Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 agains...Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 againstθ>θ_0, we have found a class of truncated sequential tests with probability of the first kindof error not exceeding α, the expected observation time of tests being asymptoticallyminimal as α ↓0.展开更多
Consider the regression model y_i=x_iβ+g(t_i)+e_i for i=1,2,...,n. Here g(·) is an unknown function, β is a parameter to be estimated, and e_i are random errors. Based on g(·) estimated by kernel type esti...Consider the regression model y_i=x_iβ+g(t_i)+e_i for i=1,2,...,n. Here g(·) is an unknown function, β is a parameter to be estimated, and e_i are random errors. Based on g(·) estimated by kernel type estimator for the case where (x_i,t_i) are i. i. d. design points, the adaptive estimator of β is investigated, and some results about the asymptotically optimal convergence rates of the estimates are also obtained. In the meantime, the family of nonparametric estimates of g(·) including the known kernel and nearest neighbor estimates is proposed. Based on the nonparametric estimate for the case that (x_i,t_i) are known and nonrandom, the asymptotic normality of least squares estimator of β is proved.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 againstθ>θ_0, we have found a class of truncated sequential tests with probability of the first kindof error not exceeding α, the expected observation time of tests being asymptoticallyminimal as α ↓0.
基金Project sunoorted by the National Natural Science Foundation of China
文摘Consider the regression model y_i=x_iβ+g(t_i)+e_i for i=1,2,...,n. Here g(·) is an unknown function, β is a parameter to be estimated, and e_i are random errors. Based on g(·) estimated by kernel type estimator for the case where (x_i,t_i) are i. i. d. design points, the adaptive estimator of β is investigated, and some results about the asymptotically optimal convergence rates of the estimates are also obtained. In the meantime, the family of nonparametric estimates of g(·) including the known kernel and nearest neighbor estimates is proposed. Based on the nonparametric estimate for the case that (x_i,t_i) are known and nonrandom, the asymptotic normality of least squares estimator of β is proved.
