Caption: FIGURE 1: The percentages of ERE for odds ratio estimation using EB, MMLE, and MMUE when ([n.sub.l], [n.sub.2]) = (10,10).
Haldane  and Gart and Zweifel  suggested to add a correction term 0.5 to each cell, when having zero cell count, which gives the modified maximum likelihood estimator (MMLE) as
Our purposed estimation tends to outperform the traditional estimator, MMLE, and MMUE without interference in the original data.
The forth section illustrates simulated results, and the efficiency of EB is compared with MMLE and MUE.
where OR denotes the usual maximum likelihood estimator of odds ratio and [[??].sub.i] denotes the estimate of odds ratio using EB, MMLE, and MMUE (i = 1, 2, 3, ...), respectively.
* However, Theorem 3.4 shows that, as n increases, the optimal choice as well as the MLE and MMLE
ones or any other "acceptable" choice (such as the SEME given by (1.3)) approach the same limiting distribution in light of Remark 3.6.
(1) Step E (expectation): For missing data point z, the equation of estimation for its MMLE, l([theta]) is expressed as
where [theta] is the parameter of the MMLE equation, m is the number of data samples, and [x.sup.(i)](i = 1, 2, ..., m) is the sample value.
(2) Step M (maximization): [theta]' is the updated parameter of the MMLE, expressed as
Step M calculates the MMLE of the parameter under the Step E hypothesis.