Distribution-free properties of some asymptotic cumulants for the Mallows Cp and its modifications in usual and ridge regression.
Distribution-free properties of some asymptotic cumulants for the Mallows Cp and its modifications in usual and ridge regression.
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Mallows Cp 的一些渐近累积量的无分布特性及其在通常回归和岭回归中的修改。
DOI：
10.1007/s41237-016-0005-5
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
H.
中科院分区：
文献类型：
--
作者：
Ogasawara;H.
在具有非负岭参数的多元多元线性回归中，当模型不足指定时，在非正态分布下，MlowsCp及其修正的渐近偏差可得到O(1)阶。对于一个不低于规定的模型，渐近偏差的阶数较小，并且被证明是无分布的。同样，在后一种情况下，统计量的阶数O(1)的公共渐近方差是无分布的。结果表明，无论脊线参数如何，上述结果都成立。正态分布和非正态分布下的数值模拟结果相似。仿真结果表明，在非正态分布情况下，模型的选择是稳健的。
In multivariate multiple linear regression with a non-negative ridge parameter, when a model is underspecified, the asymptotic biases of the MallowsCpand its modifications are derived up to orderO(1) under non-normality. For a not underspecified model, the asymptotic biases are of smaller order and are shown to be distribution free. Similarly, under the latter condition, the common asymptotic variance of orderO(1) for the statistics is distribution free. It is shown that the above results hold irrespective of the ridge parameter. Numerical illustrations with simulations under normality and non-normality give similar simulated results. These results justify the robust correct model selection under non-normality shown by simulations.