Testing independence and goodness-of-fit in linear models

  title={Testing independence and goodness-of-fit in linear models},
  author={Arnab Sen and Bodhisattva Sen},
  • Arnab Sen, B. Sen
  • Published 23 February 2013
  • Computer Science, Mathematics
  • Biometrika
We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and predictor variables and the goodness-of-fit of the parametric model. Our approach is based on testing for independence between the predictor and the residual obtained from the parametric fit by using the Hilbert–Schmidt independence criterion (Gretton et al., 2008). The proposed method requires no user-defined regularization, is simple to compute based… 

Figures and Tables from this paper

Testing independence and goodness-of-fit jointly for functional linear models

A conventional regression model for functional data involves expressing a response variable in terms of the predictor function. Two assumptions, that (i) the predictor function and the error are

A consistent test of independence and goodness-of-fit in linear regression models

Abstract We propose a new approach to simultaneously test the assumptions of independence and goodness-of-fit for a multiple linear regression model say H 0, vs. H 1: H 0 is false. Our approach is

Distance-covariance-based tests for heteroscedasticity in nonlinear regressions

We use distance covariance to introduce novel consistent tests of heteroscedasticity for nonlinear regression models in multidimensional spaces. The proposed tests require no user-defined

A joint test for parametric specification and independence in nonlinear regression models

Abstract This paper develops a testing procedure to simultaneously check (i) the independence between the error and the regressor(s), and (ii) the parametric specification in nonlinear regression

Testing against a linear regression model using ideas from shape‐restricted estimation

A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non‐parametric double‐cone alternative. For example, the test

Omnibus Model Checks of Linear Assumptions through Distance Covariance

This work proposes two omnibus tests for the goodness-of-fit of linearity inspired by the well-known distance covariance and a bootstrap scheme is devised to approximate their null distributions and its consistency is justified.

Testing against a parametric regression function using ideas from shape restricted estimation

A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test

Nonparametric independence testing via mutual information

This work proposes a test of independence of two multivariate random vectors, given a sample from the underlying population, based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently-developed efficient entropy estimators derived from nearest neighbour distances.

-consistent Density Estimation in Semiparametric Regression Models



Goodness-of-Fit Tests for Parametric Regression Models

Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from

Testing the Goodness of Fit of a Linear Model via Nonparametric Regression Techniques

Abstract This article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model. The large-sample properties of parametric goodness-of-fit tests

Alternative Goodness-of-Fit Tests for Linear Models

Fan and Huang (2001) presented a goodness-of-fit test for linear models based on Fourier transformations of the residuals of the fitted model. We present two more theoretically appealing tests in

Diagnostics for heteroscedasticity in regression

The purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present.

Testing independence in nonparametric regression

Global Validation of Linear Model Assumptions

  • E. PeñaE. Slate
  • Mathematics
    Journal of the American Statistical Association
  • 2006
An easy-to-implement global procedure for testing the four assumptions of the linear model and its performance is compared with three potential competitors, including a procedure based on the Box–Cox power transformation.

Nonparametric Inferences for Additive Models

The generalized likelihood ratio (GLR) tests are extended to additive models, using the backfitting estimator, and it is proved that the GLR tests are asymptotically optimal in terms of rates of convergence for nonparametric hypothesis testing.

Model checking in regression via dimension reduction

Lack-of-fit checking for parametric and semiparametric models is essential in reducing misspecification. The efficiency of most existing model-checking methods drops rapidly as the dimension of the

On the Use of Nonparametric Regression for Checking Linear Relationships

SUMMARY The problem of checking the linearity of a regression relationship is addressed through the idea of smoothing of a residual plot. A pseudolikelihood ratio test statistic, which measures the