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Modified likelihood root in high dimensions
Author(s) -
Tang Yanbo,
Reid Nancy
Publication year - 2020
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/rssb.12389
Subject(s) - normality , nuisance parameter , mathematics , nuisance , exponential family , exponential function , statistics , dimension (graph theory) , root (linguistics) , maximum likelihood , function (biology) , likelihood function , scale (ratio) , econometrics , combinatorics , mathematical analysis , physics , law , linguistics , philosophy , quantum mechanics , estimator , evolutionary biology , political science , biology
Summary We examine a higher order approximation to the significance function with increasing numbers of nuisance parameters, based on the normal approximation to an adjusted log‐likelihood root. We show that the rate of the correction for nuisance parameters is larger than the correction for non‐normality, when the parameter dimension p is O ( n α ) for α < 1 2 . We specialize the results to linear exponential families and location–scale families and illustrate these with simulations.