bw_select_cv_bivariate: Cross-validation for bivariate distributions

In hotneim/lg: Locally Gaussian Distributions: Estimation and Methods

Description

Uses cross-validation to find the optimal bandwidth for a bivariate locally Gaussian fit

Usage

bw_select_cv_bivariate(
  x,
  tol = 10^(-3),
  est_method = "1par",
  bw_marginal = NULL
)

Arguments

x	The matrix of data points.
tol	The absolute tolerance in the optimization, used by the optim-function.
est_method	The estimation method for the bivariate fit. If estimation method is 5par_marginals_fixed, the marginal bandwidths must be supplied as well through the argument bw_marginal. This is automatically handled by the lg_main wrapper function.
bw_marginal	The bandwidths for estimation of the marginals if method 5par_fixed_marginals is used.

Details

This function provides an implementation for the Cross Validation algorithm for bandwidth selection described in Otneim & Tjøstheim (2017), Section 4. Let \hat{f}_h(x) be the bivariate locally Gaussian density estimate obtained using the bandwidth h, then this function returns the bandwidth that maximizes

CV(h) = n^{-1} ∑_{i=1}^n \log \hat{f}_h^{(-i)}(x_i),

where \hat{f}_h^{(-i)} is the density estimate calculated without observation x_i.

The recommended use of this function is through the lg_main wrapper function.

Value

The function returns a list with two elements: bw is the selected bandwidths, and convergence is the convergence flag returned by the optim-function.

References

Otneim, Håkon, and Dag Tjøstheim. "The locally gaussian density estimator for multivariate data." Statistics and Computing 27, no. 6 (2017): 1595-1616.

Examples

  ## Not run: 
    x <- cbind(rnorm(100), rnorm(100))
    bw <- bw_select_cv_univariate(x)
  
## End(Not run)

hotneim/lg documentation built on May 9, 2020, 7:35 a.m.