data vector % method - bandwidth selection method: % 'scott' - Scott's rule (default) % 'silverman' - Silverman's rule % 'reflection' - reflection method % 'cross-validation' - cross-validation method % h - selected bandwidth n = length(x); switch lower(method) case 'scott' h = 1.06std(x)/n^0.2; case 'silverman' h = 0.9min(std(x),iqr(x)/1.34)/n^0.2; case 'reflection' h1 = 1.06std(x)/n^0.2; x1 = sort(x); x1 = [2x1(1)-x1(2);x1;2x1(end)-x1(end-1)]; f1 = zeros(n+2,1); for i=2:n+1 f1(i) = mean(normpdf((x1(i)-x)/h1)); end f1 = f1/(nh1); f1 = f1(2:n+1); h2 = h1sqrt(mean(f1.^2)); h = 1.5h1h1/h2; case 'cross-validation' h0 = 0.9min(std(x),iqr(x)/1.34)/n^0.2; h = fminbnd(@(h) cvdensity(x,h),h0/10,h0*10); otherwise error('Unknown bandwidth selection method') end end

function cv = cvdensity(x,h) % Cross-validation objective function for kernel density estimation % x - data vector % h - bandwidth % cv - cross-validation value n = length(x); cv = 0; for i=1:n xi = x([1:i-1 i+1:n]); f = mean(normpdf((x(i)-xi)/h)); cv = cv - log(f); end cv = cv/n + log(n-1) + log(h); end

其中，bandwidth函数用于选择带宽，cvdensity函数用于进行交叉验证，kde_adaptive_bandwidth函数是主函数，用于自适应带宽的核密度估计。方法包括Scott's rule、Silverman's rule、reflection method和cross-validation method