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R boot function - interpretation of t and t* in plot - modification of standard graphics

I started using the package boot in R and I am having some trouble understanding the sense of the parameters t and t* on plots.

A basic code is the following:

library(boot)
mydata <- c(0.461, 3.243, 8.822, 3.442) 
meanFunc <- function(mydata, i){mean(mydata[i])}
bootMean <- boot(mydata, meanFunc, 250)
plot(bootMean)

When using the command plot.boot I obtain this graphic:

enter image description here

What does it represent t*. Why the title says Histogram of t but in the x axis we have t*?

As an added question: How can I modify the properties of this graphic such as, for example, the color or tile or axis?

Thanks

Solution

  • In the output of boot (bootMean in your case) one can find two types of ts: t0 and t.

    From the documentation of ?boot:

    t0
    The observed value of statistic applied to data.

    This is the value of your meanFunc function on the original data set i.e.:

    > mean(mydata)
[1] 3.992

    This is called original t* or t1* in boot's output:

    > bootMean

ORDINARY NONPARAMETRIC BOOTSTRAP


Call:
boot(data = mydata, statistic = meanFunc, R = 250)


Bootstrap Statistics :
    original   bias    std. error
t1*    3.992 0.165301    1.512914

    And then you have

    t
    A matrix with sum(R) rows each of which is a bootstrap replicate of the result of calling statistic

    t here represents the matrix (vector in your case) of all the statistics produced according to your R argument i.e. 250 in your case.

    Therefore, there is a difference between t and t* and the difference is that t is the matrix of all the statistics i.e. t here is what we would call the random variable in statistics whereas t* are the estimates of the t random variable. In your case you get 250 estimates t*s as determined by the R argument. In other words t is the matrix and t* are the elements of the matrix.

    And therefore the plot makes sense as well since it is the histogram of the random variable t and the x-axis contains the estimates of the random variable i.e. the t*s.