Bayesian Bandwidth Adjusted Factor and Order Selection for Multivariate Nonparametric Models Based on Local Robust Weights
Local polynomial regression estimation is one of the commonly used non-parametric regression estimation methods.To estimate the local polynomial regression,it is necessary to select the order of the polynomial and the bandwidth of the kernel function.Nevertheless,at present,most scholars focus on the method of bandwidth selection,while the researches select both of the order of polynomial and the bandwidth at the same time are less.In order to solve this problem,based on the existing research,a local robust weighted polynomial estimation based on the Bayesian bandwidth adjust factor is proposed.A random walk metropolis algorithm is used to estimate the complex posterior probability density of the bandwidth adjusted factor.Combined with the cross-validation method,the order of the polynomial and the bandwidth adjust factor are selected and estimated at the same time.Numerical simulations are performed through two and three dimension of non-parametric models,and empirical analysis of option data is provided.Compared with traditional cross-validation rules,the feasibility of the proposed method is confirmed.
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