A convenient choice is the asymmetric Laplacian likelihood, because the mode of the resulting posterior under a flat prior is the usual quantile regression estimates.
42.
This choice of " plotting position " ( choice of quantile of the theoretical distribution ) has occasioned less controversy than the choice for Q Q plots.
43.
Because quantile regression does not normally assume a parametric likelihood for the conditional distributions of Y | X, the Bayesian methods work with a working likelihood.
44.
Otherwise a rounding or interpolation scheme is used to compute the quantile estimate from,, and . ( For notation, see floor and ceiling functions ).
45.
Furthermore, the-quantile of the sum equals of the sum of the-quantiles of its components, hence comonotonic random variables are quantile-additive.
46.
Furthermore, the-quantile of the sum equals of the sum of the-quantiles of its components, hence comonotonic random variables are quantile-additive.
47.
If is not an integer, then round up to the next integer to get the appropriate index; the corresponding data value is the-th-quantile.
48.
One advantage of quantile regression, relative to the ordinary least squares regression, is that the quantile regression estimates are more robust against outliers in the response measurements.
49.
One advantage of quantile regression, relative to the ordinary least squares regression, is that the quantile regression estimates are more robust against outliers in the response measurements.
50.
A graphical tool for assessing normality is the normal probability plot, a quantile-quantile plot ( QQ plot ) of the standardized data against the standard normal distribution.
