  In this paper, we propose a covariate-adjusted nonlinear regression model. In
this model, both the response and predictors can only be observed after being
distorted by some multiplicative factors. Because of nonlinearity, existing
methods for the linear setting cannot be directly employed. To attack this
problem, we propose estimating the distorting functions by nonparametrically
regressing the predictors and response on the distorting covariate; then,
nonlinear least squares estimators for the parameters are obtained using the
estimated response and predictors. Root $n$-consistency and asymptotic
normality are established. However, the limiting variance has a very complex
structure with several unknown components, and confidence regions based on
normal approximation are not efficient. Empirical likelihood-based confidence
regions are proposed, and their accuracy is also verified due to its self-scale
invariance. Furthermore, unlike the common results derived from the profile
methods, even when plug-in estimates are used for the infinite-dimensional
nuisance parameters (distorting functions), the limit of empirical likelihood
ratio is still chi-squared distributed. This property eases the construction of
the empirical likelihood-based confidence regions. A simulation study is
carried out to assess the finite sample performance of the proposed estimators
and confidence regions. We apply our method to study the relationship between
glomerular filtration rate and serum creatinine.
