TY - JOUR

T1 - Source apportionment with one source unknown

AU - Bandeen-Roche, Karen

AU - Ruppert, David

N1 - Funding Information:
David Ruppertw aspartially supportedb y NSF Grant DMS-8800294.B oth authors were supported by the Army ResearchO ffice through the MathematicalS ciencesI nstitute at Cornell. We thankR ay Merrill for introducingo ne of us (D-R.) to this area of researcha nd suggestingth e possibility of indirectlye stimatingth e unknowns ource. This work includesm aterialf rom the Ph.D. Dis-sertationo f K.B.-R.

PY - 1991/2

Y1 - 1991/2

N2 - Attribution of local pollution to area sources is essential to effective management of the environment. Source apportionment addresses the problem by statistical inference of source contributions to total pollution from observations of ambient air chemical composition. Mass balance methods of source apportionment use linear models with chemical composition vectors of sources as covariates. Historically, mass balance methods have assumed that at least a proxy of each covariate is available and has been accounted for. We attempt to adapt the mass balance method to the case in which unidentified sources may exist by estimating an unknown, possibly 'background', source. Further, we allow source contributions to pollution to vary over time, creating a model with a 'structural' parameter and infinitely many 'incidental' parameters. We treat the 'incidental' source contribution parameters as random quantities. Investigating the properties of the distribution governing relative source contributions is then of interest. Reasonable identifiability constraints are required in this context. Nonparametric estimation of the unknown source is possible under such constraints but is impractical for small samples which are measured with error. Therefore, we develop a parametric model for the distribution of the observations and examine estimates based on this model.

AB - Attribution of local pollution to area sources is essential to effective management of the environment. Source apportionment addresses the problem by statistical inference of source contributions to total pollution from observations of ambient air chemical composition. Mass balance methods of source apportionment use linear models with chemical composition vectors of sources as covariates. Historically, mass balance methods have assumed that at least a proxy of each covariate is available and has been accounted for. We attempt to adapt the mass balance method to the case in which unidentified sources may exist by estimating an unknown, possibly 'background', source. Further, we allow source contributions to pollution to vary over time, creating a model with a 'structural' parameter and infinitely many 'incidental' parameters. We treat the 'incidental' source contribution parameters as random quantities. Investigating the properties of the distribution governing relative source contributions is then of interest. Reasonable identifiability constraints are required in this context. Nonparametric estimation of the unknown source is possible under such constraints but is impractical for small samples which are measured with error. Therefore, we develop a parametric model for the distribution of the observations and examine estimates based on this model.

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U2 - 10.1016/0169-7439(91)80046-S

DO - 10.1016/0169-7439(91)80046-S

M3 - Article

AN - SCOPUS:0026016552

VL - 10

SP - 169

EP - 184

JO - Chemometrics and Intelligent Laboratory Systems

JF - Chemometrics and Intelligent Laboratory Systems

SN - 0169-7439

IS - 1-2

ER -