论文信息 - lspartition: Partitioning-Based Least Squares Regression

lspartition: Partitioning-Based Least Squares Regression

Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and numerical features of the R software package lspartition, which implements modern estimation and inference results for partitioning-based least squares (series) regression estimation. This article discusses the main methodological and numerical features of the R software package lspartition, which implements results for partitioning-based least squares (series) regression estimation and inference from Cattaneo and Farrell (2013) and Cattaneo, Farrell, and Feng (2019). These results cover the multivariate regression function as well as its derivatives. First, the package provides data-driven methods to choose the number of partition knots optimally, according to integrated mean squared error, yielding optimal point estimation. Second, robust bias correction is implemented to combine this point estimator with valid inference. Third, the package provides estimates and inference for the unknown function both pointwise and uniformly in the conditioning variables. In particular, valid confidence bands are provided. Finally, an extension to two-sample analysis is developed, which can be used in treatment-control comparisons and related problems

[1] David Ruppert,et al. Semiparametric Regression with R , 2018 .

[2] Adam Krzyzak,et al. A Distribution-Free Theory of Nonparametric Regression , 2002, Springer series in statistics.

[3] Amara Lynn Graps,et al. An introduction to wavelets , 1995 .

[4] Max H. Farrell,et al. On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference , 2015, Journal of the American Statistical Association.

[5] I. Daubechies,et al. Wavelets on the Interval and Fast Wavelet Transforms , 1993 .

[6] B. Ripley,et al. Semiparametric Regression: Preface , 2003 .

[7] Eric R. Ziegel,et al. The Elements of Statistical Learning , 2003, Technometrics.

[8] Max H. Farrell,et al. Coverage error optimal confidence intervals for local polynomial regression , 2018, Bernoulli.

[9] Heping Zhang,et al. Recursive Partitioning and Applications , 1999 .

[10] Jianqing Fan,et al. Local polynomial modelling and its applications , 1994 .

[11] J. S. Long,et al. Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model , 2000 .

[12] Max H. Farrell,et al. nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference , 2019 .

[13] Max H. Farrell,et al. Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators☆ , 2013 .