est_cov {TLMoments}

Covariance matrix of PWMs, TLMoments, parameters, or quantiles

Description

Calculation of the empirical or theoretical covariance matrix of objects of the classes PWMs, TLMoments, parameters, or quantiles.

Usage

est_cov(x, ...)

## S3 method for class 'PWMs'
est_cov(x, select = attr(x, "order"), ...)

## S3 method for class 'TLMoments'
est_cov(x, select = attr(x, "order"), ...)

## S3 method for class 'parameters'
est_cov(x, select = c("loc", "scale", "shape"), ...)

## S3 method for class 'quantiles'
est_cov(x, select = attr(x, "p"), ...)

Arguments

x

object of PWMs, TLMoments, parameters, or quantiles constructed using the same-named functions.

...

additional arguments given to the sub-functions: distr and np.cov (see details).

select

numeric oder character vector specifying a subset of the covariance matrix. If not specified the full covariance matrix is returned.

Details

Covariance matrices of PWMs and TLMoments are calculated without parametric assumption by default. Covariance matrices of parameters and quantiles use parametric assumption based on their stored distribution attribute (only GEV at the moment). Parametric (GEV) calculation can be enforced by specifying distr=\"gev\", non-parametric calculation by using np.cov=TRUE.

Value

numeric matrix (if x is of class PWMs, parameters, or quantiles) or a list of two matrices (lambdas and ratios, if x is of class TLMoments).

See Also

PWMs, TLMoments, parameters, quantiles

Examples

### 1: PWMs:

xvec <- rgev(100, shape = .1)
xmat <- cbind(rgev(100, shape = .1), rgev(100, shape = .3))

# Covariance estimation of PWMs normally without parametric assumption:
est_cov(PWMs(xvec))
est_cov(PWMs(xvec), select = 0:1)
est_cov(PWMs(xmat))
est_cov(PWMs(xmat), select = 3)
est_cov(PWMs(xmat[, 1, drop = FALSE]), select = 2:3)

# Parametric assumptions (only GEV by now) can be used:
est_cov(PWMs(xvec), distr = "gev")
est_cov(PWMs(xvec), distr = "gev", select = c(1, 3))

## Not run: 
cov(t(replicate(100000,
  as.vector(PWMs(cbind(rgev(100, shape = .1), rgev(100, shape = .3)), max.order = 1)))
))

## End(Not run)


### 2. TLMoments:

xvec <- rgev(100, shape = .1)
xmat <- cbind(rgev(100, shape = .1), rgev(100, shape = .3))

# Covariance estimation of TLMoments normally without parametric assumption:
est_cov(TLMoments(xvec))
est_cov(TLMoments(xvec, rightrim = 1))
est_cov(TLMoments(xvec), select = 3:4)

# Parametric assumptions (only GEV by now) can be used:
est_cov(TLMoments(xvec), distr = "gev")

# Matrix inputs
est_cov(TLMoments(xmat))
est_cov(TLMoments(xmat), select = 3:4)
est_cov(TLMoments(xmat[, 1, drop = FALSE]), select = 3:4)

# Covariance of theoretical TLMoments only with parametric assumption:
est_cov(as.TLMoments(c(14, 4, 1)), distr = "gev", set.n = 100)
est_cov(as.TLMoments(c(14, 4, 1), rightrim = 1), distr = "gev", set.n = 100)

# Regionalized TLMoments
est_cov(regionalize(TLMoments(xmat), c(.75, .25)))
est_cov(regionalize(TLMoments(xmat), c(.75, .25)), distr = "gev", select = 3:4)


### 3. Parameters:

xvec <- rgev(100, shape = .1)
xmat <- cbind(rgev(100, shape = .1), rgev(100, shape = .3))

# Covariance estimation of parameters normally with parametric assumption:
est_cov(parameters(TLMoments(xvec), "gev"))
est_cov(parameters(TLMoments(xvec, rightrim = 1), "gev"))
est_cov(parameters(TLMoments(xvec, rightrim = 1), "gev"), select = c("scale", "shape"))

# A nonparametric estimation can be enforced with np.cov:
est_cov(parameters(TLMoments(xvec), "gev"), np.cov = TRUE)
est_cov(parameters(TLMoments(xvec, rightrim = 1), "gev"), np.cov = TRUE)

# Matrix inputs
est_cov(parameters(TLMoments(xmat), "gev"))
est_cov(parameters(TLMoments(xmat), "gev"), select = "shape")
est_cov(parameters(TLMoments(xmat[, 1]), "gev"), select = "shape")

# Theoretical values (leftrim and/or rightrim have to be specified)
para <- as.parameters(loc = 10, scale = 5, shape = .2, distr = "gev")
est_cov(para, set.n = 100)
est_cov(para, rightrim = 1, set.n = 100)

## Not run: 
var(t(replicate(10000, parameters(TLMoments(rgev(100, 10, 5, .2)), "gev"))))

## End(Not run)
## Not run: 
var(t(replicate(10000, parameters(TLMoments(rgev(100, 10, 5, .2), rightrim = 1), "gev"))))

## End(Not run)

# Parameter estimates from regionalized TLMoments:
est_cov(parameters(regionalize(TLMoments(xmat), c(.75, .25)), "gev"))


### 4. Quantiles:

xvec <- rgev(100, shape = .2)
xmat <- cbind(rgev(100, shape = .1), rgev(100, shape = .3))

# Covariance estimation of parameters normally with parametric assumption:
q <- quantiles(parameters(TLMoments(xvec), "gev"), c(.9, .95, .99))
est_cov(q)
est_cov(q, select = c("0.9", "0.99"))
est_cov(q, select = .95)

# A nonparametric estimation can be enforced with np.cov:
est_cov(q, np.cov = TRUE)

# Matrix inputs
param <- parameters(TLMoments(xmat, 0, 1), "gev")
q <- quantiles(param, c(.9, .95, .99))
est_cov(q)
est_cov(q, select = .99)
param <- parameters(TLMoments(xmat[, 1, drop = FALSE], 0, 1), "gev")
q <- quantiles(param, c(.9, .95, .99))
est_cov(q, select = .99)

# Theoretical values
q <- quantiles(as.parameters(loc = 10, scale = 5, shape = .3, distr = "gev"), c(.9, .99))
est_cov(q)
est_cov(q, leftrim = 0, rightrim = 1)
est_cov(q, leftrim = 0, rightrim = 1, set.n = 100)

# Quantile estimates from regionalized TLMoments:
param <- parameters(regionalize(TLMoments(xmat), c(.75, .25)), "gev")
est_cov(quantiles(param, c(.9, .99)))