INFORMATION BIAS AND ADJUSTED PROFILE LIKELIHOODS

The bias and information bias of the ordinary profile score statistic are both typically of order O(1). Several additive adjustments to the profile score statistic that reduce its bias to order O(n(-1)) have be en proposed. In certain situations, the information bias of these adju sted profile score statistics is also reduced to order O(n(-1)); speci fically, the modified profile likelihood of Bamdorff-Nielsen yields an adjusted profile score statistic having both reduced bias and reduced information bias. In general, however, a bias reducing adjustment to the profile score statistic will not automatically reduce the order of the information bias as well. In this paper, an analytical formula is obtained for the information bias of a general bias-adjusted profile score statistic. This formula is used to compare bias reducing adjustm ents to the profile score statistic, as well as to construct further a djustments that reduce the information bias to O(n(-1)). Several examp les are presented to illustrate use of the formula for information bia s. In particular, the information bias formula may be utilized in a cr iterion for choosing between orthogonal parameterizations for the cond itional profile likelihood of Cox and Reid.