bbemkr (version 2.0)

gibbs_admkr_erro: Estimating bandwidth of the kernel-form error density

Description

Implements the random-walk Metropolis algorithm to estimate the bandwidth of the kernel-form error density

Usage

gibbs_admkr_erro(xh, inicost, k, errorsizp, errorprob, data_x, data_y)

Arguments

xh

Log of square bandwidth in the kernel-form error density

inicost

Cost value

k

Iteration number

errorsizp

Step size of random-walk Metropolis algorithm

errorprob

Optimal convergence rate for drawing single or multiple parameters

data_x

Regressors

data_y

Response variable

Value

x

Estimated bandwidth of the kernel-form error density

cost

Cost value, that is negative of log posterior

accept_erro

Accept or reject. accept_erro = 1 indicates acceptance, while accept_erro = 0 indicates rejection.

errorsizp

Step size of the random-walk Metropolis algorithm

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 bandwidth of the kernel-form 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.

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_admkr, logdensity_admkr, loglikelihood_admkr, logpriors_admkr, gibbs_admkr_nw