Package 'agfh' reference manual

Title:	Agnostic Fay-Herriot Model for Small Area Statistics
Description:	Implements the Agnostic Fay-Herriot model, an extension of the traditional small area model. In place of normal sampling errors, the sampling error distribution is estimated with a Gaussian process to accommodate a broader class of distributions. This flexibility is most useful in the presence of bounded, multi-modal, or heavily skewed sampling errors.
Authors:	Marten Thompson [aut, cre, cph], Snigdhansu Chatterjee [ctb, cph]
Maintainer:	Marten Thompson <[email protected]>
License:	GPL (>= 3)
Version:	0.2.1
Built:	2025-02-14 04:42:26 UTC
Source:	https://github.com/cran/agfh

Maker Function: Adjusted Profile Likelihood of Latent Variance

Description

A maker function that returns a function. The returned function is the adjusted profile likelihood of the data for a given (latent) variance, from Yoshimori & Lahiri (2014).

Usage

  adj_profile_likelihood_theta_var_maker(X, Y, D)
adj_profile_likelihood_theta_var_maker(X, Y, D)

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`

Value

Returns the adjusted profile likelihood as a function of the variance term in the latent model.

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  adj.lik <- adj_profile_likelihood_theta_var_maker(X, Y, D)
  adj.lik(0.5)
X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  adj.lik <- adj_profile_likelihood_theta_var_maker(X, Y, D)
  adj.lik(0.5)

Maker Function: Adjusted Residual Likelihood of Latent Variance

Description

A maker function that returns a function. The returned function is the adjusted residual likelihood of the data for a given (latent) variance, from Yoshimori & Lahiri (2014).

Usage

  adj_resid_likelihood_theta_var_maker(X, Y, D)
adj_resid_likelihood_theta_var_maker(X, Y, D)

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`

Value

Returns the adjusted residual likelihood as a function of the variance term in the latent model.

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  adj.lik <- adj_resid_likelihood_theta_var_maker(X, Y, D)
  adj.lik(0.5)
X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  adj.lik <- adj_resid_likelihood_theta_var_maker(X, Y, D)
  adj.lik(0.5)

Agnostic Fay-Herriot Hierarchical Bayesian Model Predictions at Latent Level

Description

Find predictions of $\theta$ using posterior samples from the AGFH model

Usage

  agfh_theta_new_pred(X_new, beta_samples, theta_var_samples)
agfh_theta_new_pred(X_new, beta_samples, theta_var_samples)

Arguments

`X_new`	single new independent data to be analyzed
`beta_samples`	posterior samples of latent regression parameter
`theta_var_samples`	posterior samples of latent variance parameter

Details

X_new should be $1$ x $p$ shaped.

beta_samples and theta_var_samples should contain the same number of samples (columns for the former, length of the latter).

Value

Vector containing n samples-many estimates of $\theta$ at X_new.

Source

Marten Thompson [email protected]

Examples

  p <- 3
  n.post.samp <- 10
  X.new <- matrix(rep(1,p), nrow=1)
  beta.samp <- matrix(rnorm(n.post.samp*p, mean=2, sd=0.1), ncol=n.post.samp)
  thvar.samp <- runif(n.post.samp, 0.1, 1)

  th.preds <- agfh_theta_new_pred(X.new, beta.samp, thvar.samp)
p <- 3
  n.post.samp <- 10
  X.new <- matrix(rep(1,p), nrow=1)
  beta.samp <- matrix(rnorm(n.post.samp*p, mean=2, sd=0.1), ncol=n.post.samp)
  thvar.samp <- runif(n.post.samp, 0.1, 1)

  th.preds <- agfh_theta_new_pred(X.new, beta.samp, thvar.samp)

Anderson-Darling Normality Test

Description

Test a sample against the null hypothesis that it comes from a standard Normal distribution.

Usage

  anderson_darling(samples)
anderson_darling(samples)

Arguments

samples

vector of values to be tested

Details

Wrapper function for corresponding functionality in goftest. Originally, from Anderson and Darling (1954).

Value

A list containing

`name`	authors of normality test applied i.e. 'Anderson Darling'
`statistic`	scalar value of test statistics
`p.value`	corresponding p-value of the test

Source

Anderson and Darling (1954) via goftest.

Examples

  sample <- rnorm(100)
  anderson_darling(sample)
sample <- rnorm(100)
  anderson_darling(sample)

Generate Data with Beta Sampling Errors

Description

The traditional Fay-Herriot small area model has a Normal latent variable and Normal observed response errors. This method generates data with Normal latent variables and Beta errors on the response. Note that the sampling errors are transformed so their mean and variance match the the first two moments of the traditional model.

