Inference For High Dimensional Models

高维模型的推理

• 批准号: 9802885
• 负责人: Susan Murphy
• 金额: $ 3.5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802885&HistoricalAwards=false
• 关键词: Inference; Dimensional; Models

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.

9802885Susan A Murphy 这项研究涉及高维模型中的估计。 在第一部分中，讨论了针对不完整数据使用高维模型的问题。假设不完整性模式与高维观测向量相关。 那么向量的维数就排除了直接的最大似然估计。 该研究解决了最大似然的两个修改。 在第一个修改中，矢量的维度通过平衡分数减少，而在第二个修改中，使用加权似然。 本研究的第二部分重点关注变换模型的最大似然估计，这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，通过最大似然找到的估计量是很好理解的。 然而，一般来说，该模型中的参数估计量虽然非常流行，但分析起来却相当困难。 这项研究调查了新技术的使用，例如经验过程和经验可能性，以便理解估计量。在整个科学中，存在许多未知数或未知函数（此处称为参数）的模型。 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诸如婚前生育、吸毒开始、退休时间和贫困持续时间等生活事件时间变化的原因。 高维模型试图让数据自己说话，并最大限度地减少由于对数据强加低维模型而导致的虚假信息的添加。 这项研究增进了对这些高维模型的理解。通常，应用高维模型时没有任何关于它们何时可能或可能不会产生质量估计量的理论理解。 特别是，本研究调查了通过使用常见的估计方法（最大似然估计）发现的估计量的偏差和变异性。 这很重要，因为了解生活事件发生时间变化的原因对于设计适当的社会政策和干预/预防计划至关重要。