* * ADAPTIVE.RPF * Partially described in RATS User's Guide, Section 13.1 * * 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))