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Table 1 Performance of approximations of precision of approximations to \( SE\left(\hat{\beta}\right) \) in 51 cities

From: Sample size issues in time series regressions of counts on environmental exposures

Estimator (text expression number)Distribution of % error in estimators of \( SE\left(\hat{\beta}\right) \) over the 51 cities
Mean (bias)Mean absoluteLowestHighest
A: Using known exposure distribution
 Poisson crude (1)− 39.339.3− 58.0−19.7
 Poisson (2)−3.83.9−11.52.6
 Q-Poisson (3)−2.32.5−5.04.0
B: Using exposure distribution from year 1
 Poisson_crude (1)−37.137.1−58.6−18.3
 Poisson (2)7.115.7−28.944.5
 Q-Poisson (3)9.117.1− 32.446.7
  1. The table summarises the distribution of errors in three approximations to the standard error of the coefficient of heat (\( SE\left(\hat{\beta}\right) \)) in the 51 Spanish provincial capitals
  2. % error = 100*[approximation-(true value)]/(true value)]