TY - JOUR
T1 - Semiparametric quasilikelihood and variance function estimation in measurement error models
AU - Sepanski, J. H.
AU - Carroll, R. J.
N1 - Funding Information:
Correspondence to: R.J. Carroll, Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA. *This paper is based on the first author’s Ph.D. thesis at Texas A&M University. Her research and that of the second author was supported by a grant from the National Institutes of Health. The authors would like to express their sincere thanks to a referee for a careful reading of the manuscript and useful comments.
PY - 1993/7
Y1 - 1993/7
N2 - We consider a quasilikelihood/variance function model when a predictor X is measured with error and a surrogate W is observed. When in addition to a primary data set containing (Y,W) a validation data set exists for which (X,W) is observed, we can (i) estimate the first and second moments of the response Y given W by kernel regression; (ii) use quasilikelihood and variance function techniques to estimate the regression parameters as well as variance structure parameters. The estimators are shown to be asymptotically normally distributed, with asymptotic variance depending on the size of the validation data set and not on the bandwith used in the kernel estimates. A more refined analysis of the asymptotic covariance shows that the optimal bandwidth converges to zero at the rate n- 1 3.
AB - We consider a quasilikelihood/variance function model when a predictor X is measured with error and a surrogate W is observed. When in addition to a primary data set containing (Y,W) a validation data set exists for which (X,W) is observed, we can (i) estimate the first and second moments of the response Y given W by kernel regression; (ii) use quasilikelihood and variance function techniques to estimate the regression parameters as well as variance structure parameters. The estimators are shown to be asymptotically normally distributed, with asymptotic variance depending on the size of the validation data set and not on the bandwith used in the kernel estimates. A more refined analysis of the asymptotic covariance shows that the optimal bandwidth converges to zero at the rate n- 1 3.
UR - http://www.scopus.com/inward/record.url?scp=38249001357&partnerID=8YFLogxK
U2 - 10.1016/0304-4076(93)90120-T
DO - 10.1016/0304-4076(93)90120-T
M3 - Article
AN - SCOPUS:38249001357
SN - 0304-4076
VL - 58
SP - 223
EP - 256
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1-2
ER -