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首页> 外文期刊>Frontiers in Applied Mathematics and Statistics >Regression with Ordered Predictors via Ordinal Smoothing Splines
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Regression with Ordered Predictors via Ordinal Smoothing Splines

机译：通过序数平滑样条与有序预测变量回归

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Many applied studies collect one or more ordered categorical predictors, which do not fit neatly within classic regression frameworks. In most cases, ordinal predictors are treated as either nominal (unordered) variables or metric (continuous) variables in regression models, which is theoretically and/or computationally undesirable. In this paper, we discuss the benefit of taking a smoothing spline approach to the modeling of ordinal predictors. The purpose of this paper is to provide theoretical insight into the ordinal smoothing spline, as well as examples revealing the potential of the ordinal smoothing spline for various types of applied research. Specifically, we (i) derive the analytical form of the ordinal smoothing spline reproducing kernel, (ii) propose an ordinal smoothing spline isotonic regression estimator, (iii) prove an asymptotic equivalence between the ordinal and linear smoothing spline reproducing kernel functions, (iv) develop large sample approximations for the ordinal smoothing spline, and (v) demonstrate the use of ordinal smoothing splines for isotonic regression and semiparametric regression with multiple predictors. Our results reveal that the ordinal smoothing spline offers a flexible approach for incorporating ordered predictors in regression models, and has the benefit of being invariant to any monotonic transformation of the predictor scores.
机译：许多应用研究收集了一个或多个有序的类别预测变量，这些预测变量并不完全适合经典回归框架。在大多数情况下，有序预测变量在回归模型中被视为名义变量（无序）或度量变量（连续），这在理论上和/或计算上都是不希望的。在本文中，我们讨论了采用平滑样条方法对有序预测变量进行建模的好处。本文的目的是提供对序贯平滑样条的理论见解，并举例说明序贯平滑样条在各种类型的应用研究中的潜力。具体而言，我们（i）推导有序平滑样条曲线重现核的分析形式，（ii）提出有序平滑样条线等张回归估计量，（iii）证明有序和线性平滑样条重现核函数之间的渐近等价，（iv ）开发序数平滑样条的大样本近似值，并且（v）演示了序数平滑样条在具有多个预测变量的等张回归和半参数回归中的使用。我们的结果表明，序数平滑样条为将有序预测变量合并到回归模型中提供了一种灵活的方法，并且具有对预测变量分数的任何单调变换不变的好处。

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