Maximum likelihood method for parameter estimation in linear model with belowdetection data
Abstract
The maximum likelihood (ML) method for regression analyses of leftcensored data is improved for general acceptance by considering the censored observations to be doubly censored. The existence of a lower bound (i.e., the concentration of a pollutant cannot be negative) is included; the improved ML method utilizes this information in the formulation of a likelihood function. The improved ML method has been translated into an equivalent least squares (LS) method, and an iterative algorithm is presented to estimate the statistical parameters from this LS translation. The LS translation is easy to explain to nonstatisticians, and computational requirements for implementing the LS method are minimal. The methodology is applied to a mechanistic model for air transport and deposition of polycyclic aromatic hydrocarbons (PAH) to a snow surface. For a censored data set, parameter estimates of the model, namely, dry deposition velocities and washout ratios, were obtained for various PAH species by using the following three procedures: (1) the NAG15 routine for maximization of a likelihood function; (2) the proposed algorithm for the equivalent LS method; and (3) the modified iterative least squares method.
 Authors:
 Univ. of Waterloo, Ontario (Canada). Dept. of Civil Engineering
 CRA, Ltd., Waterloo, Ontario (Canada)
 Publication Date:
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 162994
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Environmental Engineering; Journal Volume: 121; Journal Issue: 11; Other Information: PBD: Nov 1995
 Country of Publication:
 United States
 Language:
 English
 Subject:
 54 ENVIRONMENTAL SCIENCES; POLYCYCLIC AROMATIC HYDROCARBONS; ENVIRONMENTAL TRANSPORT; ALGORITHMS; LEAST SQUARE FIT; WASHOUT; AIR POLLUTION
Citation Formats
Sharma, M., Thomson, N., and McBean, E.A. Maximum likelihood method for parameter estimation in linear model with belowdetection data. United States: N. p., 1995.
Web. doi:10.1061/(ASCE)07339372(1995)121:11(776).
Sharma, M., Thomson, N., & McBean, E.A. Maximum likelihood method for parameter estimation in linear model with belowdetection data. United States. doi:10.1061/(ASCE)07339372(1995)121:11(776).
Sharma, M., Thomson, N., and McBean, E.A. Wed .
"Maximum likelihood method for parameter estimation in linear model with belowdetection data". United States.
doi:10.1061/(ASCE)07339372(1995)121:11(776).
@article{osti_162994,
title = {Maximum likelihood method for parameter estimation in linear model with belowdetection data},
author = {Sharma, M. and Thomson, N. and McBean, E.A.},
abstractNote = {The maximum likelihood (ML) method for regression analyses of leftcensored data is improved for general acceptance by considering the censored observations to be doubly censored. The existence of a lower bound (i.e., the concentration of a pollutant cannot be negative) is included; the improved ML method utilizes this information in the formulation of a likelihood function. The improved ML method has been translated into an equivalent least squares (LS) method, and an iterative algorithm is presented to estimate the statistical parameters from this LS translation. The LS translation is easy to explain to nonstatisticians, and computational requirements for implementing the LS method are minimal. The methodology is applied to a mechanistic model for air transport and deposition of polycyclic aromatic hydrocarbons (PAH) to a snow surface. For a censored data set, parameter estimates of the model, namely, dry deposition velocities and washout ratios, were obtained for various PAH species by using the following three procedures: (1) the NAG15 routine for maximization of a likelihood function; (2) the proposed algorithm for the equivalent LS method; and (3) the modified iterative least squares method.},
doi = {10.1061/(ASCE)07339372(1995)121:11(776)},
journal = {Journal of Environmental Engineering},
number = 11,
volume = 121,
place = {United States},
year = {Wed Nov 01 00:00:00 EST 1995},
month = {Wed Nov 01 00:00:00 EST 1995}
}

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