Usage

  beta_err_gen (M, p, D, lambda, a, b)
beta_err_gen (M, p, D, lambda, a, b)

Arguments

`M`	number of areal units
`p`	dimension of regressors i.e. $x \in R^p$
`D`	vector of precisions for response, length `M`
`lambda`	value of latent variance
`a`	first shape parameter of Beta distribution
`b`	second shape parameter of Beta distribution

Value

A list containing

`D`	copy of argument 'D'
`beta`	vector of length 'p' latent coefficients
`lambda`	copy of argument 'lambda'
`X`	matrix of independent variables
`theta`	vector of latent effects
`Y`	vector of responses
`err`	vector of sampling errors
`name`	name of sampling error distribution, including shape parameters

Source

Marten Thompson [email protected]

Examples

  M <- 50
  p <- 3
  D <- rep(0.1, M)
  lamb <- 1/2
  dat <- beta_err_gen(M, p, D, lamb, 1/2, 1/4)
M <- 50
  p <- 3
  D <- rep(0.1, M)
  lamb <- 1/2
  dat <- beta_err_gen(M, p, D, lamb, 1/2, 1/4)

Cramer-Von Mises Normality Test

Description

Test a sample against the null hypothesis that it comes from a standard Normal distribution.

Usage

  cramer_vonmises(samples)
cramer_vonmises(samples)

Arguments

samples

vector of values to be tested

Details

Wrapper function for corresponding functionality in goftest. Originally developed in Cramer (1928), Mises (1931), and Smirnov (1936).

Value

A list containing

`name`	authors of normality test applied i.e. 'Cramer von Mises'
`statistic`	scalar value of test statistics
`p.value`	corresponding p-value of the test

Source

Cramer (1928), Mises (1931), and Smirnov (1936) via goftest.

Examples

  sample <- rnorm(100)
  cramer_vonmises(sample)
sample <- rnorm(100)
  cramer_vonmises(sample)

Generate Data with Gamma Sampling Errors

Description

The traditional Fay-Herriot small area model has a Normal latent variable and Normal observed response errors. This method generates data with Normal latent variables and Gamma errors on the response. Note that the sampling errors are transformed so their mean and variance match the the first two moments of the traditional model.

Usage

  gamma_err_gen (M, p, D, lambda, shape, rate)
gamma_err_gen (M, p, D, lambda, shape, rate)

Arguments

`M`	number of areal units
`p`	dimension of regressors i.e. $x \in R^p$
`D`	vector of precisions for response, length `M`
`lambda`	value of latent variance
`shape`	shape parameter of Gamma distribution
`rate`	rate parameter of Gamma distribution

Value

A list containing

`D`	copy of argument 'D'
`beta`	vector of length 'p' latent coefficients
`lambda`	copy of argument 'lambda'
`X`	matrix of independent variables
`theta`	vector of latent effects
`Y`	vector of responses
`err`	vector of sampling errors
`name`	name of sampling error distribution, including shape and rate parameters

Source

Marten Thompson [email protected]

Examples

  M <- 50
  p <- 3
  D <- rep(0.1, M)
  lamb <- 1/2
  dat <- gamma_err_gen(M, p, D, lamb, 1/2, 10)
M <- 50
  p <- 3
  D <- rep(0.1, M)
  lamb <- 1/2
  dat <- gamma_err_gen(M, p, D, lamb, 1/2, 10)

Traditional Fay-Herriot Hierarchical Bayesian Model Predictions

Description

Find predictions using posterior samples from the traditional Fay-Herriot hierarchical bayesian model

Usage

  hb_theta_new_pred(X_new, beta_samples, theta_var_samples)
hb_theta_new_pred(X_new, beta_samples, theta_var_samples)

Arguments

`X_new`	single new independent data to be analyzed
`beta_samples`	posterior samples of latent regression parameter
`theta_var_samples`	posterior samples of latent variance parameter

Details

X_new should be $1$ x $p$ shaped.

beta_samples and theta_var_samples should contain the same number of samples (columns for the former, length of the latter).

Value

Vector containing n samples-many estimates of $\theta$ at X_new.

