Wang, XiaogangEeden, Constance vanZidek, James V.2007-03-272007-03-272004Wang, X., van Eeden, C. and Zidek, J.V. (2004). Asymptotic Properties of Weighted Likelihood Estimators.Journal of Statistical Planning and Inference. Vol 119, pp. 37-54.0378-3758http://hdl.handle.net/10315/921https://doi.org/10.1016/S0378-3758(02)00410-XThe relevance weighted likelihood method was introduced by Hu and Zidek (Technical Report No. 161, Department of Statistics, The University of British Columbia, Vancouver, BC, Canada, 1995) to formally embrace a variety of statistical procedures for trading bias for precision. Their approach combines all relevant information through a weighted version of the likelihood function. The present paper is concerned with the asymptotic properties of a class of maximum weighted likelihood estimators that contains those considered by Hu and Zidek (Technical Report No. 161, Department of Statistics, The University of British Columbia, Vancouver, BC, Canada, 1995, in: Ahmed, S.E. Reid, N. (Eds.), Empirical Bayes and Likelihood Inference, Springer, New York, 2001, p. 211). Our results complement those of Hu (Can. J. Stat. 25 (1997) 45). In particular, we invoke a di>erent asymptotic paradigm than that in Hu (Can. J. Stat. 25 (1997) 45). Moreover, our adaptive weights are allowed to depend on the data.en© 2004. This manuscript version is made available under the CC-BY-NC-ND 4.0Asymptotic normalityConsistencyJames-SteinWeighted likelihoodArticle