Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating linear functionals in nonlinear regression with responses
  missing at random   We consider regression models with parametric (linear or nonlinear)
regression function and allow responses to be ``missing at random.'' We assume
that the errors have mean zero and are independent of the covariates. In order
to estimate expectations of functions of covariate and response we use a fully
imputed estimator, namely an empirical estimator based on estimators of
conditional expectations given the covariate. We exploit the independence of
covariates and errors by writing the conditional expectations as unconditional
expectations, which can now be estimated by empirical plug-in estimators. The
mean zero constraint on the error distribution is exploited by adding suitable
residual-based weights. We prove that the estimator is efficient (in the sense
of H\'{a}jek and Le Cam) if an efficient estimator of the parameter is used.
Our results give rise to new efficient estimators of smooth transformations of
expectations. Estimation of the mean response is discussed as a special
(degenerate) case.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph