Testing parametric models in linear‐directional regression

@article{GarciaPortugues2016TestingPM,
  title={Testing parametric models in linear‐directional regression},
  author={Eduardo Garc'ia-Portugu'es and Ingrid Van Keilegom and Rosa M. Crujeiras and and Wenceslao Gonz'alez-Manteiga},
  journal={Scandinavian Journal of Statistics},
  year={2016},
  volume={43},
  pages={1178 - 1191}
}
This paper presents a goodness‐of‐fit test for parametric regression models with scalar response and directional predictor, that is, a vector on a sphere of arbitrary dimension. The testing procedure is based on the weighted squared distance between a smooth and a parametric regression estimator, where the smooth regression estimator is obtained by a projected local approach. Asymptotic behaviour of the test statistic under the null hypothesis and local alternatives is provided, jointly with a… 
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References

SHOWING 1-10 OF 37 REFERENCES
Goodness‐of‐fit Test for Directional Data
In this paper, we study the problem of testing the hypothesis on whether the density f of a random variable on a sphere belongs to a given parametric class of densities. We propose two test
Tests and Diagnostic Plots for Detecting Lack‐of‐Fit for Circular‐Linear Regression Models
TLDR
A graphical diagnostic tool and a closely related lack-of-fit test, which does not require a natural starting point, which is based on regional residuals which are defined on arcs of the circle, are proposed.
Nonparametric Regression for Spherical Data
We develop nonparametric smoothing for regression when both the predictor and the response variables are defined on a sphere of whatever dimension. A local polynomial fitting approach is pursued,
Goodness-of-fit test for linear models based on local polynomials
Kernel density estimation for directional-linear data
A study of variable bandwidth selection for local polynomial regression
A decisive question in nonparametric smoothing techniques is the choice of the bandwidth or smoothing parameter. The present paper addresses this question when using local polynomial approximations
Multivariate Locally Weighted Least Squares Regression
Nonparametric regression using locally weighted least squares was first discussed by Stone and by Cleveland. Recently, it was shown by Fan and by Fan and Gijbels that the local linear kernel-weighted
Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations
1. Density estimation for exploring data 2. Density estimation for inference 3. Nonparametric regression for exploring data 4. Inference with nonparametric regression 5. Checking parametric
Distribution free laws of the iterated logarithm for kernel estimator of regression function based on directional data
The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all
Nonparametric Smoothing and Lack-of-Fit Tests
TLDR
The nonparametric smoothing and lack of fit tests is one book that the authors really recommend you to read, to get more solutions in solving this problem.
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