Asymptotics of a wavelet estimator in the nonparametric regression model with repeated measurements under a NA error process

作者：Zhou Xing cai^*; Lin Jin guan

来源：Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas, 2015, 109(1): 153-168.

DOI：10.1007/s13398-014-0172-8

• Wavelet estimator
• Nonparametric model
• Repeated measurements
• NA error

Consider the nonparametric regression model with repeated measurements: Y-(j)(x(ni)) = g (x(ni)) + e((j)) (x(ni)), where Y-(j)(x(ni)) is the jth response at the point x(ni), x(ni)'s are known and nonrandom, and g(.) is unknown function defined on a closed interval [0, 1]. For exhibiting the correlation among the units and avoiding any assumptions among the observations within the same unit, we consider the model with negative associated (NA) error structures, that is, {e((j))(x), j >= 1} is a mean zero NA error process. The wavelet procedures are developed to estimate the regression function. Some asymptotics of wavelet estimator are established under suitable conditions.

• 出版日期2015
• 单位铜陵学院; 东南大学