bbemkr (version 1.3)

np_gibbs: Estimating bandwidths of the regressors and the variance of error density

Description

Implements the random-walk Metropolis algorithm to estimate the bandwidths of the regressors and the variance of the error density for finite samples

Usage

np_gibbs(data_x, data_y, xh, inicost, kerntype = c("Gaussian", "Epanechnikov", "Quartic", "Triweight", "Triangular", "Uniform"), prior_p = 2, sizep, ...)

Arguments

data_x

Regressors

data_y

Response variable

xh

Log bandwidths of the regressors

inicost

Initial cost value

kerntype

Type of kernel function. By default, Gaussian kernel is used

prior_p

A tuning parameter in the prior of the error density

sizep

A tuning parameter in the random-walk Metropolis algorithm. A large value of sizep decreases the acceptance rate, whereas a small value of sizep increases the acceptance rate

...

Other arguments

Value

• xh
  Log bandwidths of the regressors
• sigma
  Variance of the error density
• inicost
  Initial cost value
• accept_h
  Acceptance rate 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 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

bbeMCMCrecording, bbelogdensity

Examples

inicost = bbecost(data_x, data_y, nrr(data_x))
np_gibbs(data_x, data_y, nrr(data_x), inicost, prior_p = 2, sizep = 1.2)