单调B-spline分位数回归与保序回归方法的模拟比较

Comparison of Monotone B-spline Quantile Regression and Isotonic Regression with Simulations

本文主要对单调B-spline分位数回归方法和保序回归方法进行模拟比较分析.首先简单介绍两种方法含义、模型,然后对几组单调数据例子使用R软件模拟,进行比较分析.结果显示单调B-spline分位数回归方法对光滑数据模拟效果明显比保序回归好,而且保序回归对异常值尤其是末端异常值很敏感,但是不光滑数据特别是由某些折线形函数产生的数据B-spline分位数回归拟合较差.

In statistical issues,item response curves are wildly used in the area of economics,medical science,finance and so on.The data used in fitting such curves have the property that fits a monotone function to filter out noise in data.This kind of data is named monotonic data here.Studying regression of the monotonic data is useful.Also,comparing different methods is important.In this article,we mainly compare monotone B-spline quantile regression with isotonic regression in application of monotonic data with simulations.First,we introduce two methods including their models and arithmetic.Then we simulate in several examples with software R and compare the results.From the comparing,we draw a conclusion that monotone B-spline quantile regression fits better than isotonic regression in smoothing monotonic data.But non-smoothing monotonic data,especially data produced by certain mansard function B-spline B-spline quantile regression are not good.