Residuals method for unitquantreg objects

Usage

# S3 method for unitquantreg
residuals(object, type = c("quantile", "cox-snell", "working", "partial"), ...)

Arguments

object

fitted model object of class unitquantreg.

type

character indicating type of residuals. The options are "quantile", "cox-snell", "working" and "partial".

...

currently not used.

Value

Numeric vector of residuals extract from an object of class unitquantreg.

Details

The residuals method can compute quantile and Cox-Snell residuals. These residuals are defined, respectively, by

$$r_{Q} = \Phi^{-1}\left[ F(y_i \mid \widehat{\mu}_i, \widehat{\theta}_i)\right]$$

and

$$r_{CS} = -\log\left[1- F(y_i \mid \widehat{\mu}_i, \widehat{\theta}_i)\right]$$ where $\widehat{\mu}_i$ and $\widehat{\theta}_i$ are the fitted values of parameters $\mu$ and $\theta$, $F(\cdot \mid \cdot, \cdot)$ is the cumulative distribution function (c.d.f.) and $\Phi(\cdot)$ is the c.d.f. of standard Normal distribution.

Apart from the variability due the estimates of parameters,if the fitted regression model is correctly specified then the quantile residuals, $r_Q$, follow a standard Normal distribution and the Cox-Snell residuals, $r_{CS}$, follow a standard exponential distribution.

References

Cox, D. R. and Snell E. J., (1968). A general definition of residuals. Journal of the Royal Statistical Society - Series B, 30(2), 248--265.

Dunn, P. K. and Smyth, G. K., (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5(3), 236--244.

Author

André F. B. Menezes