Uncertain Semiparametric Model with Bernstein Polynomials

Assuming the observations are imprecise and modeling the observations by uncertain variables, this paper proposes statistical inferences for uncertain semiparametric regression model when nonparametric function is subject to monotonicity constraint. Monotonic Bernstein polynomials are used to approximate the nonparametric function and quadratic programming algorithm is used to compute the estimate. A numerical example is given to illustrate the proposed methods.