Penalty, non-penalty shrinkage and ensemble methods for low and high dimensional data

该提案是一项倡议，i）提供非惩罚、惩罚和惩罚后收缩方法，以及ii）联合收割机模型，以实现对低维和高维数据的更鲁棒预测。这些数据出现在包括基因组学和健康科学在内的各个科学领域。 当数据集包含许多预测因子的信息时，统计模型会受到与改进参数估计相关的问题的影响，其中一些预测因子与研究人员的响应无关或不是主要兴趣。预检验和非惩罚收缩方法（P-STIM）将这些非活性预测因子作为辅助信息，并将其纳入估计过程，以改进回归参数的经典估计。在低维数据中，我的计划是研究纵向和生存数据的联合建模（JM）的P-STIM。然后，我计划通过在JM环境中简单地选择不同的纵向和生存模型来扩展工作。JM在癌症临床试验中的应用历史悠久。我也有一个计划，以发展的P-S在广义部分线性模型的独立和纵向的数据，因为这些模型允许建模的预测非参数沿着与线性部分。我们定义高维数据（HDD）时，预测的数量大于样本大小。HDD的分析是许多研究领域的重要特征，如社交媒体，人工智能，MRI和生物医学研究。大多数现有的方法来处理硬盘开始与模型选择进一步的调查。惩罚方法是不稳定的，除非施加非常严格的条件。我考虑了广义线性模型（GLM）的后惩罚收缩策略，以解决从惩罚方法继承的一些问题。这些策略将改善基于所选子模型的预测误差。 我还建议集中研究GLM的集成方法来分析HDD。这些都是提高预测准确性的非常强大的技术。然后，我将根据集合方法计算模型的聚合预测，并将其与文献中基于现有惩罚方法的模型的预测进行比较。包围盒方法在各种应用中工作良好，如图像识别、医学、网络安全等。这一建议强调了统计学家在解决非正态分析问题中的重要作用（例如，二进制或计数）、纵向和存活数据。它还将为培训各级高素质人员提供机会。这种培训有三个组成部分：方法，计算和分析真实的生活数据。这一建议的成果预计将帮助利益相关者在医疗保健服务，并在其他领域的应用程序中出现这样的数据，在正确的统计推断的基础上作出适当的决定。

This proposal is an initiative to i) provide non-penalty, penalty, and post penalty shrinkage methods and ii) combine models to enable a more robust prediction for low and high dimensional data. These data arise in various fields of sciences including genomics and health sciences. A statistical model is affected by problems associated with improved estimation of parameters when the datasets contain information on many predictors, some of which are not actively associated with the response or not of primary interest to the researcher. The pretest and non-penalty shrinkage methods (P-NPS) consider such inactive predictors as auxiliary information and incorporate them into the estimation procedure to improve the classical estimator of the regression parameters. In low dimensional data, my plan is to work on the P-NPS for joint modeling (JM) of longitudinal and survival data. I then plan to extend the work by simply choosing different longitudinal and survival models in a JM setting. The application of JM has a long history of being used in cancer clinical trials. I also have a plan to develop the P-NPS in generalized partially linear models for independent and longitudinal data as these models allow modeling the predictors nonparametrically along with the linear part. We define high dimensional data (HDD) when the number of predictors is larger than the sample size. The analysis of HDD is an important feature in a host of research areas such as social media, artificial intelligence, MRI and biomedical research. Most of the existing methods for dealing with HDD begin with model selection for further investigation. Penalty methods are unstable unless very stringent conditions are imposed. I consider the post penalty shrinkage strategies for generalized linear models (GLMs) to combat some of the issues inherited from penalty methods. These strategies will improve the prediction errors based on the selected submodels. I also propose to focus on investigating ensemble methods for GLMs to analyze HDD. These are very powerful techniques for improving the accuracy of predictions. I will then calculate aggregated predictions from the models based on the ensemble methods and compare them with the predictions from the model based on the existing penalty methods in the literature. Ensemble methods work well in various applications like image recognition, medicine, network security, and others. This proposal emphasizes that statisticians play an important role in solving problems in the analysis of non-normal (e.g., binary or count), longitudinal and survival data. It will also provide opportunities for training highly qualified personnel at all levels. This training has three components: methodology, computation, and analysis of real life data. Outcomes of this proposal are expected to aid stakeholders in health care services, and in other areas of applications where such data arise, in making proper decisions based on correct statistical inferences.