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Estimation of a Variance Function, with Application to Immunoassay
Author(s) -
Raab Gillian M.
Publication year - 1981
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346655
Subject(s) - statistics , estimation , mathematics , variance function , variance (accounting) , immunoassay , function (biology) , econometrics , likelihood function , maximum likelihood , estimator , economics , medicine , biology , accounting , evolutionary biology , management , antibody , immunology
S ummary The problem of estimating variances by pooling information from a large number of small samples is tackled. Maximum likelihood methods are shown to be inconsistent, but a modified maximum likelihood method is described which gives consistent estimators. A modified likelihood ratio test of fit is also developed, and the application of these results to immunoassay data is described. Comparison with a regression method shows that if the variance function is given by an exponential model, and the observations are in sets of 2, 3 or 4, the modified maximum likelihood method has much greater efficiency.