Create a pdqr-function for distribution of sample estimate

Source: R/form-other.R

Based on pdqr-function, statistic function, and sample size describe the distribution of sample estimate. This might be useful for statistical inference.

form_estimate(f, stat, sample_size, ..., n_sample = 10000, args_new = list())

Arguments

f

A pdqr-function.
stat

Statistic function. Should be able to accept numeric vector of size sample_size and return single numeric or logical output.
sample_size

Size of sample for which distribution of sample estimate is needed.
...

Other arguments for stat.
n_sample

Number of elements to generate from distribution of sample estimate.
args_new

List of extra arguments for new_*() function to control density().

Value

A pdqr-function of the same class and type (if not forced otherwise in args_new) as f.

Details

General idea is to create a sample from target distribution by generating n_sample samples of size sample_size and compute for each of them its estimate by calling input stat function. If created sample is logical, boolean pdqr-function (type "discrete" with elements being exactly 0 and 1) is created with probability of being true estimated as share of TRUE values (after removing possible NA). If sample is numeric, it is used as input to new_*() of appropriate class with type equal to type of f (if not forced otherwise in args_new).

Notes:

  • This function may be very time consuming for large values of n_sample and sample_size, as total of n_sample*sample_size numbers are generated and stat function is called n_sample times.

  • Output distribution might have a bias compared to true distribution of sample estimate. One useful technique for bias correction: compute mean value of estimate using big sample_size (with mean(as_r(f)(sample_size))) and then recenter distribution to actually have that as a mean.

See also

Other form functions: form_mix(), form_regrid(), form_resupport(), form_retype(), form_smooth(), form_tails(), form_trans()

Examples

# These examples take some time to run, so be cautious
# \donttest{
set.seed(101)

# Type "discrete"
d_dis <- new_d(data.frame(x = 1:4, prob = 1:4 / 10), "discrete")
## Estimate of distribution of mean
form_estimate(d_dis, stat = mean, sample_size = 10)

#> Probability mass function of discrete type
#> Support: [1.8, 4] (23 elements)
## To change type of output, supply it in `args_new`
form_estimate(
  d_dis, stat = mean, sample_size = 10,
  args_new = list(type = "continuous")
)

#> Density function of continuous type
#> Support: ~[1.67226, 4.12774] (511 intervals)

# Type "continuous"
d_unif <- as_d(dunif)
## Supply extra named arguments for `stat` in `...`
plot(form_estimate(d_unif, stat = mean, sample_size = 10, trim = 0.1))

lines(
  form_estimate(d_unif, stat = mean, sample_size = 10, trim = 0.3),
  col = "red"
)

lines(
  form_estimate(d_unif, stat = median, sample_size = 10),
  col = "blue"
)


# Statistic can return single logical value
d_norm <- as_d(dnorm)
all_positive <- function(x) {
  all(x > 0)
}
## Probability of being true should be around 0.5^5
form_estimate(d_norm, stat = all_positive, sample_size = 5)

#> Probability mass function of discrete type
#> Support: [0, 1] (2 elements, probability of 1: 0.0318)
# }