Testing for constant variance in a linear model

Diblasi, Ángela Magdalena; Bowman, Adrian

doi:10.1016/s0167-7152(96)00115-0

Cited by 46 publications

(31 citation statements)

References 9 publications

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“…This comparison is carried out with respect to common reference variables S k followingtheideasbyAzzaliniandBowman(1993), Diblasi and Bowman (1997), and Diblasi and Bowman (2001). In fact, the variogram fitting to a parametric family can be viewed as a curve fitting to a parametric model.…”

Section: The Testmentioning

confidence: 99%

Exploring a valid model for the variogram of an isotropic spatial process

Maglione

Diblasi

2004

Stochastic Environmental Research and Risk Assessment

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The variogram is one of the most important tools in the assessment of spatial variability and a crucial parameter for kriging. It is widely known that an estimator for the variogram cannot be used as its representator in some contexts because of its lack of conditional semi negative definiteness. Consequently, once the variogram is estimated, a valid family must be chosen to fit an appropriate model. Under isotropy, this selection is carried out ''by eye'' from the observation of the variogram estimated curve. In this paper, a statistical methodology is proposed to explore a valid model for the variogram. The statistic for this approach is based on quadratic forms depending on smoothed random variables which gather the underlying spatial variation. The distribution of the test statistic is approximated by a shifted chi-square distribution. A simulation study is also carried out to check the power and size of the test. Reference bands, as a complementary graphical tool, are calculated. An example from the literature is used to illustrate the methodologies presented.

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Section: The Testmentioning

confidence: 99%

Exploring a valid model for the variogram of an isotropic spatial process

Maglione

Diblasi

2004

Stochastic Environmental Research and Risk Assessment

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“…In this context the importance of being able to detect heteroscedasticity has been widely recognized because under the additional assumption of a constant scale function the statistical analysis can be simplified substantially. Early work on this problem considering parametric specifications for the regression and scale function can be found in Harrison and McCabe (1979), Breusch and Pagan (1979), Cook and Weisberg (1983) and Diblasi and Bowman (1997) among others. The problem of testing for heteroscedasticity in the classical nonparametric regression model with conditional expectation m and conditional variance σ 2 has been considered in Dette and Munk (1998), Dette (2002), Liero (2003), Dette and Hetzler (2009) Francisco-Fernández and Vilar-Fernández (2005), Dette et al (2007) or Dette and Hetzler (2009).…”

Section: Introductionmentioning

confidence: 99%

A robust test for homoscedasticity in nonparametric regression

Dette

Marchlewski

2010

Journal of Nonparametric Statistics

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We consider a nonparametric location scale model and propose a new test for homoscedasticity (constant scale function). The test is based on an estimate of a deterministic function which vanishes if and only if the hypothesis of a constant scale function is satisfied and an empirical process estimating this function is investigated. Weak convergence to a scaled Brownian bridge is established, which allows a simple calculation of critical values. The new test can detect alternatives converging to the null hypothesis at a rate n −1/2 and is robust with respect to the presence of outliers. The finite sample properties are investigated by means of a simulation study, and the test is compared with some non-robust tests for a constant scale function, which have recently been proposed in the literature.

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“…Koenker and Basset (1981), Cook and Weisberg (1983), Diblasi and Bowman (1997), Dette and Munk (1998a), Liero (2003) among many others]. Recently, You and Chen (2005) proposed a test for homoscedasticity in the partial linear regression model (1.1), which is based on an estimate of the L 2 -distance between the variance function σ 2 (·) and its best constant approximation.…”

Section: Introductionmentioning

confidence: 99%

A test for the parametric form of the variance function in a partial linear regression model

Dette¹,

Marchlewski²

2008

Journal of Statistical Planning and Inference

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We consider the problem of testing for a parametric form of the variance function in a partial linear regression model. A new test is derived, which can detect local alternatives converging to the null hypothesis at a rate n −1/2 and is based on a stochastic process of the integrated variance function. We establish weak convergence to a Gaussian process under the null hypothesis, fixed and local alternatives. In the special case of testing for homoscedasticity the limiting process is a scaled Brownian bridge. We also compare the finite sample properties with a test based on an L 2 -distance, which was recently proposed by You and Chen (2005).

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Testing for constant variance in a linear model

Cited by 46 publications

References 9 publications

Exploring a valid model for the variogram of an isotropic spatial process

Exploring a valid model for the variogram of an isotropic spatial process

A robust test for homoscedasticity in nonparametric regression

A test for the parametric form of the variance function in a partial linear regression model

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