Nonparametric regression analysis is a useful method to explore the relationships among the variables when a parametric form is not known. Assuming the observations of the model are imprecise and modeling the observed data via uncertain variables, this paper proposes least squares estimation of uncertain nonparametric regression model to explore the functional relationships between response variable and explanatory variable. In particular, we employ B-Splines and local polynomials to approximate the nonparametric function, respectively. Estimation of unknown function can be obtained as a solution of least squares and quadratic programming algorithm can be used to compute efficiently the estimator. Numerical examples are given to illustrate the proposed methods.

当不知道参数形式时，非参数回归分析是探索变量之间关系的有用方法。假设模型的观测不精确，并通过不确定变量对观测数据建模，本文提出了不确定非参数回归模型的最小二乘估计，以探讨响应变量与解释变量之间的函数关系。特别是，我们分别采用B样条和局部多项式来逼近非参数函数。可以通过最小二乘的解来获得未知函数的估计，并且可以使用二次规划算法来有效地计算估计量。数值例子说明了所提出的方法。