np_gibbs: Estimating bandwidths of the regressors

In bbemkr: Bayesian bandwidth estimation for multivariate kernel regression with Gaussian error

Description

Implements the random-walk Metropolis algorithm to estimate the bandwidths of the regressors

Usage

np_gibbs(xh, inicost, k, mutsizp, prob, data_x, data_y, prior_p, prior_st)

Arguments

xh	Log of square bandwidths
inicost	Cost value
k	Iteration number
mutsizp	Step size of random-walk Metropolis algorithm
prob	Optimal covergence rate
data_x	Regressors
data_y	Response variable
prior_p	Hyperparameter used in the inverse-gamma prior
prior_st	Hyperparameter used in the inverse-gamma prior

Details

1) The log bandwidths of the regressors are initialized using the normal reference rule of Silverman (1986).

2) Conditioning on the variance parameter of the error density, we implement random-walk Metropolis algorithm to update the bandwidths, in order to achieve the minimum cost value.

3) The variance of the error density can be directly sampled.

4) Iterate steps 2) and 3) until the cost value is minimized.

5) Check the convergence of the parameters by examining the simulation inefficient factor (sif) value. The smaller the sif value is, the better convergence of the parameters is.

Value

x	Estimated bandwidths of the regression function
sigma2	Estimated variance of the normal error density
cost	Cost value
accept_h	Accept or reject. accept_h=1 indicates acceptance, while accept_h=0 indicates rejection.
mutsizp	Step size of random-walk Metropolis

Author(s)

Han Lin Shang

References

X. Zhang and R. D. Brooks and M. L. King (2009) A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation, Journal of Econometrics, 153, 21-32.

B. W. Silverman (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York.

See Also

mcmcrecord_gaussian, logdensity_gaussian, loglikelihood_gaussian, logpriors_gaussian

bbemkr documentation built on May 1, 2019, 10:53 p.m.