*
* ADAPTIVE.RPF
* RATS Version 8, User's Guide, Example 13.2
* Adapted from Pagan and Ullah, Nonparametric Econometrics, Cambridge, 1999,
* pp 250-251.
*
open data housing.csv
data(format=prn,org=columns) 1 59 price age aircon baths bedrms cond corner $
  culd dish fence firepl floors garage irreg lajolla lndry patio pool rooms $
  sprink sqft view yard
set lsqft = log(sqft)/log(10)
set lyard = log(yard)/log(10)
*
* Estimate linear regression with White standard errors
*
linreg(robusterrors) price / resids
# sqft yard pool lajolla baths firepl irreg sprink view lsqft lyard constant
*
* Adaptive kernel estimator. For the regression equation y=Xb+u, if the
* density of u is the (unknown) f, the gradient of the log likelihood is
* - sum {x(t) f'(u(t))/f(u(t)}. The adaptive kernel estimator is a
* two-step estimator starting with OLS and using kernel estimates of
* psi=f'/f.
*
* We need to compute the density at the given data points, so grid=input
* is used with the resids providing the evaluation points.
*

density(type=gauss,derives=f1,grid=input) resids / resids fu
set psi = f1/fu
*
* The information matrix is computed by using MCOV with the NOZUDEP
* option as u and X are assumed to be independent.
*
mcov(lastreg,matrix=ibxx,nozudep) / psi
*
* The same but with ZUDEP is needed for the center of the "sandwich".
* We also need the gradient, which will be %nobs * the mean vector of
* the products of psi with the regressors.
*
mcov(lastreg,matrix=ib,meanvector=mv) / psi
compute d=mv*%nobs
*
* Display the regression output with the adjusted beta and sandwich
* estimator of the covariance matrix.
*
linreg(create,lastreg,form=chisquared,title="Adaptive Kernel Estimator",$
  coeffs=%beta-inv(ibxx)*d,covmat=inv(ibxx)*ib*inv(ibxx))