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19.1: Jackknife sampling

Last updated

Sep 4, 2024
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- 19: Distribution-free methods
- 19.2: Bootstrap sampling

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Introduction

edits: — under construction —

R packages

There are several R packages one could use. The package bootstrap may be the the most general, and includes a jackknife routine suitable for any function. This page demonstrates jackknife estimate of correlation.

Example data set of cars, showing stopping distance by speed of car (scroll down or click here).

install package bootstrap

Jackknife estimates on linear models

These procedures can be done with the bootstrap package, but lmboot is a specific package to solve the problem

install package lmboot

Example data set, Tadpoles from Chapter 14, copied to end of this page for your convenience (scroll down or click here).

R code

jackknife(VO2~Body.mass, data = Tadpoles)

R returns two values:

bootEstParam, which are the jackknife parameter estimates. Each column in the matrix lists the values for a coefficient. For this model, bootEstParam$[,1] is the intercept and bootEstParam$[,2] is the slope.
origEstParam, a vector with the original parameter estimates for the model coefficients.

$bootEstParam
     (Intercept) Body.mass
[1,]   -660.8403  472.6841
[2,]   -539.5951  430.3990
[3,]   -612.8495  454.5188
[4,]   -512.5914  423.0815
[5,]   -543.1577  434.2789
[6,]   -572.3895  442.9176
[7,]   -613.7873  451.2656
[8,]   -594.0366  446.2571
[9,]   -582.1833  443.5404
[10,]  -598.2244  456.0599
[11,]  -531.3152  415.2467
[12,]  -555.7287  430.5604
[13,]  -726.8522  512.1268

$origEstParam
[,1]
(Intercept) -583.0454
Body.mass 444.9512

Get necessary statistics and plots

#95% CI slope
quantile(jack.model.1$bootEstParam[,2], probs=c(.025, .975))

R returns

    2.5%    97.5% 
417.5971 500.2940

#95% CI intercept
quantile(jack.model.1$bootEstParam[,1], probs=c(.025, .975))

R returns

     2.5%     97.5% 
-707.0486 -518.2085

Coefficient estimates

Slope

#plot the sampling distribution of the slope coefficient
par(mar=c(5,5,5,5)) #setting margins to my preferred values
hist(jack.model.1$bootEstParam[,2], col="blue", main="Jackknife Sampling Distribution",
xlab="Slope Estimate")

Intercept

#95% CI intercept
quantile(jack.model.1$bootEstParam[,1], probs=c(.025, .975))
par(mar=c(5,5,5,5))
hist(jack.model.1$bootEstParam[,1], col="blue", main="Jackknife Sampling Distribution",
xlab="Intercept Estimate")

Questions

edits: pending

Cars data set used in this page

speed	dist
4	2
4	10
7	4
7	22
8	16
9	10
10	18
10	26
10	34
11	17
11	28
12	14
12	20
12	24
12	28
13	26
13	34
13	34
13	46
14	26
14	36
14	60
14	80
15	20
15	26
15	54
16	32
16	40
17	32
17	40
17	50
18	42
18	56
18	76
18	84
19	36
19	46
19	68
20	32
20	48
20	52
20	56
20	64
22	66
23	54
24	70
24	92
24	93
24	120
25	85

Tadpole data set used in this page (sorted)

Gosner	Body mass	VO2
I	1.76	109.41
I	1.88	329.06
I	1.95	82.35
I	2.13	198
I	2.26	607.7
II	2.28	362.71
II	2.35	556.6
II	2.62	612.93
II	2.77	514.02
II	2.97	961.01
II	3.14	892.41
II	3.79	976.97
NA	1.46	170.91