Variance of Weighted Regression Estimators when Sampling Errors are Independent and Heteroscedastic

Bement, Thomas R.; Williams, J. S.

doi:10.1080/01621459.1969.10501063

Cited by 30 publications

(16 citation statements)

References 5 publications

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“…The effect of estimated variance and covariance parameters on mean squared error of estimation or prediction has been considered previously in the context of time series models (Yamamoto (1976), Reinsel (1980), Fuller andHasza (1981)), random and mixed linear models (Khatri and Shah (1981), Reinsel (1984), Kackar and Harville (1984)), the heteroscedastie regression model (Bement and Williams (1969), Carroll et al (1988)), and the general linear model (Toyooka (1982), Rothenberg (1984), Eaton (1985), Harville (1985), Harville and Jeske (1992)). The present paper follows closely the development of Harville (1985) and Harville and Jeske (1992), and much of it may be viewed as an extension of their results to models with generalized covariances.…”

Section: Introductionmentioning

confidence: 99%

Mean squared prediction error in the spatial linear model with estimated covariance parameters

1992

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Abstract. The problem considered is that of predicting the value of a linear functional of a random field when the parameter vector 0 of the covariance function (or generalized covariance function) is unknown. The customary predictor when 0 is unknown, which we call the EBLUP, is obtained by substituting an estimator 0 for 0 in the expression for the best linear unbiased predictor (BLUP). Similarly, the customary estimator of the mean squared prediction error (MSPE) of the EBLUP is obtained by substituting 0 for 0 in the expression for the BLUP's MSPE; we call this the EMSPE. In this article, the appropriateness of the EMSPE as an estimator of the EBLUP's MSPE is examined, and alternative estimators of the EBLUP's MSPE for use when the EMSPE is inappropriate are suggested. Several illustrative examples show that the performance of the EMSPE depends on the strength of spatial correlation; the EMSPE is at its best when the spatial correlation is strong.

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Section: Introductionmentioning

confidence: 99%

Mean squared prediction error in the spatial linear model with estimated covariance parameters

1992

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“…Unweighted regression involves the assumption that the r 2 i are equal, which is unlikely to be true. However, unlike the weighted regression methods, it does not require estimation of r 2 p and does not depend on how well the r 2 i are estimated; Bement & Williams (1969) suggest that at least ten degrees of freedom are required when estimating each r 2 i in a weighted regression.…”

Section: A P P R O a C H E S T O T H E S E C O N D S T A G E O F T H mentioning

confidence: 99%

“…It is difficult to obtain a simple expression for the bias inVb W , owing to the estimation of the weights (Bement & Williams 1969). For unweighted regression, the bias inVb U can be written as (Appendix A)…”

Section: )mentioning

confidence: 99%

Modelling data from different sites, times or studies: weighted vs. unweighted regression

Fletcher¹,

Dixon²

2011

Methods Ecol Evol

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Summary 1.We consider the use of weighted regression when modelling data from different sites, times or studies. Our primary focus is on the coverage rate of the 95% confidence interval for the slope parameter when we have a single predictor variable. We use simulation to assess this coverage rate for both weighted and unweighted regression, across a range of scenarios likely to be encountered in ecology. 2. Our results are surprising: unweighted regression will often be more reliable than weighted regression. The well-known advantages of weighted regression are offset by having to estimate the process error variance. Although unweighted regression involves assuming that the measurement error variances are equal, the coverage rate is remarkably robust to departures from this assumption. Unweighted regression will often be more robust because it does not make use of potentially poor information on the measurement error variances. The only situation in which unweighted regression will perform poorly is when there is a strong relationship between the precision of an estimate and its leverage in the regression. We propose a simple diagnostic tool to assess when this might be the case. 3. The implications of our results are important in a management context as they indicate the benefits obtained from using a simple, readily understood approach to combining information.

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“…In [2], the efficiency of the weighted mean with estimate variances was studied. The variance of the weighted regression was derived in [3]. A new estimator that is more efficient than the maximum likelihood estimate was developed in [4].…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Fusion of Observations Provided by Two Sensors

Azmani

Reboul

Benjelloun

2013

Entropy

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When we try to make the best estimate of some quantity, the problem of combining results from different experiments is encountered. In multi-sensor data fusion, the problem is seen as combining observations provided by different sensors. Sensors provide observations and information on an unknown quantity, which can differ in precision. We propose a combined estimate that uses prior information. We consider the simpler aspects of the problem, so that two sensors provide an observation of the same quantity. The standard error of the observations is supposed to be known. The prior information is an interval that bounds the parameter of the estimate. We derive the proposed combined estimate methodology, and we show its efficiency in the minimum mean square sense. The proposed combined estimate is assessed using synthetic data, and an application is presented.

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Variance of Weighted Regression Estimators when Sampling Errors are Independent and Heteroscedastic

Cited by 30 publications

References 5 publications

Mean squared prediction error in the spatial linear model with estimated covariance parameters

Mean squared prediction error in the spatial linear model with estimated covariance parameters

Modelling data from different sites, times or studies: weighted vs. unweighted regression

Non-Linear Fusion of Observations Provided by Two Sensors

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