Bootstrapping in Nonparametric Regression: Local Adaptive Smoothing and Confidence Bands

1988 ◽  
Vol 83 (401) ◽  
pp. 102 ◽  
Author(s):  
Wolfgang Hardle ◽  
Adrian W. Bowman
Keyword(s):  
Nonparametric Regression ◽  
Confidence Bands ◽  
Adaptive Smoothing

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

scholarly journals Resampling methods for functional data

2018 ◽  
Author(s):  
Timothy McMurry ◽  
Dimitris Politis
Keyword(s):  
Data Analysis ◽  
Density Estimation ◽  
Nonparametric Regression ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Real Data ◽  
Confidence Bands ◽  
Resampling Methods ◽  
Current State ◽  
Inference Techniques

This article examines the current state of methodological and practical developments for resampling inference techniques in functional data analysis, paying special attention to situations where either the data and/or the parameters being estimated take values in a space of functions. It first provides the basic background and notation before discussing bootstrap results from nonparametric smoothing, taking into account confidence bands in density estimation as well as confidence bands in nonparametric regression and autoregression. It then considers the major results in subsampling and what is known about bootstraps, along with a few recent real-data applications of bootstrapping with functional data. Finally, it highlights possible directions for further research and exploration.

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