Source

Marten Thompson [email protected]

Examples

  p <- 3
  n.post.samp <- 10
  X.new <- matrix(rep(1,p), nrow=1)
  beta.samp <- matrix(rnorm(n.post.samp*p, mean=2, sd=0.1), ncol=n.post.samp)
  thvar.samp <- runif(n.post.samp, 0.1, 1)

  th.preds <- hb_theta_new_pred(X.new, beta.samp, thvar.samp)
p <- 3
  n.post.samp <- 10
  X.new <- matrix(rep(1,p), nrow=1)
  beta.samp <- matrix(rnorm(n.post.samp*p, mean=2, sd=0.1), ncol=n.post.samp)
  thvar.samp <- runif(n.post.samp, 0.1, 1)

  th.preds <- hb_theta_new_pred(X.new, beta.samp, thvar.samp)

Kolmogorov-Smirnov Normality Test

Description

Test a sample against the null hypothesis that it comes from a standard Normal distribution.

Usage

  kolmogorov_smirnov(samples)
kolmogorov_smirnov(samples)

Arguments

samples

vector of values to be tested

Details

Wrapper function for corresponding functionality in stats. Originally, from Kolmogorov (1933).

Value

A list containing

`name`	name of normality test applied i.e. 'Komogorov Smirnov'
`statistic`	scalar value of test statistics
`p.value`	corresponding p-value from test

Source

Kolmogorov (1933) via stats.

Examples

  sample <- rnorm(100)
  kolmogorov_smirnov(sample)
sample <- rnorm(100)
  kolmogorov_smirnov(sample)

Maker Function: Agnostic Fay-Herriot Sampler

Description

A maker function that returns a function. The returned function is a sampler for the agnostic Fay-Herriot model.

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`
`var_gamma_a`	latent variance prior parameter, `rgamma` shape
`var_gamma_b`	latent variance prior parameter, `rgamma` rate
`S`	vector of starting support values for $g(\cdot)$
`kern.a0`	scalar variance parameter of GP kernel
`kern.a1`	scalar lengthscale parameter of GP kernel
`kern.fuzz`	scalar noise variance of kernel

Details

Creates a Metropolis-within-Gibbs sampler of the agnostic Fay-Herriot model (AGFH).

Value

Returns a sampler, itself a function of initial parameter values (a list with values for $\beta, \theta$ , the latent variance of $\theta$ , and starting values for $g(.)$ , typically zeros), number of samples, thinning rate, and scale of Metropolis-Hastings jumps for $\theta$ sampling.

Source

Marten Thompson [email protected]

Examples

  n <- 10
  X <- matrix(1:n, ncol=1)
  Y <- 2*X + rnorm(n, sd=1.1)
  D <- rep(1, n)
  ag <- make_agfh_sampler(X, Y, D)

  params.init <- list(
    beta=1,
    theta=rep(0,n),
    theta.var=1,
    gamma=rep(0,n)
  )
  ag.out <- ag(params.init, 5, 1, 0.1)
n <- 10
  X <- matrix(1:n, ncol=1)
  Y <- 2*X + rnorm(n, sd=1.1)
  D <- rep(1, n)
  ag <- make_agfh_sampler(X, Y, D)

  params.init <- list(
    beta=1,
    theta=rep(0,n),
    theta.var=1,
    gamma=rep(0,n)
  )
  ag.out <- ag(params.init, 5, 1, 0.1)

Maker Function: Traditional Fay-Herriot Gibbs Sampler

Description

A maker function that returns a function. The returned function is a Gibbs sampler for the traditional Fay-Herriot model.

Usage

  make_gibbs_sampler(X, Y, D, var_gamma_a=1, var_gamma_b=1)
make_gibbs_sampler(X, Y, D, var_gamma_a=1, var_gamma_b=1)

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`
`var_gamma_a`	latent variance prior parameter, `rgamma` shape
`var_gamma_b`	latent variance prior parameter, `rgamma` rate

Value

Returns a Gibbs sampler, itself a function of initial parameter values (a list with values for $\beta, \theta$ , and latent variance of $\theta$ ), number of samples, and thinning rate.

Source

Marten Thompson [email protected]

Examples

  n <- 10
  X <- matrix(1:n, ncol=1)
  Y <- 2*X + rnorm(n, sd=1.1)
  D <- rep(1, n)
  gib <- make_gibbs_sampler(X, Y, D)

  params.init <- list(
    beta=1,
    theta=rep(0,n),
    theta.var=1
  )
  gib.out <- gib(params.init, 5, 1)
n <- 10
  X <- matrix(1:n, ncol=1)
  Y <- 2*X + rnorm(n, sd=1.1)
  D <- rep(1, n)
  gib <- make_gibbs_sampler(X, Y, D)

  params.init <- list(
    beta=1,
    theta=rep(0,n),
    theta.var=1
  )
  gib.out <- gib(params.init, 5, 1)

Calculate the MAP Estimate from Posterior Samples

Description

Find maximum a posteriori estimate using posterior samples

Usage

  map_from_density(param.ts, plot=FALSE)
map_from_density(param.ts, plot=FALSE)

Arguments

`param.ts`	vector of scalar samples
`plot`	boolean, plot or not

Details

Finds location of max of density from samples.

