Testing parametric models in linear‐directional regression

  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},
  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… 
Goodness-of-fit tests for parametric regression models with circular response
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially
Goodness-of-fit tests for multiple regression with circular response
Testing procedures for assessing a parametric regression model with a circular response and an -valued covariate are proposed and analysed in this work. The test statistics are based on a circular
Improving kernel-based nonparametric regression for circular–linear data
The result shows that choosing a higher degree improves performance under the finite sample in homoscedastic or heterogeneous scenarios, and in some scenarios where the regression function is wiggly, higher-order estimators perform significantly better than local constant and linear estimators.
Smoothing-Based Tests with Directional Random Variables
This work reviews some of the smoothing-based testing procedures for density and regression models that comprise directional variables and presents the asymptotic distributions of the revised proposals, jointly with some numerical illustrations justifying the need of employing resampling mechanisms for effective test calibration.
Testing covariate significance in spatial point process first-order intensity
A test statistic based on a $L^2$-distance is proposed; it is proved the asymptotic normality of the statistic and a bootstrap procedure is suggested to calibrate the test.
Testing first-order intensity model in non-homogeneous Poisson point processes with covariates
This paper proposes a new test based on an $L^2$-distance for first-order intensity function and proves the asymptotic normality of the statistic and suggests a bootstrap procedure to accomplish the calibration.
Nonparametric inference with directional and linear data
The term directional data refers to data whose support is a circumference, a sphere or, generally, an hypersphere of arbitrary dimension. This kind of data appears naturally in several applied
Recent advances in directional statistics
This paper provides a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics, and considers developments for the exploratory analysis of directional data.
Local binary regression with spherical predictors


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
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
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.