How I See Bootstrap, Tests and KDE

Yihui Xie

Stat546 Final Project

https://yihui.org

1

Bootstrap is easy

but it took me a long while to understand it (I'm an MBA?)

library(animation) boot.iid()

3

Variablility plot?

when it is difficult to calculate the exact CI

library(animation) boot.lowess()

4

Test of randomness

a tale of two coins

Coin A 11110000000000100000101100000100000101001111001100 01111110010110110101101001111001100011011101100000 10001001111110100100001011001011101101110001010010 01100111111100011100101000101001110011100010100111 Coin B 01110010010010100010011110010100010011010111001110 01111011010111101101001000111001101011010101101001 00101001110110100100001110101101101001110101100110 01110011110110001110011010111001110011110010100111

5

See tests

how do runs look like in our eyes?

6

Kernel density estimation

do we really need to care about the binwidth?

library(gWidgetsRGtk2) options(guiToolkit = 'RGtk2') tips = read.csv('http://dicook.public.iastate.edu/Army/tips.csv') x = tips$tip gslider(from = 1, to = 100, by = 1, container = gwindow('Change the number of bins'), handler = function(h, ...) { hist(x, breaks = seq(min(x), max(x), length = svalue(h$obj))) })

7

2D KDE

histograms are so mundane!

library(rgl) demo('bivar')

8

Same story

	## adpated from demo('bivar') in rgl
	rgl.demo.bivar = function(x, y, bw, ngrid = 25, ...) {
	library(MASS); library(rgl)
	n = length(x)
	denobj = kde2d(x, y, bw, n = ngrid)
	den.z = denobj$z; xgrid = denobj$x; ygrid = denobj$y
	bi.z = dnorm(xgrid) %*% t(dnorm(ygrid))
	zscale = 20; clear3d()
	spheres3d(x, y, rep(0, n), radius = 0.1, color = "#CCCCFF")
	surface3d(xgrid, ygrid, den.z * zscale, color = "#FF2222", alpha = 0.5)
	surface3d(xgrid, ygrid, bi.z * zscale, color = "#CCCCFF", front = "lines")
	}

	set.seed(31415)
	n = 50; x = rnorm(n); y = rnorm(n)
	rgl.demo.bivar(x, y, 2)

	## change binwidth interactively
	library(gWidgetsRGtk2)
	options(guiToolkit = 'RGtk2')
	gslider(from = 0.1, to = 10, by = 0.1,
	container = gwindow("Change binwidth"),
	handler = function(h, ...) {
	rgl.demo.bivar(x, y, bw = svalue(h$obj))
	})

	## what you should really do
	res = kde2d(x, y)
	contour(res$x, res$y, res$z)
	points(x, y, pch = 20)

view raw kde2d-gwidgets.R hosted with ❤ by GitHub

9

Vote Compass

beautiful but...

10