R Under development (unstable) (2024-05-25 r86622 ucrt) -- "Unsuffered Consequences"
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> rq.fit.panel <- function(X,y,s,w=c(.25,.5,.25),taus=(1:3)/4,lambda = 1){
+ # prototype function for panel data fitting of QR models
+ # the matrix X is assumed to contain an intercept
+ # the vector s is a strata indicator assumed (so far) to be a one-way layout
+ # NB:  
+ # 0.  This is an altered version from that originally posted -- the definition
+ #     of the rhs vector now incorporates a factor of 1/2 for the penalty.
+ # 1.  The value of the shrinkage parameter lambda is an open research problem in
+ #   the simplest homogneous settings it should be the ratio of the scale parameters
+ #   of the fixed effects and the idiocyncratic errors
+ # 2.  On return the coefficient vector has m*p + n elements where m is the number
+ # quantiles being estimated, p is the number of colums of X, and n is the
+ # number of distinct values of s.  The first m*p coefficients are the 
+ # slope estimates, and the last n are the "fixed effects"
+ # 3.  Like all shrinkage (regularization) estimators, asymptotic inference is somewhat
+ # problematic... so the bootstrap is the natural first resort.
+   require(SparseM)
+   require(quantreg)
+   K <- length(w)
+   if(K != length(taus))
+     stop("length of w and taus must match")
+   X <- as.matrix(X)
+   p <- ncol(X)
+   n <- length(levels(as.factor(s)))
+   N <- length(y)
+   if(N != length(s) || N != nrow(X))
+     stop("dimensions of y,X,s must match")
+   Z <- as.matrix.csr(model.matrix(~as.factor(s)-1))
+   Fidelity <- cbind(as(w,"matrix.diag.csr") %x% X,w %x% Z)
+   Penalty <- cbind(as.matrix.csr(0,n,K*p),lambda*as(n,"matrix.diag.csr"))
+   D <- rbind(Fidelity,Penalty)
+   y <- c(w %x% y,rep(0,n))
+   a <- c((w*(1-taus)) %x% (t(X)%*%rep(1,N)),
+     sum(w*(1-taus)) * (t(Z) %*% rep(1,N)) + lambda * rep(1/2,n))
+   rq.fit.sfn(D,y,rhs=a)
+ }
> 
> proc.time()
   user  system elapsed 
   0.15    0.09    0.23