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大型系统的实验设计与观测AI 解读

SUMMARY Large systems require new methods of experimental designs suitable for the highly adaptive models which are employed to cope with complex non-linear responses and high dimensionality of input spaces. The area of computer experiments has started to provide such designs especially Latin hypercube and lattice designs. System decomposition, prevalent in several branches of engineering, can be employed to decrease complexity. A combination of system decomposition using a…

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一维自回归误差过程下的最优与极小极大精确处理设计AI 解读

A theory is developed following work by Williams (1952) and Kiefer (1960) for exact treatment designs in one dimension in which the errors are a stationary process. It is shown that the designs which achieve the minimax value of any of a wide class of functionals on the information matrix for estimation of treatment differences have a special property. If the process is autoregressive of order $p$ then a random piece of the design of length $p + 1$ exhibits uncorrelated…

一维多项式回归的精确置信带AI 解读

An exact piecewise polynomial simultaneous confidence band is described for one-dimensional (p—1)th order polynomial regression. The band is constructed by placing intervals around the estimated response at the zeros of the pth order orthogonal polynomial with respect to the design points. Since under the usual assumptions the response estimates are uncorrelated at these zeros, the construction of the exact band in the normal case is made easy.

有限总体的连通抽样方案AI 解读

Plans for sampling a finite population without replacement are called disconnected if the population separates into twodisjoint sets such that a sample cannot contain units from both sets. It is shown that disconnected plans can achieve, under certain conditions, a maximum variance for the Horvitz-Thompson estimator not achieved by connected plans. Under these conditions simple random sampling is minimax. No plan, however, gives uniformly minimum variance.

有限总体的连通抽样方案AI 解读

Plans for sampling a finite population without replacement are called disconnected if the population separates into twodisjoint sets such that a sample cannot contain units from both sets. It is shown that disconnected plans can achieve, under certain conditions, a maximum variance for the Horvitz-Thompson estimator not achieved by connected plans. Under these conditions simple random sampling is minimax. No plan, however, gives uniformly minimum variance.