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Estimating long term trends in tropospheric ozone
International Statistical Review (2002)
  • Michael S Smith, Melbourne Business School
  • Paul Yau
  • Tom Shively
  • Robert Kohn

This paper develops methodology for estimating long ­term trends in the daily maxima of tropospheric ozone. The methods are then applied to study long­term trends in ozone at six monitoring sites in the state of Texas. The methodology controls for the effects of me­teorological variables because it is known that variables such as temperature, wind speed and humidity substantially affect the formation of tropospheric ozone. A semiparametric regression model is estimated in which a nonparametric trivariate surface is used to model the relationship between ozone and these meteorological variables because, while it is known the relationship is a complex nonlinear one, its functional form is unknown. The model also allows for the effects of wind direction and seasonality. The errors are modeled as an au­toregression, which is methodologically challenging because the observations are unequally spaced over time. Each function in the model is represented as a linear combination of basis functions located at all of the design points. We also estimate an appropriate data transfor­mation simultaneously with the functions. The functions are estimated nonparametrically by a Bayesian hierarchical model that uses indicator variables to allow a non­zero probability that the coefficient of each basis term is zero. The entire model, including the nonparametric surfaces, data transformation and autoregression for the unequally spaced errors, is esti­mated using a Markov chain Monte Carlo sampling scheme with a computationally efficient transition kernel for generating the indicator variables. The empirical results indicate that key meteorological variables explain most of the variation in daily ozone maxima through a nonlinear interaction and that their effects are consistent across the six sites. However, the estimated trends vary considerably from site to site, even within the same city.

  • Autoregression with unequally spaced data,
  • Bayesian model averaging,
  • Bayesian semiparametric regression,
  • Data transformation,
  • Nonparametric regression,
  • Radial bases
Publication Date
Citation Information
Michael S Smith, Paul Yau, Tom Shively and Robert Kohn. "Estimating long term trends in tropospheric ozone" International Statistical Review Vol. 70 (2002)
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