回归曲线比较是统计学中的热点问题之一。虽然一元非参数回归曲线比较已有广泛研究，多元非参数回归曲线比较的研究却较少见。在多元情形下，直接推广一元情形的理论方法会出现维数祸根问题，导致统计量无法较好地控制第一类错误并且检验功效不佳。本项目致力于多元非参数回归曲线比较问题，主要研究内容为：1. 建立多元非参数回归曲线比较的理论和方法，即采用投影来规避维数的影响，基于经验过程或非参数回归估计构造检验统计量并研究统计量的渐近性质；2. 考虑若干拓展问题的研究。由于条件分布函数是一种特殊的回归函数，考虑将非参数回归曲线比较的理论推广到条件分布函数比较问题上。单指标模型是重要的半参数回归模型之一，对其进行曲线比较研究；3. 将完全数据下的检验问题及理论方法推广到缺失数据中，运用插补法和逆概率加权法处理缺失数据，进而研究统计量的构造及其渐近性质；4. 将上述理论结果应用到经济管理领域体现本项目的应用价值。

The comparison of regression curves is one of the principal problems in statistics. Although there have been many studies for the comparison of univariate nonparametric regression curves, the investigations of comparison of multivariate nonparametric regression curves are scarce. In the multivariate case, directly generalizing theories and methods in the univariate case can lead the problem of curse of dimensionality. To be precise, the constructed test statistics can not maintain the type I error well and have low powers. In this project, we aim to study the comparison of multivariate nonparametric regression curves. The main research work includes: 1. Establish the theories and methods for comparison of multivariate nonparametric regression curves. That is, use projections to avoid the effect of dimension, construct test statistics based on empirical process or nonparametric regression estimators, and study the asymptotic properties of test statistics; 2. Consider several related problems. Note that the conditional distribution function is a special kind of regression function. We extend the theories of comparison of nonparametric regression curves to the problem of comparison of conditional distribution functions. Single index model is an important semiparametric regression model. We study its curves comparison problem; 3. We extend the problem and related theories and methods to missing data. Construct test statistics by using imputation and inverse probability weighting methods. The asymptotic properties will also be studied; 4. The theoretical results will be applied to economics and management areas to see the contribution of this proposal.