Value

Scalar MAP estimate.

Source

Marten Thompson [email protected]

Examples

  n.post.samp <- 10
  beta.samp <- rnorm(n.post.samp, 0, 1/2)

  map_from_density(beta.samp)
n.post.samp <- 10
  beta.samp <- rnorm(n.post.samp, 0, 1/2)

  map_from_density(beta.samp)

Calculate the Mean Squared Error Between two Vectors

Description

Merely wanted to use such a function by name; nothing fancy

Usage

  mse(x,y)
mse(x,y)

Arguments

`x`	vector of values
`y`	vector of values

Value

A scalar: the MSE between x and y.

Source

Marten Thompson [email protected]

Examples

  mse(seq(1:10), seq(10:1))
mse(seq(1:10), seq(10:1))

Generate Data with Normal Sampling Errors

Description

The Fay-Herriot small area model has a Normal latent variable and Normal observed response. This generates data according to that specification.

Usage

  null_gen (M, p, D, lambda)
null_gen (M, p, D, lambda)

Arguments

`M`	number of areal units
`p`	dimension of regressors i.e. $x \in R^p$
`D`	vector of precisions for response, length `M`
`lambda`	value of latent variance

Value

A list containing

`D`	copy of argument 'D'
`beta`	vector of length 'p' latent coefficients
`lambda`	copy of argument 'lambda'
`X`	matrix of independent variables
`theta`	vector of latent effects
`Y`	vector of responses
`err`	vector of sampling errors
`name`	name of sampling error distribution

Source

Marten Thompson [email protected]

Examples

  M <- 50
  p <- 3
  D <- rep(0.1, M)
  lamb <- 1/2
  dat <- null_gen(M, p, D, lamb)
M <- 50
  p <- 3
  D <- rep(0.1, M)
  lamb <- 1/2
  dat <- null_gen(M, p, D, lamb)

Maker Function: Residual Likelihood of Latent Variance

Description

A maker function that returns a function. The returned function is the (non-adjusted) residual likelihood of the data for a given (latent) variance, from Yoshimori & Lahiri (2014).

Usage

  resid_likelihood_theta_var_maker(X, Y, D)
resid_likelihood_theta_var_maker(X, Y, D)

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`

Value

Returns the (non-adjusted) residual likelihood as a function of the variance term in the latent model.

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  resid.lik <- resid_likelihood_theta_var_maker(X, Y, D)
  resid.lik(0.5)
X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  resid.lik <- resid_likelihood_theta_var_maker(X, Y, D)
  resid.lik(0.5)

Traditional EBLUE Estimator of Beta

Description

Traditional EBLUE Estimator of Beta

Usage

  RM_beta_eblue(X, Y, D, theta_var_est)
RM_beta_eblue(X, Y, D, theta_var_est)

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`
`theta_var_est`	estimate of variance term for latent model

Details

Traditional EBLUE estimator of beta.

Value

Returns a vector estimate of beta.

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  th.var.est <- 0.1
  RM_beta_eblue(X, Y, D, th.var.est)
X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  th.var.est <- 0.1
  RM_beta_eblue(X, Y, D, th.var.est)

Traditional EBLUP Estimator of Theta

Description

Traditional EBLUP Estimator of Theta

Usage

  RM_theta_eblup(X, Y, D, theta.var.est)
RM_theta_eblup(X, Y, D, theta.var.est)

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`
`theta.var.est`	estimate of variance term for latent model; if `NA`, will automatically use method-of-moments

Details

Traditional EBLUP estimator of latent values theta.

Value

Returns a vector of estimates of theta.

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  th.var.est <- 0.1
  RM_theta_eblup(X, Y, D, th.var.est)

  RM_theta_eblup(X, Y, D)
X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  th.var.est <- 0.1
  RM_theta_eblup(X, Y, D, th.var.est)

  RM_theta_eblup(X, Y, D)

Traditional EBLUP Estimator of Theta for new `X` values

Description

Traditional EBLUP Estimator of Theta for new X values

Usage

  RM_theta_new_pred(X.new, beta.est)
RM_theta_new_pred(X.new, beta.est)

Arguments

`X.new`	new independent data to be analyzed
`beta.est`	estimate of regression term for latent model

Details

Simply X'beta.est

Value

Returns a vector of estimates of theta.

