On the Polynomial Measurement Error Model

Cheng, Chi-Lun; Schneeweiß, Hans

doi:10.1007/978-94-017-3552-0_12

Cited by 14 publications

(10 citation statements)

References 29 publications

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“…Moreover, the ALS estimator σ ε 2 : = y 2 -t y ( ) ′β (4) converges in probability to σ ε 2 as n → ∞.…”

Section: Model and Estimatormentioning

confidence: 96%

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

Cheng¹,

Kukush

2004

Ukr Math J

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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.

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“…Moreover, the ALS estimator σ ε 2 : = y 2 -t y ( ) ′β (4) converges in probability to σ ε 2 as n → ∞.…”

Section: Model and Estimatormentioning

confidence: 96%

“…In [3], a small sample modification of the ALS estimator was constructed, which shows good results in small sample and is asymptotically equivalent to the ALS estimator. For a further discussion of related models, see [1,4].…”

Section: Introductionmentioning

confidence: 99%

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

Cheng¹,

Kukush

2004

Ukr Math J

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“…Indeed, this problem seems not even being mentioned, as can be inferred from important references on the subject, such as Chan and Mak (1985), Fuller (1987), Moon and Gunst (1993), Cheng and Schneeweiss (1998), Schneeweiss and Nittner (2001), Cheng and Schneeweiss (2002), Kuha and Temple (2003), and Kukush et al (2005). A goodness-of-fit test is presented in Cheng and Kukush (2004).…”

Section: Introductionmentioning

confidence: 94%

Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models

Zavala

Bolfarine

Castro

2006

AISM

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“…Quite often only the conditional mean function E(y|ξ) = m * (ξ, β), the regression in the narrower sense, is given, supplemented by a conditional variance function V(y|ξ) = v * (ξ, β, ϕ), where θ comprises β and ϕ plus possibly other parameters describing the distribution of y. Two major examples, that we will often refer to, are the polynomial model (for a survey see Cheng and Schneeweiss, 2002),…”

Section: Measurement Error Modelsmentioning

confidence: 99%

Some recent advances in measurement error models and methods

Schneeweiß

Augustin

2006

Allgemeines Statistisches Arch

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A measurement error model is a regression model with (substantial) measurement errors in the variables. Disregarding these measurement errors in estimating the regression parameters results in asymptotically biased estimators. Several methods have been proposed to eliminate, or at least to reduce, this bias, and the relative efficiency and robustness of these methods have been compared. The paper gives an account of these endeavors. In another context, when data are of a categorical nature, classification errors play a similar role as measurement errors in continuous data. The paper also reviews some recent advances in this field.

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On the Polynomial Measurement Error Model

Cited by 14 publications

References 29 publications

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

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

Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models

Some recent advances in measurement error models and methods

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