SmallMetrics: Small Sample Metrics

Description

This function performs Monte Carlo simulations to estimate the main metrics (bias, variance, and RMSE) characterizing the small (finite) sample behavior of an estimator. The function evaluates the metrics as a function of a single parameter, keeping the other ones constant. See Details.

Usage

SmallMetrics(D, est, df)
small_metrics(
  D,
  prm,
  est = c("same", "me", "mle"),
  obs = c(20, 50, 100),
  sam = 10000,
  seed = 1,
  bar = TRUE,
  ...
)

Value

An object of class SmallMetrics with slots D, est, and df.

Arguments

D: A subclass of Distribution. The distribution family of interest.
est: character. The estimator of interest. Can be a vector.
df: data.frame. a data.frame with columns named "Row", "Col", "Parameter", "Estimator", and "Value".
prm: A list containing three elements (name, pos, val). See Details.
obs: numeric. The size of each sample. Can be a vector.
sam: numeric. The number of Monte Carlo samples used to estimate the metrics.
seed: numeric. Passed to set.seed() for reproducibility.
bar: logical. Should a progress bar be printed?
...: extra arguments.

Details

The distribution D is used to specify an initial distribution. The list prm contains details concerning a single parameter that is allowed to change values. The quantity of interest is evaluated as a function of this parameter.

The prm list includes two elements named "name" and "val". The first one specifies the parameter that changes, and the second one is a numeric vector holding the values it takes.

In case the parameter of interest is a vector, a third element named "pos" can be specified to indicate the exact parameter that changes. In the example shown below, the evaluation will be performed for the Dirichlet distributions with shape parameters (0.5, 1), (0.6, 1), ..., (2, 1). Notice that the initial shape parameter value (1) is not utilized in the function.

Examples

Run this code

# \donttest{
# -----------------------------------------------------
# Beta Distribution Example
# -----------------------------------------------------

D <- Beta(shape1 = 1, shape2 = 2)

prm <- list(name = "shape1",
            val = seq(0.5, 2, by = 0.1))

x <- small_metrics(D, prm,
                   est = c("mle", "me", "same"),
                   obs = c(20, 50),
                   sam = 1e2,
                   seed = 1)

plot(x)

# -----------------------------------------------------
# Dirichlet Distribution Example
# -----------------------------------------------------

D <- Dir(alpha = 1:2)

prm <- list(name = "alpha",
            pos = 1,
            val = seq(0.5, 2, by = 0.1))

x <- small_metrics(D, prm,
                   est = c("mle", "me", "same"),
                   obs = c(20, 50),
                   sam = 1e2,
                   seed = 1)

plot(x)
# }