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.Comment: Published in at http://dx.doi.org/10.1214/08-AOS627 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Abstract. Climate warming is changing streamflow regimes and groundwater storage in cold alpine regions. In this study, the Yangbajain headwater catchment in the Lhasa River basin is adopted as the study area to assess streamflow changes and active groundwater storage in response to climate warming. The results show that both annual streamflow and the mean air temperature increase significantly at respective rates of about 12.30 mm per decade and 0.28 ∘C per decade from 1979 to 2013 in the study area. The results of gray relational analysis indicate that the air temperature acts as a primary factor for the increased streamflow. Due to climate warming, the total glacier volume has retreated by over 25 % during the past 50 years, and the areal extent of permafrost has degraded by 15.3 % over the last 20 years. Parallel comparisons with other subbasins in the Lhasa River basin indirectly reveal that the increased streamflow at the Yangbajain Station is mainly fed by the accelerated glacier retreat. Using baseflow recession analysis, we also find that the estimated groundwater storage that is comparable with the GRACE data increases significantly at rates of about 19.32 mm per decade during the abovementioned period. That is to say, as permafrost thaws, more spaces have been made available to accommodate the increasing meltwater. Finally, a large water imbalance (of more than 5.79×107 m3 a−1) between the melt-derived runoff and the actual increase in runoff as well as the groundwater storage is also observed. The results from this study suggest that the impacts of glacial retreat and permafrost degradation show compound behaviors on the storage–discharge mechanism due to climate warming, and that this fundamentally affects the water supply and the mechanisms of streamflow generation and change.

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