scholarly journals Simultaneous confidence bands for nonparametric regression with functional data

2011 ◽  
Vol 21 (4) ◽  
Author(s):  
David A. Degras
Keyword(s):  
Nonparametric Regression ◽  
Functional Data ◽  
Confidence Bands ◽  
Simultaneous Confidence Bands

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.

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.

Assessing bias, precision, and agreement in method comparison studies

2019 ◽  
Vol 29 (3) ◽  
pp. 778-796 ◽  
Author(s):  
Patrick Taffé
Keyword(s):  
Measurement Method ◽  
Method Comparison ◽  
Estimation Procedure ◽  
Measurement Methods ◽  
Repeated Measurements ◽  
Confidence Bands ◽  
The Other ◽  
Reference Standard ◽  
Simultaneous Confidence Bands ◽  
Index Of Agreement

Recently, a new estimation procedure has been developed to assess bias and precision of a new measurement method, relative to a reference standard. However, the author did not develop confidence bands around the bias and standard deviation curves. Therefore, the goal in this paper is to extend this methodology in several important directions. First, by developing simultaneous confidence bands for the various parameters estimated to allow formal comparisons between different measurement methods. Second, by proposing a new index of agreement. Third, by providing a series of new graphs to help the investigator to assess bias, precision, and agreement between the two measurement methods. The methodology requires repeated measurements on each individual for at least one of the two measurement methods. It works very well to estimate the differential and proportional biases, even with as few as two to three measurements by one of the two methods and only one by the other. The repeated measurements need not come from the reference standard but from either measurement methods. This is a great advantage as it may sometimes be more feasible to gather repeated measurements with the new measurement method.

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