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  b <- 1
  RM_theta_new_pred(X, b)
X <- matrix(1:10, ncol=1)
  b <- 1
  RM_theta_new_pred(X, b)

Moment-Based Estimator of Latent Model Variance

Description

Simple moment-based estimator of the variance of the latent model.

Usage

  RM_theta_var_moment_est(X, Y, D)
RM_theta_var_moment_est(X, Y, D)

Arguments

`X`	observed independent data to be analyzed
`Y`	observed dependent data to be analyzed
`D`	known precisions of response `Y`

Details

Simple moment-based estimator of the variance of the latent model.

Value

Returns a scalar estimate of variance.

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  RM_theta_var_moment_est(X, Y, D)
X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  RM_theta_var_moment_est(X, Y, D)

Shaprio-Wilk Normality Test

Description

Test a sample against the null hypothesis that it comes from a standard Normal distribution.

Usage

  shapiro_wilk(samples)
shapiro_wilk(samples)

Arguments

samples

vector of values to be tested

Details

Wrapper function for corresponding functionality in stats. Originally, from Shapiro and Wilk (1975).

Value

A list containing

`name`	authors of normality test applied i.e. 'Shapiro Wilk'
`statistic`	scalar value of test statistics
`p.value`	corresponding p-value of the test

Source

Shapiro and Wilk (1975) via stats.

Examples

  sample <- rnorm(100)
  shapiro_wilk(sample)
sample <- rnorm(100)
  shapiro_wilk(sample)

Normality Test

Description

Test a sample against the null hypothesis that it comes from a standard Normal distribution with the specified test.

Usage

  test_u_normal(samples, test)
test_u_normal(samples, test)

Arguments

`samples`	vector of values to be tested
`test`	name of test, one of `'SW'`, `'KS'`, `'CM'`, `'AD'`

Details

Convenience function for consistent syntax in calling shapiro_wilk, kolmogorov_smirnov, cramer_vonmises, and anderson_darling tests.

Value

A list containing

`name`	authors of normality test applied
`statistic`	scalar value of test statistics
`p.value`	corresponding p-value from test

Source

Marten Thompson [email protected]

Examples

  sample <- rnorm(100)
  test_u_normal(sample, 'SW')
sample <- rnorm(100)
  test_u_normal(sample, 'SW')

Basic Grid Optimizer for Likelihood

Description

A basic grid search optimizer. Here, used to estimate the variance in the latent model by maximum likelihood.

Usage

  theta_var_est_grid(likelihood_theta_var)
theta_var_est_grid(likelihood_theta_var)

Arguments

likelihood_theta_var

some flavor of likelihood function in terms of latent variance

Details

likelihood_theta_var may be created using adj_resid_likelihood_theta_var_maker or similar.

We recommended implementing a more robust optimizer.

Value

The scalar value that optimizes likelihood_theta_var, or an error if this value is on the search boundary $[10^{-6}, 10^2]$ .

Source

Marten Thompson [email protected]

Examples

  X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  adj.lik <- adj_resid_likelihood_theta_var_maker(X, Y, D)
  theta_var_est_grid(adj.lik)
X <- matrix(1:10, ncol=1)
  Y <- 2*X + rnorm(10, sd=1.1)
  D <- rep(1, 10)
  adj.lik <- adj_resid_likelihood_theta_var_maker(X, Y, D)
  theta_var_est_grid(adj.lik)

Package 'agfh'

Help Index

Maker Function: Adjusted Profile Likelihood of Latent Variance

Description

Usage

Arguments

Value

Source

Examples

Maker Function: Adjusted Residual Likelihood of Latent Variance

Description

Usage

Arguments

Value

Source

Examples

Agnostic Fay-Herriot Hierarchical Bayesian Model Predictions at Latent Level

Description

Usage

Arguments

Details

Value

Source

Examples

Anderson-Darling Normality Test

Description

Usage

Arguments

Details

Value

Source

Examples

Generate Data with Beta Sampling Errors

Description

Usage

Arguments

Value

Source

Examples

Cramer-Von Mises Normality Test

Description

Usage

Arguments

Details

Value

Source

Examples

Generate Data with Gamma Sampling Errors

Description

Usage

Arguments

Value

Source

Examples

Traditional Fay-Herriot Hierarchical Bayesian Model Predictions

Description

Usage

Arguments

Details

Value

Source

Examples

Kolmogorov-Smirnov Normality Test

Description

Usage

Arguments

Details

Value

Source

Examples

Maker Function: Agnostic Fay-Herriot Sampler

Description

Arguments

Details

Value

Source

Examples

Maker Function: Traditional Fay-Herriot Gibbs Sampler

Description

Usage

Traditional EBLUP Estimator of Theta for new `X` values