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、惩罚和惩罚后的收缩方法，ii)结合模型，以便对低维和高维数据进行更稳健的预测。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，统计模型会受到与参数改进估计相关的问题的影响，其中一些预测因子与响应没有积极关联，或者不是研究人员的主要兴趣。预检验和非惩罚收缩方法（P-NPS）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中，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-NPS。然后，我计划通过在JM设置中简单地选择不同的纵向和生存模型来扩展这项工作。JM在癌症临床试验中的应用有着悠久的历史。我还计划在独立和纵向数据的广义部分线性模型中开发P-NPS，因为这些模型允许与线性部分一起非参数地建模预测器。当预测因子的数量大于样本数量时，我们定义高维数据（HDD）。对硬盘的分析是社交媒体、人工智能、核磁共振和生物医学研究等许多研究领域的重要特征。大多数现有的处理HDD的方法都是从模型选择开始的，以便进一步研究。除非施加非常严格的条件，否则惩罚方法是不稳定的。我考虑了广义线性模型（GLMs）的惩罚后收缩策略，以对抗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。我还建议重点研究glm分析HDD的集成方法。这些都是非常强大的技术，可以提高预测的准确性。然后，我将计算基于集成方法的模型的汇总预测，并将它们与基于文献中现有惩罚方法的模型的预测进行比较。集成方法在图像识别、医学、网络安全等各种应用中都很有效。该建议强调统计学家在解决非正态（例如，二进制或计数）、纵向和生存数据分析中的问题方面发挥重要作用。它还将提供培训各级高度合格人员的机会。这个培训有三个组成部分：方法论、计算和对现实生活数据的分析。这项提案的成果预计将有助于保健服务和其他应用领域的利益攸关方根据正确的统计推断作出适当的决定。

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.