HAZARD REGRESSION AND OTHER POLYNOMIAL SPLINE METHODS

描述：在许多情况下，观察到的数据是 产生的一些未知的机制，其中利益在于估计一个 与数据模型相关的函数。 建议建模 分段光滑线性空间中相应的未知函数 多项式 一种逐步增删基的算法 函数用于自适应地确定该空间。 在比例风险模型中，生存时间对 协变量完全参数化建模。 风险回归（HARE） 采用基于分段多项式的自适应算法来建模， 条件对数风险函数 它并没有假设成比例的风险 模型 建议开发和研究一些扩展， 涉及缺失数据、时间依赖性协变量、分类的HARE 多水平预测因子、相关数据和家系研究。 对于中等规模的问题，提出者的POLYCLASS方法和 多分类回归和分类的合作者声称， 与其他分类方法竞争，同时提供可靠的 条件类概率的估计。 一种基于 随机梯度方法使得POLYCLASS方法适用于大型 数据集。 建议制定相应的选型方案 算法 三角形是提议者给一个函数起的名字 估计方法，使用分段线性，二元样条的基础上， 自适应构建的三角测量。 建议制定方法 基于三重图，其产生的估计比当前的 方法，更有效地选择基函数。 提出了用自由结点样条研究统计建模， 其中节点位置被视为参数。 据称， 使得有可能获得考虑到 结位置的不确定性，并应提供新的见解， 自适应多项式样条方法推理。 用于拟议方法的公开软件将 开发

DESCRIPTION: There are numerous situations in which observed data is generated by some unknown mechanism, where interest lies in estimating a function that is related to a model for the data. It is proposed to model the corresponding unknown functions in a linear space of smooth piecewise polynomials. An algorithm employing stepwise addition and deletion of basis functions is used to determine this space adaptively. In the proportional hazards model, the dependence of the survival times on the covariates is modeled fully parametrically. Hazard regression (HARE) employs an adaptive algorithm based on piecewise polynomials to model the conditional log-hazard function. It does not assume a proportional hazard model. It is proposed to develop and investigate a number of extensions to HARE involving missing data, time dependent covariates, categorical predictors with many levels, dependent data and family studies. For problems of moderate size the POLYCLASS method of the proposer and collaborators for polychotomous regression and classification is claimed to be competitive with other classification methods while providing reliable estimates of conditional class probabilities. An algorithm based on the stochastic gradient method makes the POLYCLASS method applicable to large data sets. It is proposed to develop a corresponding model selection algorithm. Triogram is the name given by the proposer for a function estimation method which using piecewise linear, bivariate splines based on an adaptively constructed triangulation. It is proposed to develop methods based on the triogram that yield smoother estimates than do the current methods and that select the basis functions more effectively. It is proposed to investigate statistical modeling with free knot splines, where knot locations are treated as parameters. It is claimed that this makes it possible to obtain standard errors that take into account the uncertainty in the knot positions and should provide new insight about inference for adaptive polynomial spline methodologies. Publicly available software for the proposed methodologies will be developed.