Inference For High Dimensional Models

苏珊·A·默菲这项研究涉及高维模型中的估计。在第一部分中，讨论了高维模型对不完整数据的使用。假设不完备性模式与高维观测向量有关。然后，向量的维度排除了直接的最大似然估计。这项研究解决了两个最大似然性的修改。在第一个修改中，将向量的维度减少平衡分数，并且在第二个修改中，使用加权似然。第二部分研究的重点是变换模型的极大似然估计，它是线性回归模型的高维推广。该模型规定，响应的未知变换遵循线性回归。在特殊情况下，例如比例风险模型，最大似然法得到的估计量是很容易理解的。然而，总的来说，这个模型中的参数估计器虽然非常流行，但相当难分析。这项研究调查了新技术的使用，如经验过程和经验似然，以了解估计。模型中有许多未知或未知函数(这里称为参数)出现在整个科学。通常，这些模型是为了解决经典线性回归模型的不足而制定的。例如，社会科学家在事件史中使用高维模型来分析生活事件的时间变化的原因，如婚前出生、开始滥用药物、退休时间和贫困时期。高维模型试图允许数据自己说话，并最大限度地减少由于将低维模型强加于数据而导致的虚假信息的添加。这项研究促进了对这些高维模型的理解。通常，高维模型在应用时没有任何理论上的理解，不知道它们何时可以或可能不会产生高质量的估计值。特别是，这项研究调查了通过使用一种常见的估计方法--最大似然估计所发现的估计者的偏差和可变性。这一点很重要，因为了解生活事件时间变化的原因对于制定适当的社会政策和干预/预防计划至关重要。

9802885Susan A MurphyThis research concerns estimation in high dimensional models. In the first part the use of high dimensional models for incomplete data is addressed. Suppose the pattern of incompleteness is related to an high dimensional vector of observations. Then the dimensionality of the vector precludes straightforward maximum likelihood estimation. The research addresses two modifications of maximum likelihood. In the first modification, the dimension of the vector is reduced by a balancing score and in the second modification, a weighted likelihood is used. The second part of this research focuses on maximum likelihood estimation for the transformation model, a high dimensional generalization of the linear regression model. This model stipulates that an unknown transformation of the response follows a linear regression. In special cases, such as the proportional hazards model, the estimators found by maximum likelihood are well understood. Yet in general, estimators of parameters in this model, although extremely popular, are rather difficult to analyze. This research investigates the use of new techniques, such as empirical processes and empirical likelihood in order to understand the estimators.Models in which there are many unknowns or unknown functions (called parameters here) appear throughout the sciences. Often these models are formulated to address inadequacies of the classical linear regression model. For example, social scientists use high dimensional models in event history analysis of the causes of variability in the timing of life events such as premarital births, initiation of drug abuse, timing of retirement and duration of poverty spells. High dimensional models attempt to allow the data to speak for itself and to minimize the addition of spurious information caused by imposing a low-dimensional model on the data. This research advances the understanding of these high dimensional models. Often high dimensional models are applied without any theoretical understanding of when they may or may not produce quality estimators. In particular, this research investigates the bias and variability of of estimators found by the use of a common estimation method, maximum likelihood estimation. This is important as understanding the causes of variability in the timing of life events is crucial to designing appropriate social policies and intervention/prevention programs.