Note on a linear model with errors in the variables and with trend

a b s t r a c tWe study a multivariate ultrastructural measurement error (MUME) model with more than one response variable. This model is a synthesis of multivariate functional and structural models. Three consistent estimators of regression coefficients, satisfying the exact linear restrictions have been proposed. Their asymptotic distributions are derived under the assumption of a non-normal measurement error and random error components. A simulation study is carried out to investigate the small sample properties of the estimators. The effect of departure from normality of the measurement errors on the estimators is assessed.

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“…In the long run, the possibility of any trend in the observations is avoided by using assumption 5 (Refs. [17,18]). …”

Section: Model Specificationsmentioning

confidence: 97%

Restricted estimation in multivariate measurement error regression model

Jain

Singh

Sharma

2011

Journal of Multivariate Analysis

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“…They also rule out the presence of any trend in observations; see Schneeweiss (1991). Let 1 = + 2 I p + 2 I p , 2 = + 2 I p , and 3 = + .…”

Section: Model and Assumptionsmentioning

confidence: 98%

Estimation of Regression Coefficients in a Restricted Measurement Error Model Using Instrumental Variables

Shalabh¹,

Garg²,

Misra³

2011

Communications in Statistics - Theory and Methods

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The use of instrumental variable approach is extended in measurement error models to the case when regression coefficients are subjected to exact linear restrictions. Some consistent estimators of regression coefficients are obtained which satisfy the restrictions also. We do not make any assumption the distribution of measurement errors and they need not to have necessarily a normal distribution. The asymptotic properties of the estimators are studied. A simulation study is simultaneously conducted to investigate the finite sample properties and compare the efficiencies of the proposed estimators.

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“…This assumption implies that lim n−→∞ 1 n M M = σ µ σ µ = Σ µ (say) and lim n−→∞ 1 n M e n = σ µ , where e n is a n × 1 vector of elements unity. This assumption is needed to avoid the presence of any trend in the observations -see [32] and for the existence of the asymptotic distribution of the estimators.…”

Section: The Ultrastructural Model and Prior Informationmentioning

confidence: 99%

Use of prior information in the consistent estimation of regression coefficients in measurement error models

Shalabh

Garg

Misra

2009

Journal of Multivariate Analysis

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a b s t r a c tA multivariate ultrastructural measurement error model is considered and it is assumed that some prior information is available in the form of exact linear restrictions on regression coefficients. Using the prior information along with the additional knowledge of covariance matrix of measurement errors associated with explanatory vector and reliability matrix, we have proposed three methodologies to construct the consistent estimators which also satisfy the given linear restrictions. Asymptotic distribution of these estimators is derived when measurement errors and random error component are not necessarily normally distributed. Dominance conditions for the superiority of one estimator over the other under the criterion of Löwner ordering are obtained for each case of the additional information. Some conditions are also proposed under which the use of a particular type of information will give a more efficient estimator.

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Note on a linear model with errors in the variables and with trend

Cited by 23 publications

References 5 publications

Restricted estimation in multivariate measurement error regression model

Restricted estimation in multivariate measurement error regression model

Estimation of Regression Coefficients in a Restricted Measurement Error Model Using Instrumental Variables

Use of prior information in the consistent estimation of regression coefficients in measurement error models

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