DIMENSION REDUCTION IN A SEMIPARAMETRIC REGRESSION MODEL WITH ERRORS IN COVARIATES

摘要: We consider a semiparametric estimation method for general regression models when some of the predictors are measured with error. The technique relies on kernel "true" covariate all observed covariates and surrogates. This requires nonparametric in as many dimensions there usual theory copes such higher-dimensional problems by using higher-order kernels, but this is unrealistic most problems. show that essentially good one can do technique. Instead we propose use dimension reduction techniques. assume depends only linear combination If were known, could apply one-dimensional versions problem, which standard kernels applicable. if estimate directions at root-$n$ rate, then asymptotically resulting estimator parameters main model behaves known. Simulations lend credence to asymptotic results.