Minimax optimal designs for nonparametric regression - a further optimality property of the uniform distribution
نویسندگان
چکیده
In the common nonparametric regression model yi g ti ti i i n with i i d noise and nonrepeatable design points ti we consider the problem of choosing an optimal design for the estimation of the regression function g A minimax approach is adopted which searches for designs minimizing the maximum of the asymptotic integrated mean squared error where the maximum is taken over an appropriately bounded class of functions g The minimax designs are found explicitly and for certain special cases the optimality of the uniform distribution can be established
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