Abstract
In nonparametric regression estimation, the estimation of the derivatives of regression curve is already investigated. As the domain of density function is bounded, it is known that the kernel regression estimator of Mack and Muller (1989) will also encounter the problem of the boundary effects for the estimation of the derivatives. In order to improve the boundary effects and bias reduction, one follow the idea of the minimizing quadratic form to construct a new kernel regression estimator in this paper. The new proposed estimator, the compact form of the asymptotic bias, the asymptotic variance and some properties are given. Besides, the proposed estimator will not produce the boundary effects and be improved the kernel regression estimator of Mack and Muller (1989) as above, its convergence rate is achieved(abbreviate equation)
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