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Invariance principles and almost sure central limit theorem for the error variance estimator in linear models |
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| Authors: | Yu Miao Wei-Qiang Geng Saralees Nadarajah |
| Affiliation: | 1. College of Mathematics and Information Science, Henan Normal University, XinXiang, Chinayumiao728@gmail.com;3. College of Mathematics and Information Science, Henan Normal University, XinXiang, China;4. School of Mathematics, University of Manchester, Manchester, UK |
| Abstract: | A number of score statistics are derived for a heterogeneous spatial Poisson process which has a composite intensity. The intensity consists of a 'background' process which is estimated from a control point process by kernel density estimation. The parametric form of the composite intensity yields score tests for particular spatial effects. A numerical example concerning respiratory cancer mortality is given. |
| Keywords: | Invariance principles Almost sure central limit theorem error variance estimator linear models. |