rq(x, y, tau=-1, alpha=.1, dual=TRUE, int=TRUE, tol=1e-4, ci = TRUE, method="score", interpolate=TRUE, tcrit=TRUE, hs=TRUE) rq.formula(formula, data=list(), subset, na.action, tau=-1, alpha = 0.10000000000000001, dual = TRUE, tol = 0.0001, ci = TRUE, method="score", interpolate = TRUE, tcrit = TRUE, hs=TRUE)
x
| vector or matrix of explanatory variables. If a matrix, each column represents a variable and each row represents an observation (or case). This should not contain column of 1s unless the argument intercept is FALSE. The number of rows of x should equal the number of elements of y, and there should be fewer columns than rows. If x is missing, rq() computes the ordinary sample quantile(s) of y. |
y
| response vector with as many observations as the number of rows of x. |
tau
| desired quantile. If tau is missing or outside the range [0,1] then all the regression quantiles are computed and the corresponding primal and dual solutions are returned. |
alpha
| level of significance for the confidence intervals; default is set at 10%. |
dual
| return the dual solution if TRUE (default). |
int
| flag for intercept; if TRUE (default) an intercept term is included in the regression. |
tol
| tolerance parameter for rq computations. |
ci
| flag for confidence interval; if TRUE (default) the confidence intervals are returned. |
method
| if method="score" (default), ci is computed using regression rank score inversion; if method="sparsity", ci is computed using sparsity function. |
interpolate
| if TRUE (default), the smoothed confidence intervals are returned. |
tcrit
| if tcrit=T (default), a finite sample adjustment of the critical point is performed using Student's t quantile, else the standard Gaussian quantile is used. |
hs
| logical flag to use Hall-Sheather's sparsity estimator (default); otherwise Bofinger's version is used. |
coef
| the estimated parameters of the tau-th conditional quantile function. |
resid
| the estimated residuals of the tau-th conditional quantile function. |
dual
| the dual solution (if dual=T). |
h
| the index of observations in the basis. |
ci
| confidence intervals (if ci=T). |
[2] Koenker, R.W. and d'Orey (1987). Computing Regression Quantiles. Applied Statistics, 36, 383-393.
[3] Gutenbrunner, C. Jureckova, J. (1991). Regression quantile and regression rank score process in the linear model and derived statistics, Annals of Statistics, 20, 305-330.
[4] Koenker, R.W. and d'Orey (1994). Remark on Alg. AS 229: Computing Dual Regression Quantiles and Regression Rank Scores, Applied Statistics, 43, 410-414.
[5] Koenker, R.W. (1994). Confidence Intervals for Regression Quantiles, in P. Mandl and M. Huskova (eds.), Asymptotic Statistics, 349-359, Springer-Verlag, New York.
data(stackloss) rq(stack.x, stack.loss, .5) #the l1 estimate for the stackloss data rq(stack.x, stack.loss, tau=.5, ci=T, method="score") #same as above with #regression rank score inversion confidence interval rq(stack.x, stack.loss, .25) #the 1st quartile, #note that 8 of the 21 points lie exactly #on this plane in 4-space rq(stack.x, stack.loss, -1) #this gives all of the rq solutions rq(y=rnorm(10), method="sparsity") #ordinary sample quantiles data(Patacamaya) # an example with formula z0.1 <- rq.formula(y ~ a+tipo, data=Patacamaya, na.action=na.omit, tau=0.1) z0.1$coef z0.1$ci