A Bayesian approach for nonparametric regression in the presence of correlated errors

2021 ◽  
pp. 1-10
Author(s):  
Mohamed Megheib
Keyword(s):  
Nonparametric Regression ◽  
Bayesian Approach ◽  
Correlated Errors

scholarly journals Modeling Compositional Regression With Uncorrelated and Correlated Errors: A Bayesian Approach

2021 ◽  
pp. 221-250
Author(s):  
Taciana K. O. Shimizu ◽  
Francisco Louzada ◽  
Adriano K. Suzuki ◽  
Ricardo S. Ehlers
Keyword(s):  
Bayesian Approach ◽  
Correlated Errors

scholarly journals Using bimodal kernel for inference in nonparametric regression with correlated errors

2009 ◽  
Vol 100 (7) ◽  
pp. 1487-1497 ◽  
Author(s):  
Tae Yoon Kim ◽  
Byeong U. Park ◽  
Myung Sang Moon ◽  
Chiho Kim
Keyword(s):  
Nonparametric Regression ◽  
Correlated Errors

scholarly journals Asymptotically Sufficient Statistics in Nonparametric Regression Experiments with Correlated Noise

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
Andrew V. Carter
Keyword(s):  
Nonparametric Regression ◽  
Nuisance Parameter ◽  
Correlated Noise ◽  
Correlated Errors ◽  
Sufficient Statistics ◽  
Regression Problems ◽  
The Mean ◽  
Mean Function ◽  
Available Information ◽  
Continuous Gaussian Process

We find asymptotically sufficient statistics that could help simplify inference in nonparametric regression problems with correlated errors. These statistics are derived from a wavelet decomposition that is used to whiten the noise process and to effectively separate high-resolution and low-resolution components. The lower-resolution components contain nearly all the available information about the mean function, and the higher-resolution components can be used to estimate the error covariances. The strength of the correlation among the errors is related to the speed at which the variance of the higher-resolution components shrinks, and this is considered an additional nuisance parameter in the model. We show that the NPR experiment with correlated noise is asymptotically equivalent to an experiment that observes the mean function in the presence of a continuous Gaussian process that is similar to a fractional Brownian motion. These results provide a theoretical motivation for some commonly proposed wavelet estimation techniques.

scholarly journals Bayesian local extremum splines

Biometrika ◽  
2017 ◽  
Vol 104 (4) ◽  
pp. 939-952 ◽  
Author(s):  
M W Wheeler ◽  
D B Dunson ◽  
A H Herring
Keyword(s):  
Nonparametric Regression ◽  
Differentiable Function ◽  
Bayesian Approach ◽  
Local Extremum ◽  
Simulation Studies ◽  
Closed Set ◽  
Testing Hypotheses ◽  
Nonparametric Prior ◽  
Local Extrema ◽  
Sampling Algorithms

SummaryWe consider shape-restricted nonparametric regression on a closed set $\mathcal{X} \subset \mathbb{R},$ where it is reasonable to assume that the function has no more than $H$ local extrema interior to $\mathcal{X}$. Following a Bayesian approach we develop a nonparametric prior over a novel class of local extremum splines. This approach is shown to be consistent when modelling any continuously differentiable function within the class considered, and we use itto develop methods for testing hypotheses on the shape of the curve. Sampling algorithms are developed, and the method is applied in simulation studies and data examples where the shape of the curve is of interest.

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