ALL‐BIAS DESIGNS FOR POLYNOMIAL SPLINE REGRESSION MODELS
ALL‐BIAS DESIGNS FOR POLYNOMIAL SPLINE REGRESSION MODELS
复制标题
多项式样条回归模型的全偏差设计
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Lewis
中科院分区：
文献类型：
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作者：
D. Woods;S. Lewis
当简单多项式模型不适用时，低次多项式样条回归模型在科学和工程设计实验的响应建模中已被证明是有用的。如果样条曲线的节点或断点的数量和位置存在不确定性，则最大限度地减少模型误设定导致的系统误差的设计可能是适当的。本文给出了当假设模型和真实模型中的不同节点来自某个特定集合时，构造单变量样条的全偏设计的一种方法。根据结间区间定义了一类设计，并得到了该类设计在线性、二次和三次样条模型下为全偏设计的充分条件。给出了一个构造全偏设计的例子。
Polynomial spline regression models of low degree have proved useful in modeling responses from designed experiments in science and engineering when simple polynomial models are inadequate. Where there is uncertainty in the number and location of the knots, or breakpoints, of the spline, then designs that minimize the systematic errors resulting from model misspecification may be appropriate. This paper gives a method for constructing such all‐bias designs for a single variable spline when the distinct knots in the assumed and true models come from some specified set. A class of designs is defined in terms of the inter‐knot intervals and sufficient conditions are obtained for a design within this class to be all‐bias under linear, quadratic and cubic spline models. An example of the construction of all‐bias designs is given.