BRISC_variogram.ci {BRISC} R Documentation

## Function for plotting estimated Variogram and confidence region

### Description

The function `BRISC_variogram.ci` plots estimated Variogram and associated confience region. `BRISC_variogram.ci` uses the parameter estimates from `BRISC_estimation` and associated confidence interval from `BRISC_bootstrap`.

### Usage

```BRISC_variogram.ci(BRISC_Out, confidence_est,
plot.variogram = FALSE)
```

### Arguments

 `BRISC_Out` an object of class `BRISC_Out`, obtained as an output of `BRISC_estimation`. `confidence_est` bootstrp sample of the Theta parameters, obtained from `BRISC_bootstrap`. `plot.variogram` if `TRUE`, plots the variogram and the associated confidence region. Default is `FALSE`.

### Value

A list comprising of the following:

 `variogram` variogram and associated confidence region corresponding to lag ranging from 0 to 20, evaluated at 0.01 frequency. `Plot` plots the Variogram and associated confidence region with legends.

### Author(s)

Arkajyoti Saha arkajyotisaha93@gmail.com,
Abhirup Datta abhidatta@jhu.edu

### Examples

```
rmvn <- function(n, mu = 0, V = matrix(1)){
p <- length(mu)
if(any(is.na(match(dim(V),p))))
stop("Dimension not right!")
D <- chol(V)
t(matrix(rnorm(n*p), ncol=p)%*%D + rep(mu,rep(n,p)))
}

set.seed(1)
n <- 300
coords <- cbind(runif(n,0,1), runif(n,0,1))

beta <- c(1,5)
x <- cbind(rnorm(n), rnorm(n))

sigma.sq = 1
phi = 5
tau.sq = 0.1

B <- as.matrix(beta)
D <- as.matrix(dist(coords))
R <- exp(-phi*D)
w <- rmvn(1, rep(0,n), sigma.sq*R)

y <- rnorm(n, x%*%B + w, sqrt(tau.sq))

estimation_result <- BRISC_estimation(coords, y, x)
bootstrap_result <- BRISC_bootstrap(estimation_result, n_boot = 10)
varg <- BRISC_variogram.ci(estimation_result,
bootstrap_result\$boot.Theta,
plot.variogram = TRUE)

```

[Package BRISC version 1.0.2 Index]