Mathematical Sciences: New Methodology for Predictive Inference

发展了一种非参数方法来选择分类和生存数据的模型，以期帮助得出预测因素和预后因素。所提出的检验采用归一化得分函数的中心极限定理的形式。考虑了数据收集的顺序方面。研究的目的是为这些诊断学奠定坚实的理论基础，并证明它们的实用性。对于生存模型，还将研究在充分统计条件下的概率积分变换残差的分布特性。在这些属性容易表征的情况下，将寻求变换的顺序应用导致对模型的预测有效性进行测试的条件。基于结构化先验的经验贝叶斯可信区间的构造是在预测框架中设置的，并且将通过分析方法和自举样本来处理。与几个验证标准的比较将区分现有技术和拟议技术。以可观测为中心，研究基于经验贝叶斯分布的预测区间的特征。提出了一种分类数据和生存数据选择模型的新方法。这一方法将有助于发现预测因素和预后因素。考虑了数据收集的顺序方面。研究的目的是为这些诊断学奠定坚实的理论基础，并证明它们的实用性。在预测框架中，基于结构化先验的经验贝叶斯可信区间的构建。这些区间的构建将通过分析方法和自举样本来解决。与几个验证标准的比较将区分现有技术和拟议技术。以可观测为中心，研究基于经验贝叶斯分布的预测区间特征。

A non-parametric approach is developed to select models for categorical and survival data, with a view to helping the elicitation of predictors and prognostic factors. The tests put forward take the form of central limit theorems for normalized scoring functions. The sequential aspect of the data collection is taken into account. The goal of the research is to establish sound theoretical foundations for these diagnostics and to demonstrate their practicality. For survival models, the distributional properties of residuals from the probability integral transform conditional on sufficient statistics will also be studied. In the event that these properties are easily characterized, conditions, under which a sequential application of the transformation leads to a test of predictive validity of the model, will be sought. The construction of empirical Bayes confidence intervals based on structured priors is set in a predictive framework and will be addressed via both analytical methods and bootstrap samples. Comparison with respect to several validation criteria will discriminate between existing and proposed techniques. Focussing on observables, the characteristics of prediction intervals based on empirical Bayes distributions will be looked into. A novel approach for the selection models for categorical and survival data, is developed. This methodology will help in the elicitation of predictors and prognostic factors. The sequential aspect of the data collection is taken into account. The goal of the research is to establish sound theoretical foundations for these diagnostics and to demonstrate their practicality. The construction of empirical Bayes confidence intervals based on structured priors in a predictive framework. The construction of these intervals will be addressed via both analytical methods and bootstrap samples. Comparison with respect to several validation criteria will discriminate between existing and proposed techniques. Focussing on observables, t he characteristics of prediction intervals based on empirical Bayes distributions will be looked into.