After reading some recent posts written by Atabey Kaygun, I thought I would go back to my old LispStat code to see whether it is still a thing.¹ Back at that time I started to write tutorials about LispStat. It was 10 years ago, and long after the R’s era, that I learned some LispStat, and I even bought the book. I’m actually using xlispstat version 3.52.23, which I installed from GitHub.

Today, we’ll do some bootstrap resampling. First, we need a little helper function to compute a given statistic on a sample data $b$ times:

(defun simulate (stat k fun)
  (let ((out ()))
    (dotimes (i k)
      (push (funcall stat (funcall fun))
            out))
    out))

Let’s test it using this simple instruction:

(simulate #'mean 20 #'(lambda () (normal-rand 25)))

Note that we could easily write a little procedure to compute the estimated slope of a linear regression model and plug it in place of the mean function above, like I did in an R example.

Now we can implement our bootstrap procedure. Note that LispStat comes with a built-in sample function, so we don’t need to implement this part of the algorithm (the last parameter t meansto sample with replacement):

(defun bootstrap (stat data b)
  (let ((n (length data))  )
    (simulate stat b
              #'(lambda () (sample data n t)))))

Let’s see it in action:

(setf seed (make-random-state *random-state*))
(def x (normal-rand 100))
(def bs (bootstrap #'mean x 1000))
(histogram bs :title "1000 bootstrap samples")

The bias is quite small ((- (mean x) (mean bs)) < 0.005 on my sample).