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

Eubank, R. L.; Spiegelman, Clifford H.

doi:10.1080/01621459.1990.10476211

Cited by 178 publications

(105 citation statements)

References 14 publications

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“…Consider the following null hypothesis: Interestingly even when x is observable, that is, for ordinary regression models, the above testing attracted attention in the late 1980's. Since then there are many proposals in the [4] , Eubank and Spiegeman [5] , Hall and Hart [7] , Härdle and Mammen [8] , Härdle, Mammen and Müller [9] , Hart [10] , He and Ng [11] , He and Zhu [12] , King [13] , Müller [14] , Stute [15] , Müller [14] , Stute et al [16] , Stute et al [17] , Stute and Zhu [18] , Zhu [19] , Zhu and Ng [20] , among others, and for more general models, many tests are also proposed. Most of the literature in the errors-in-variables context, though, was devoted to estimation rather than testing.…”

Section: Introductionmentioning

confidence: 98%

Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

Zhu

Cui

2004

Acta Mathematicae Applicatae Sinica, English Series

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The relationship between the linear errors-in-variables model and the corresponding ordinary linear model in statistical inference is studied. It is shown that normality of the distribution of covariate is a necessary and sufficient condition for the equivalence. Therefore, testing for lack-of-fit in linear errors-in-variables model can be converted into testing for it in the corresponding ordinary linear model under normality assumption. A test of score type is constructed and the limiting chi-squared distribution is derived under the null hypothesis. Furthermore, we discuss the power of the test and the choice of the weight function involved in the test statistic.

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Section: Introductionmentioning

confidence: 98%

Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

Zhu

Cui

2004

Acta Mathematicae Applicatae Sinica, English Series

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“…There has been an extensive literature on using nonparametric smoothing techniques to check parametric regression relationships (see, for example, [1][2][3][4], [7], [11] and among others). Recently, a new procedure was proposed by Gijbels and Rousson [6] to test for a polynomial relationship of degree smaller than or equal to p. Therein, pth derivative of the regression function is first estimated via the local polynomial fit at some properly selected points and then the classical least-squares test for a general linear model is employed to check whether or not the pth derivative is constant.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

Mei

Wang

2003

Acta Mathematicae Applicatae Sinica, English Series, English Se

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Recently, Gijbels and Rousson [6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson's approach.Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory.

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“…The proposed method is simple in use and some simulations conducted in this article demonstrate that it performs satisfactorily in identifying the non-varying coefficients in a varying-coefficient model. Recall that there has been a great deal of literature on testing various forms of parametric structure in a general nonparametric setting (for example, see [1,6,7,11,17] and the references therein). Most of these work focuses on comparing a nonparametric estimate of the whole regression function with its parametric counterpart by defining some distance between them.…”

Section: Introductionmentioning

confidence: 99%

Identification of Non-Varying Coefficients in Varying-Coefficient Models

Mei

Zhang

2005

Acta Mathematicae Applicatae Sinica, English Series

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A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know a priori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F -approximation and three-moment χ 2 approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory.

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

Cited by 178 publications

References 14 publications

Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

Identification of Non-Varying Coefficients in Varying-Coefficient Models

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