Fan, Jianqing; Truong, Young K. Nonparametric regression with errors in variables. (English) Zbl 0791.62042 Ann. Stat. 21, No. 4, 1900-1925 (1993). Summary: The effect of errors in variables in nonparametric regression estimation is examined. To account for errors in covariates, deconvolution is involved in the construction of a new class of kernel estimators. It is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution.In fact, there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth. It is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate, which is rich enough for many practical applications. Furthermore, to achieve optimality, we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators. Cited in 140 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62J99 Linear inference, regression Keywords:errors in variables; nonparametric regression; errors in covariates; deconvolution; new class of kernel estimators; optimal local and global rates of convergence; tail behavior; characteristic function; error distribution; ordinary smooth; super smooth; lower bound × Cite Format Result Cite Review PDF Full Text: DOI