ABSTRACT 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. 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 jeopardise 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 . We also derive some results for the mean squared error (MSE) 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.

中文翻译：

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利用通用缺失数据机制减少最大近似条件似然估计器的偏差

摘要 在缺失数据分析中，缺失数据机制的假设至关重要。在不同的假设下，必须相应地制定不同的统计方法；然而，实际上这种假设通常是无法验证的。因此，优选不太严格且更灵活的假设。在本文中，我们考虑了一种普遍适用的缺失数据机制。在这种一般的缺失数据机制下，我们引入条件似然及其近似版本作为估计感兴趣的未知参数的基础。由于这种近似条件似然仅使用完全观察到的样本，因此可能会导致较大的估计偏差，这可能会恶化统计推断并危及其他统计过程。为了解决这个问题，我们建议使用一些重采样技术来减少估计偏差。我们在论文中考虑了 Jackknife 和 Bootstrap。我们通过高达 的高阶展开来比较它们的渐近偏差。我们还得出了估计精度方面均方误差 (MSE) 的一些结果。我们在不同情况下进行了全面的模拟研究来说明我们提出的方法。我们还将我们的方法应用于前列腺癌数据分析。