A further study of the relationship between PM10 level and daily mortality in El Paso, Texas using a historical functional linear model

The purpose of this research is to study how PM10 (air pollutant particle concentrations in μg/m 3, particles with median aerodynamic diameter less than 10 um) during the past days continuously influences the mortality of the current day using a historical functional linear model. Regression analysis of daily mortality on PM10 typically uses a linear model in the daily average of PM10 for the previous 1 to 3 days, whereas the historical functional linear model uses the unprocessed hourly PM10 observations for all past days. The historical functional linear model is formulated in terms of a coefficient β( t), indexed by time t, convoluted with the PM10 hourly data. This research lays out the estimating equations for non-parametric estimation of β( t) using P-splines. A likelihood ratio test statistic is provided for testing significance of the PM10 as a predictor of daily mortality. Computer simulations are used to investigate the properties of the estimator of β( t) and the power of the likelihood ratio test. This research makes a novel contribution in the sense that it breaks through limitations of the available methodology by: (1) Allowing for the influence of PM10 of all the past days; (2) Avoiding the loss of information suffered from using the daily average of 24 hourly PM10 data