A goodness-of-fit test for a polynomial errors-in-variables model

被引：7

作者：

Cheng C.-L. ^{[1
]}

Kukush A.G. ^{[2
]}

机构：

[1] Academia Sinica, Taipei

[2] Shevchenko Kiev University, Kiev

来源：

Ukrainian Mathematical Journal | 2004年 / 56卷 / 4期

关键词：

Regression Model; Normal Distribution; Null Hypothesis; Weight Function; Polynomial Regression;

D O I：

10.1007/s11253-005-0095-9

中图分类号：

学科分类号：

摘要：

Polynomial regression models with errors in variables are considered. A goodness-of-fit test is constructed, which is based on an adjusted least-squares estimator and modifies the test introduced by Zhu et al. for a linear structural model with normal distributions. In the present paper, the distributions of errors are not necessarily normal. The proposed test is based on residuals, and it is asymptotically chi-squared under null hypothesis. We discuss the power of the test and the choice of an exponent in the exponential weight function involved in test statistics. © 2004 Springer Science+Business Media, Inc.

引用

页码：641 / 661

页数：20

共 8 条

[1]

Cheng C.-L., Schneeweiss H., Polynomial regression with errors in the variables, J. R. Statist. Soc. B, 60, pp. 189-199, (1998)

[2]

Carroll R.J., Ruppert D., Stefanski L.A., Measurement Error in Nonlinear Models, (1995)

[3]

Cheng C.-L., Schneeweiss H., Thamerus M., A small sample estimator for a polynomial regression with errors in the variables, J. R. Statist. Soc. B, 62, pp. 699-709, (2000)

[4]

Cheng C.-L., Schneeweiss H., On the polynomial measurement error model, Total Least Squares and Errors-in-Variables Modeling, pp. 131-143, (2002)

[5]

Zhu L., Cui H., Ng K.W., Testing lack-of-fit for linear errors-in-variables model, Acta Appl. Math.

[6]

Rosenthal H.P., On the subspaces of L <sup>p</sup> (p > 2) spanned by sequences of independent random variables, Isr. J. Math., 8, pp. 273-303, (1970)

[7]

Schneeweiss H., Nittner T., Estimating A Polynomial Regression with Measurement Errors in the Structural and in the Functional Case - A Comparison, (2000)

[8]

Kukush A., Schneeweiss H., A comparison of asymptotic covariance matrices of adjusted least squares and structural least squares in error ridden polynomial regression, J. Statist. Plan. Inference

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