Estimating Regression Models with Multiplicative Heteroscedasticity

Harvey, Andrew

doi:10.2307/1913974

Cited by 775 publications

(333 citation statements)

References 6 publications

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“…In order to account for this, we used weighted regression, by weighting each observation by the inverse of its variance (σ i 2 ). Although this variance is unknown, it is commonly assumed that the variance of the error of the ith individual can be modelled as a power function of a subset of the independent variables, i.e., σ i 2 = (X i ) r [62]. The exponential term r was optimized to yield the most homogeneous studentized residual plot.…”

Section: Autocorrelation and Heteroscedasticitymentioning

confidence: 99%

Compatible System for Predicting Total and Merchantable Stem Volume over and under Bark, Branch Volume and Whole-Tree Volume of Pine Species

Corral-Rivas

Vega-Nieva

Rodríguez‐Soalleiro

et al. 2017

Forests

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Accurate quantification of branch volume in trees is important for sustainable forest management, especially as these fractions are increasingly used for bioenergy, and for precise forest CO 2 quantification. Whereas a large focus has been placed on the compatible estimation of tree taper and bole volume with and without bark, little effort has been made to develop models that allow a simultaneous prediction of these variables together with tree branch volume. In this study, 595 Pinus cooperi trees and 700 Pinus durangensis trees were sampled in pine-oak forests in the Sierra Madre Occidental, Mexico. A compatible system for predicting two segmented taper functions, over and under bark; the corresponding merchantable volumes; coarse branch volume and whole-tree volume was fitted using a modified continuous autoregressive structure to account for autocorrelation. The proposed compatible equations explained more than 97% of the observed variability in diameter over and under bark, volume over and under bark, and total tree volume and more than 64% of the observed variability in branch volume in both species. The method described can theoretically be replicated for any tree species, thus providing a better understanding of the patterns of volume distribution by components, potentially improving carbon accounting system and forest bioenergy planning.

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Section: Autocorrelation and Heteroscedasticitymentioning

confidence: 99%

Compatible System for Predicting Total and Merchantable Stem Volume over and under Bark, Branch Volume and Whole-Tree Volume of Pine Species

Corral-Rivas

Vega-Nieva

Rodríguez‐Soalleiro

et al. 2017

Forests

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“…This form of the variance function is due to (Harvey, 1976) and subsequently employed by several studies (Isik and Devadoss 2006, Isik and Khanna 2003, Asche and Tveteras 1999. The main advantage of this form is that it ensures positive output variance.…”

Section: Methodsmentioning

confidence: 99%

A Hybrid Model to Quantify the Impact of Climate Change on Agriculture in Godavari Basin, India

Palanisami¹,

Ranganathan²,

Kakumanu³

et al. 2011

EER

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A hybrid model incorporating the econometric and programming models was developed to quantify the impact of climate change on agriculture in Godavari basin, India. The Just and Pope production function was used to estimate the mean yield of crops and the variance associated with the mean yield and using the estimated yield, the multiple goal programming model was used to optimize the land and water use under mid and end century climate change scenarios. The results indicated that rice production will reduce during mid and end-century periods by 16% and 36% respectively and by incorporating the water and labour saving technologies in the crop production, the reduction in rice production will be eliminated during mid-century and it will be only 19% during end-century period. The overall water saving will be about 20% due to the adoption of these technologies. Technology up-scaling programs are suggested. Areas for future research are also indicated.

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“…and the corresponding empirical distribution by F (n) β ZX β (u) (see (27)), i. e. I β Z j X j β < u .…”

Section: Appendixmentioning

confidence: 99%

“…Remark 1.3. The problems, resulting from ignoring the heteroscedasticity, were recognized very early, see e. g. [14,15] or [27]. It is known that the efficient estimator (under the normality of disturbances) isβ…”

Section: Introduction Of Basic Frameworkmentioning

confidence: 99%

Instrumental weighted variables under heteroscedasticity, Part I -- Consistency

Víšek¹

2017

Kybernetika

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Estimating Regression Models with Multiplicative Heteroscedasticity

Cited by 775 publications

References 6 publications

Compatible System for Predicting Total and Merchantable Stem Volume over and under Bark, Branch Volume and Whole-Tree Volume of Pine Species

Compatible System for Predicting Total and Merchantable Stem Volume over and under Bark, Branch Volume and Whole-Tree Volume of Pine Species

A Hybrid Model to Quantify the Impact of Climate Change on Agriculture in Godavari Basin, India

Instrumental weighted variables under heteroscedasticity, Part I -- Consistency

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