estimators (version 0.7.3)

avar: Asymptotic Variance

Description

Calculates the asymptotic variance (or variance - covariance matrix in the multidimensional case) of an estimator, given a specified family of distributions and the true parameter values.

Usage

avar(distr, type, ...)
vbeta(shape1, shape2, type = "mle")
vbinom(size, prob, type = "mle")
vdirich(shape, type = "mle")
vexp(rate, type = "mle")
vgamma(shape, scale, type = "mle")
vmgamma(shape, scale, type = "mle")
vnorm(mean, sd, type = "mle")
vpois(lambda, type = "mle")

Value

A named matrix. The asymptotic covariance matrix of the estimator.

Arguments

distr

A subclass of Distribution. The distribution family assumed.

type

character, case ignored. The estimator type (mle, me, or same).

...

extra arguments.

shape1, shape2, size, prob, shape, rate, scale, mean, sd, lambda

numeric. Distribution parameters.

References

Ye, Z.-S. & Chen, N. (2017), Closed-form estimators for the gamma distribution derived from likelihood equations, The American Statistician 71(2), 177–181.

Van der Vaart, A. W. (2000), Asymptotic statistics, Vol. 3, Cambridge university press.

Tamae, H., Irie, K. & Kubokawa, T. (2020), A score-adjusted approach to closed-form estimators for the gamma and beta distributions, Japanese Journal of Statistics and Data Science 3, 543–561.

Mathal, A. & Moschopoulos, P. (1992), A form of multivariate gamma distribution, Annals of the Institute of Statistical Mathematics 44, 97–106.

Oikonomidis, I. & Trevezas, S. (2023), Moment-Type Estimators for the Dirichlet and the Multivariate Gamma Distributions, arXiv, https://arxiv.org/abs/2311.15025

See Also

avar_mle, avar_me, avar_same

Examples

# -------------------------------------------
# Beta Distribution Example
# -------------------------------------------

# Simulation
set.seed(1)
shape1 <- 1
shape2 <- 2
x <- rbeta(100, shape1, shape2)

library(distr)
D <- Beta(shape1, shape2)

# Likelihood - The ll Functions

llbeta(x, shape1, shape2)
ll(x, c(shape1, shape2), D)
ll(x, c(shape1, shape2), "beta")

# Point Estimation - The e Functions

ebeta(x, type = "mle")
ebeta(x, type = "me")
ebeta(x, type = "same")

mle(x, D)
me(x, D)
same(x, D)

estim(x, D, type = "mle")

# Asymptotic Variance - The v Functions

vbeta(shape1, shape2, type = "mle")
vbeta(shape1, shape2, type = "me")
vbeta(shape1, shape2, type = "same")

avar_mle(D)
avar_me(D)
avar_same(D)

avar(D, type = "mle")