Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism.

In missing data analysis, the assumption of the missing data mechanism is crucial. Under different assumptions, different statistical methods have to be developed accordingly; however, in reality this kind of assumption is usually unverifiable. Therefore a less stringent, and hence more flexible, assumption is preferred. In this paper, we consider a generally applicable missing data mechanism, which includes various instances in all three scenarios: missing completely at random, missing at random, and missing not at random. Under this general missing data mechanism, we introduce the conditional likelihood and its approximate version as the base for estimating the unknown parameter of interest. Since this approximate conditional likelihood uses the completely observed samples only, it may result in large estimation bias, which could deteriorate the statistical inference and also jeopardize other statistical procedure. To tackle this problem, we propose to use some resampling techniques to reduce the estimation bias. We consider both the Jackknife and the Bootstrap in our paper. We compare their asymptotic biases through a higher order expansion up to O(n -1). We also derive some results for the mean squared error in terms of estimation accuracy. We conduct comprehensive simulation studies under different situations to illustrate our proposed method. We also apply our method to a prostate cancer data analysis.