On Consistent Estimators in Nonlinear Functional Errors-In-Variables Models

Kukush, Alexander; Zwanzig, Silvelyn

doi:10.1007/978-94-017-3552-0_13

Cited by 16 publications

(4 citation statements)

References 9 publications

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“…This model is known as error in variables (EIV) models, considered by Fuller [1] and others. The contemplated ME model is also known as the simple structural linear relation model with model error, and we refer to Hsiao [5] and Kukush and Zwanzig [8] where other pertinent references are cited.…”

Section: The Me Modelmentioning

confidence: 99%

The Theil–Sen estimator in a measurement error perspective

Sen¹,

Saleh²

2010

Institute of Mathematical Statistics Collections

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In a simple measurement error regression model, the classical least squares estimator of the slope parameter consistently estimates a discounted slope, though sans normality, some other properties may not hold. It is shown that for a broader class of error distributions, the Theil-Sen estimator, albeit nonlinear, is a median-unbiased, consistent and robust estimator of the same discounted parameter. For a general class of nonlinear (including R−, M− and L− estimators), study of asymptotic properties is greatly facilitated by using some uniform asymptotic linearity results, which are, in turn, based on contiguity of probability measures. This contiguity is established in a measurement error model under broader distributional assumptions. Some asymptotic properties of the Theil-Sen estimator are studied under slightly different regularity conditions in a direct way bypassing the contiguity approach.

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Section: The Me Modelmentioning

confidence: 99%

The Theil–Sen estimator in a measurement error perspective

Sen¹,

Saleh²

2010

Institute of Mathematical Statistics Collections

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“…The method used is the adjustment procedure is due to Kukush and Zwanzig (2002). We give conditions, under which the estimator is strongly consistent.…”

Section: Discussionmentioning

confidence: 99%

“…We propose an adjustment procedure, that deÿnes a consistent estimator. The proposed approach is due to Kukush and Zwanzig (2002), and it is related to the method of corrected score functions, (see Carroll et al, 1995, Section 6.5). The model (3) is quadratic and similar adjustment for a bilinear model, arising in motion analysis, is proposed in We deÿne the elementary ALS cost function q als (ÿ; x) by Eq als (ÿ; x + e) = q ols (ÿ; x) for all ÿ ∈ V and x ∈ R n ;…”

Section: Als Estimator With Known Noise Variancementioning

confidence: 99%

Consistent estimation in an implicit quadratic measurement error model

Kukush

Markovsky

Huffel

2004

Computational Statistics & Data Analysis

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An adjusted least squares estimator is derived that yields a consistent estimate of the parameters of an implicit quadratic measurement error model. In addition, a consistent estimator for the measurement error noise variance is proposed. Important assumptions are: (1) all errors are uncorrelated identically distributed and (2) the error distribution is normal. The estimators for the quadratic measurement error model are used to estimate consistently conic sections and ellipsoids. Simulation examples, comparing the adjusted least squares estimator with the ordinary least squares method and the orthogonal regression method, are shown for the ellipsoid ÿtting problem.

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“…We propose an adjustment procedure, that defines a consistent estimator. The proposed approach is due to [KZ02], and it is related to the method of corrected score functions, see [CRS95, Sec. 6.5].…”

Section: Adjusted Least Squares Estimationmentioning

confidence: 99%

Consistent least squares fitting of ellipsoids

2004

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Summary.A parameter estimation problem for ellipsoid fitting in the presence of measurement errors is considered. The ordinary least squares estimator is inconsistent, and due to the nonlinearity of the model, the orthogonal regression estimator is inconsistent as well, i.e., these estimators do not converge to the true value of the parameters, as the sample size tends to infinity. A consistent estimator is proposed, based on a proper correction of the ordinary least squares estimator. The correction is explicitly given in terms of the true value of the noise variance. Classification (2000): 65D15, 65D10, 15A63 Mathematics Subject

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On Consistent Estimators in Nonlinear Functional Errors-In-Variables Models

Cited by 16 publications

References 9 publications

The Theil–Sen estimator in a measurement error perspective

The Theil–Sen estimator in a measurement error perspective

Consistent estimation in an implicit quadratic measurement error model

Consistent least squares fitting of ellipsoids

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