bbemkr (version 1.5)

np_gibbs: Estimating bandwidths of the regressors

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

Value

• x
• 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

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.

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.

See Also

mcmcrecord, logdensity, loglikelihood, logpriors