bbemkr (version 2.0)

gibbs_admkr_nw: Estimating bandwidths of the regressors

Description

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

Usage

gibbs_admkr_nw(xh, inicost, k, mutsizp, prob, data_x, data_y)

Arguments

xh

Log of square bandwidths in the regression function

inicost

Cost value

k

Iteration number

mutsizp

Step size of random-walk Metropolis algorithm

prob

Optimal convergence rate for drawing single or multiple parameters

data_x

Regressors

data_y

Response variable

Value

x

Estimated bandwidths of the regression function

cost

Cost value, that is negative of log posterior

accept_h

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

mutsizp

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_erro