Jackknife Interval Estimation of Air-Pollutant Concentrations from Road Traffic in Athens

In this paper the air-pollutant concentration is denoted as a random variable C(t), t = 1, 2, ... , 24, from an unknown distribution F(mu, sigma[superscript 2]). Fixing the time t of the day, the data have the form C [subscript 1], C [subscript 2], ... , C [subscript 360]. The aim is to find a distribution-free confidence interval for the mean (mu) of the unknown distribution F. The Classical large-sample confidence interval for mu has a large expected length because the variance estimate [superscript 2] of sigma[superscript 2] is biased. For this reason, we propose the subsampling statistical technique of bias reduction and robust interval estimation, commonly known as quot;Jackknife technique,quot; in order to construct distribution-free confidence intervals for the mean concentration, based on Tukey's conjecture, (Tukey, 1958). We find 24 confidence intervals for (mu) corresponding to the 24 hours of the day. We compare the lengths of the above intervals and we find the maximum and the minimum. The Jackknife confidence intervals, which we obtain in this way, are robust in the presence of different distributions of the concentration random variable C and they have smaller mean lengths than the Classical confidence intervals for (mu). We also find the sampling variance of the lengths of the confidence intervals and we perform tests of hypothesis for the mean mu. For a fixed day, we consider the time series of the observations of the concentrations over 24 hours. We propose an autoregressive model to predict future observations of concentrations. Because the quot;errorsquot; of this model suffer from the presence of non-normality, we propose the estimation of the parameters of this model by the statistical methodology quot;Bootstrapquot; (Efron, Tibshirani, 1993)