Consider the design problem for estimation and extrapolation in approximately linear regression models with possible misspecification. The design space is a discrete set consisting of finitely many points, and the mod...Consider the design problem for estimation and extrapolation in approximately linear regression models with possible misspecification. The design space is a discrete set consisting of finitely many points, and the model bias comes from a reproducing kernel Hilbert space. Two different design criteria are proposed by applying the minimax approach for estimating the parameters of the regression response and extrapolating the regression response to points outside of the design space. A simulated annealing algorithm is applied to construct the minimax designs. These minimax designs are compared with the classical D-optimal designs and all-bias extrapolation designs. Numerical results indicate that the simulated annealing algorithm is feasible and the minimax designs are robust against bias caused by model misspecification.展开更多
In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a b...In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.展开更多
In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and ...In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and construct circular neighbor-balanced designs (CNBDs) by the method of cyclic shifts or sets of shifts. An important feature of this method is that the properties of a design can be easily obtained from the sets of shifts instead of constructing the actual blocks of the design. That is, the off-diagonal elements of the concurrence matrix can be easily obtained from the sets of shifts. Since the suggested designs are circular, balanced and binary, so they are universally optimal.展开更多
基金Supported by National Natural Science Foundation of China(11471216,11301332)E-Institutes of Shanghai Municipal Education Commission(E03004)+1 种基金Central Finance Project(YC-XK-13105)Shanghai Municipal Science and Technology Research Project(14DZ1201902)
文摘Consider the design problem for estimation and extrapolation in approximately linear regression models with possible misspecification. The design space is a discrete set consisting of finitely many points, and the model bias comes from a reproducing kernel Hilbert space. Two different design criteria are proposed by applying the minimax approach for estimating the parameters of the regression response and extrapolating the regression response to points outside of the design space. A simulated annealing algorithm is applied to construct the minimax designs. These minimax designs are compared with the classical D-optimal designs and all-bias extrapolation designs. Numerical results indicate that the simulated annealing algorithm is feasible and the minimax designs are robust against bias caused by model misspecification.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10671007,10471127)Zhejiang Provincial Natural Science Foundation of China (Grant No. R604001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China and a CERG grant from Research Grants Council of Hong Kong
文摘In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.
文摘In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and construct circular neighbor-balanced designs (CNBDs) by the method of cyclic shifts or sets of shifts. An important feature of this method is that the properties of a design can be easily obtained from the sets of shifts instead of constructing the actual blocks of the design. That is, the off-diagonal elements of the concurrence matrix can be easily obtained from the sets of shifts. Since the suggested designs are circular, balanced and binary, so they are universally optimal.
