IMPROVED EMPIRICAL LIKELIHOOD FUNCTION BASED ON NORMALIZATION-DEPENDENT REPLICATE MEASUREMENTS

Abstract

Abstract Based on $n$ replicate measurements that require known normalization factors and assuming an underlying normal distribution for individual measurements but with unknown standard deviation, a combined likelihood function is derived that takes the form of a Student’s $t$-distribution with $\nu = n-1$ degrees of freedom and $t=(\psi -\overline{Y})/s$, where $\psi $ is the true value of the measurement quantity calculated from the forward model, and $\overline{Y}$ and $s$ are average and standard error of the mean obtained from the $n$ measurements defined with weighting proportional to the inverse of the normalization factor squared. Assuming an underlying triangle distribution rather than a normal distribution does not produce a large change for six replicates. Examples of replicate data from an animal study and sequential occupational urine and fecal monitoring are given. The use of the empirical likelihood function in data modeling is discussed.