Quantile Regression

[s3alfisc]

What this PR does:

• Implements quantile regression via a quantreg function via the Frisch-Newton Interior Point solver as described in Koenker and Ng or Portnoy & Koenker.
• Additionally, implements preprocessing as explained in Chernozkukov et al or Portnoy & Koenker mentioned above.
• Implements skeleton of Algo 2 in Chernozhukov et al "Preprocessing for the quantile regression process"
• Implements a qplot method for visualization.

Status:

• Runs, with some minor bugs (i.e. poorly initialised starting values), non-convergence.
• Tests against R implemented.
• Tests against R pass.
• Only one vcov type supported so far, no clustering. Seems to have bugs as SEs are completely off (see below).
• Add function arguments to quantreg function: rng, tol, maxiter.
• Get @kinto-b to port the FN algo to Rust ;-)

Example:

%load_ext autoreload

import pyfixest as pf
data = pf.get_data(N = 1000)

fit_1_pf = pf.quantreg("Y ~ X1 + X2 + f1", data = data, quantile = 0.1)
fit_1_pf.tidy()

# Estimate	Std. Error	t value	Pr(>|t|)	2.5%	97.5%
# Coefficient						
# Intercept	-2.030300	0.000023	-90149.457722	0.0	-2.030344	-2.030256
# X1	    -0.938896	0.000097	-9704.853077	0.0	-0.939086	-0.938706
# X2	    -0.190710	0.000004	-51162.093928	0.0	-0.190718	-0.190703
# f1	     0.011888	0.000480	24.749725	0.0	0.010946	0.012831

R instead:

quantreg::rq(formula = Y ~ X1 + X2 + f1, tau = 0.1, data = data, method = "fn")
# Coefficients:
# (Intercept)          X1          X2          f1 
# -2.03029974 -0.93889613 -0.19071031  0.01188816