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bbemkr (version 2.0)

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
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

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.

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