Inference For High Dimensional Models

9802885 Susan A Murphy本研究关注高维模型中的估计。 在第一部分中使用了高维模型 数据不完整的问题。假设不完全性模式与一个高维观测向量有关。 然后，向量的维数排除了直接的最大似然估计。 该研究解决了最大似然法的两个修改。 在第一修改中，向量的维度减少了平衡分数，并且在第二修改中，使用加权似然。 本文的第二部分研究了线性回归模型的高维推广--变换模型的极大似然估计。 该模型规定响应的未知变换遵循线性回归。 在特殊情况下，如比例风险模型，估计发现最大似然很好理解。 然而，在一般情况下，在这个模型中的参数估计，虽然非常流行，是相当困难的分析。 本研究探讨了新技术的使用，如经验过程和经验似然，以了解估计。模型中有许多未知数或未知函数（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，社会科学家在事件历史分析中使用高维模型来分析生活事件时间变化的原因，如婚前生育，开始吸毒，退休时间和贫困持续时间。 高维模型试图让数据为自己说话，并尽量减少由于对数据施加低维模型而导致的虚假信息的增加。 这项研究推进了对这些高维模型的理解。通常，高维模型的应用没有任何理论上的理解，当他们可能会或可能不会产生质量估计。 特别是，本研究调查的偏差和变异的估计发现使用一种常见的估计方法，最大似然估计。 这一点很重要，因为了解生活事件时间变化的原因对于设计适当的社会政策和干预/预防方案至关重要。

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.