The meaning is analogous to the previous two plots. The slope of the trend is proportional to the difference (kurtosis-3). When the kurtosis is very different from normal, the plot shows a clear trend. Pairs of data points (first–last, second–second largest, etc.) are used when ...
Typically the function Ψ is assumed to be odd, meaning that Ψ(−x) = −Ψ(x) for any x. (The reason for this will become clear in Chapter 3.) The value μm that satisfies Eq. (2.10) is called an M-measure of location. Obviously the class of odd functions is too large for...
This asymmetry suggests the process is heteroskedastic, the variance in the lower end is higher than in the higher end so we get “fan” like figure instead of parallel lines. The economic meaning of it is that when this index is high, steps are takes to depress it. Steps like lowering ...
Not specifying this option is equivalent to specifying quantiles(.25 .75), meaning the interquantile range. qreg — Quantile regression 7 reps(#) specifies the number of bootstrap replications to be used to obtain an estimate of the variance–covariance matrix of the estimators (standard errors...
The theorem implies that the M-estimator is consistent with respect to the class of forecasts indexed by Θ, meaning that |R(θ̂NT,τ,τ)−infθ∈ΘR(θ,τ)|→p0 as T→∞. In other words, the M-estimator achieves asymptotically the optimal forecasting performance attainable within ...
The existing quantile regression methodology works well in the case of a fixed quantile level, or in the case of a quantile that is only moderately high, that is, τn→1 and n(1−τn)→∞ as n→∞, meaning that there are sufficient observations above the τn level. For more ...
resource pollution; (2) the quantile model regression results showed that the relationship between economic growth and ecological pollution followed the so-called environmental Kuznets inverted U-curve. Wastewater discharge per capita was low in areas with low per capita GDP, meaning that the ...
Herman H. Rieke, in Probability in Petroleum and Environmental Engineering, 2005 STATISTICAL MEANING OF QUANTILES Suppose that one performs a certain stochastic experiment n times, and some random variableξ gets the values ξ1,ξ2,…, ξn in successive trials. These values of ξ are usually ...
The main issue with quantile panel data models is that the standard de-meaning (or differencing) techniques used in standard models do not represent feasible approaches. When the number of panels is large, this entails a huge number of estimated αi (individual effects) parameters. The so-calle...
(Mulholland et al.1998). In that sense, we expect PM10pollution estimates in the south, where there are sparser data due to fewer monitoring stations, to have larger standard errors; meaning, that these errors may influence the results. As monitoring stations are not equally distributed across...