# small_metrics: Small Sample Metrics In estimators: Parameter Estimation

 small_metrics R Documentation

## Small Sample Metrics

### Description

This function performs Monte Carlo simulations to estimate the main metrics (bias, variance, and RMSE) characterizing the small 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

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

### Arguments

 `D` A subclass of `Distribution`. The distribution family of interest. `prm` A list containing three elements (name, pos, val). See Details. `est` character. The estimator of interest. Can be a vector. `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. `...` 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.

Specifically, `prm` includes three elements named "name", "pos", and "val". The first two elements determine the exact parameter that changes, while the third one is a numeric vector holding the values it takes. For example, in the case of the Multivariate Gamma distribution, `D <- MGamma(shape = c(1, 2), scale = 3)` and `prm <- list(name = "shape", pos = 2, val = seq(1, 1.5, by = 0.1))` means that the evaluation will be performed for the MGamma distributions with shape parameters `⁠(1, 1)⁠`, `⁠(1, 1.1)⁠`, ..., `⁠(1, 1.5)⁠` and scale `3`. Notice that the initial shape parameter `2` in `D` is not utilized in the function.

### Value

For the small sample, a data.frame with columns named "Parameter", "Observations", "Estimator", "Metric", and "Value". For the large sample, a data.frame with columns "Row", "Col", "Parameter", "Estimator", and "Value".

plot_small_metrics large_metrics, plot_large_metrics

### Examples

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

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

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

plot_small_metrics(x)

``````

estimators documentation built on May 29, 2024, 8:57 a.m.