cnqr_est: Estimate Vine Parameters using CNQR

In vincenzocoia/cmc: Copula-Marginal Composition Method

Description

Estimate copula parameters using CNQR. More specifically, for a given object of type 'rvine' that you would like to extend by adding more rows to its last column, estimates the parameters for the specified copula families of each edge.

Usage

cnqr_est(rv, a, cop, cpar_init, sc, y, uind, QY = identity,
  verbose = FALSE)

Arguments

rv	Object of type 'rvine', to be augmented.
a	Vector of variable numbers (of the predictors) to augment to the end of the array of rv (i.e., the last column).
cop	Character vector of copulas to augment rv with (with reflections already chosen). Each entry corresponds to a new edge/row in the vine (corresponding to a).
cpar_init	Starting values for the copula families in cop. Should be a list with entries being parameter vectors.
sc	Scoring rule to use for the regression, as in the output of scorer.
y	Vector of response data.
uind	Matrix of independent uniform predictors, as in the output of pcondseq, of the predictors up to the last entry in a. So, if "b" is the non-zero entries of the last column of the array in rv after removing the first variable (the response) and appending a, the matrix will be the PIT scores of variables b[1]; b[2]|b[1]; b[3]|b[1:2]; etc.
QY	Quantile function of the response y, which accepts a vector of values (quantile levels) in (0,1). It should return quantiles, either in the form of a vector corresponding to the input, or in the form of a matrix with columns corresponding to the inputted quantile levels and rows corresponding to the observations of y (thus allowing for each value in y to come from different distributions).
verbose	verbose?

Details

Here's how the estimation is done.

1. You begin with a vine rv, where the top-right corner of the array is the response variable. There may or may not be variables (representing the predictors) underneath this response. Note that, to be able to condition the response on predictors, those predictors must appear below the response variable in the vine array.

2. Your objective is to add more variables (predictors, already existing in the vine) to the last column of the vine array. Package these additional variables in the argument a, with corresponding copula families cop.

3. The copula parameters of cop need estimation. This is done by optimizing quantile predictions of the response, conditional on the predictors in a AND the predictors already listed below the response in the vine array of rv.

4. The "optimization" in the previous step refers to optimizing a scoring rule, which is indicated in the sc argument.

Value

Returns a list of copula parameters (the same structure as cpar_init), estimated with CNQR.

See Also

cnqr_sel for CNQR when the model space is a finite selection of vines.

vincenzocoia/cmc documentation built on Nov. 18, 2019, 12:04 a.m.