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In this article, we develop estimation approaches for nonparametric multiple regression measurement error models when both independent validation data on covariables and primary data on the response variable and surrogate covariables are available. An estimator which integrates Fourier series estimation and truncated series approximation methods is derived without any error model structure assumption between the true covariables and surrogate variables. Most importantly, our proposed methodology can be readily extended to the case that only some of covariates are measured with errors with the assistance of validation data. Under mild conditions, we derive the convergence rates of the proposed estimators. The finite-sample properties of the estimators are investigated through simulation studies.
Melatonin, as an endogenous hormone produced mainly in the pineal gland in a clear circadian fashion, has diverse physiological functions, such as the control of circadian rhythms, sleep regulation, antioxidant, etc. Recently, accumulating researches about melatonin and pain have been reported. In this review, comparison and summary about analgesic/proalgesic effect of melatonin in inflammatory and neuropathic pain will be made. Some possible pathways of melatonin involved in dual pain modulation might help to explain all these conflicting results in various situations.