A law of the iterated logarithm for the product limit estimator with doubly censored data

2011 ◽  
Vol 81 (8) ◽  
pp. 1241-1244 ◽  
Author(s):  
Fatiha Messaci ◽  
Nahima Nemouchi
Keyword(s):  
Censored Data ◽  
Iterated Logarithm ◽  
Product Limit Estimator ◽  
Doubly Censored Data ◽  
Doubly Censored ◽  
Product Limit

Linear regression analyses with censored data: estimation of PAH washout ratios and dry deposition velocities to a snow surface

1995 ◽  
Vol 22 (4) ◽  
pp. 819-833 ◽  
Author(s):  
Mukesh Sharma ◽  
Neil R. Thomson ◽  
Edward A. McBean
Keyword(s):  
Least Squares ◽  
Censored Data ◽  
Dry Deposition ◽  
Least Squares Method ◽  
Deposition Velocity ◽  
Snow Surface ◽  
Regression Analyses ◽  
Doubly Censored Data ◽  
Doubly Censored ◽  
Censored Observations

Detection limits of analyzing instruments are the main reason for censored observations of pollutant concentrations. An iterative least squares method for regression analyses is developed to suit the doubly censored data commonly observed in environmental engineering. The modified iterative least squares method utilizes the expected values of censored observations estimated from the probability density function of doubly censored data in a regression process. The modified method is examined for bias in the estimation of the parameters of a linear model, and in the estimation of the standard deviation of the regression. A mechanistic model for atmospheric transport and deposition of polycyclic aromatic hydrocarbons (PAHs) to a snow surface is formulated by utilizing the long-term PAH retention property of deep snowpacks. The modified iterative least squares method is applied to estimate the deposition parameters (dry deposition velocity and washout ratio) for various PAH species, since some of the PAH deposition levels were below the minimum detection limit of the analyzing instrument. The estimated parameters are examined statistically, and compare favourably with previously reported estimates of these parameters. Key words: censored data, regression, iterative least squares, PAHs, dry deposition velocity, washout ratio.

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