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Simultaneous inference of linear models with time varying coefficients
Author(s) -
Zhou Zhou,
Wu Wei Biao
Publication year - 2010
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2010.00743.x
Subject(s) - inference , linear regression , mathematics , parametric statistics , confidence interval , linear model , series (stratigraphy) , gaussian , regression , set (abstract data type) , statistical inference , statistics , computer science , artificial intelligence , paleontology , physics , quantum mechanics , biology , programming language
Summary. The paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models. Using a Gaussian approximation result for non‐stationary multiple time series, we show that the constructed simultaneous confidence tubes have asymptotically correct nominal coverage probabilities. Our results are applied to the problem of testing whether the regression coefficients are of certain parametric forms, which is a fundamental problem in the inference of functional linear models. As an application, we analyse an environmental data set and study the association between levels of pollutants and hospital admissions.