dlg {lg}

The locally Gaussian density estimator (LGDE)

Description

Estimate a multivariate density function using locally Gaussian approximations

Usage

dlg(lg_object, grid, level = 0.95, normalization_points = NULL,
  bootstrap = F, B = 500)

Arguments

lg_object

An object of type lg, as produced by the lg_main-function.

grid

A matrix of grid points, where we want to evaluate the density estimate.

level

Specify a level if asymptotic standard deviations and confidence intervals should be returned.

normalization_points

How many grid points for approximating the integral of the density estimate, to use for normalization?

bootstrap

Calculate bootstrapped confidence intervals instead.

B

Number of bootstrap replications if using bootstrapped confidence intervals.

Details

This function does multivariate density estimation using the locally Gaussian density estimator (LGDE), that was introduced by Otneim & Tjøstheim (2017). The function takes as arguments an lg-object as produced by the main lg_main-function (where all the running parameters are specified), and a grid of points where the density estimate should be estimated.

Value

A list containing the density estimate as well as all the running parameters that has been used. The elements are:

• f_est: The estimated multivariate density.

• loc_mean: The estimated local means if est_method is "5par" or "5par_marginals_fixed", a matrix of zeros if est_method is "1par".

• loc_sd: The estimated local st. deviations if est_method is "5par" or "5par_marginals_fixed", a matrix of ones if est_method is "1par".

• loc_cor: Matrix of estimated local correlations, one column for each pair of variables, in the same order as specified in the bandwidth object.

• x: The data set.

• bw: The bandwidth object.

• transformed_data: The data transformed to approximate marginal standard normality.

• normalizing_constants: The normalizing constants used to transform data and grid back and forth to the marginal standard normality scale, as seen in eq. (8) of Otneim & Tjøstheim (2017).

• grid: The grid where the estimation was performed, on the original scale.

• transformed_grid: The grid where the estimation was performed, on the marginal standard normal scale.

• normalization_points Number of grid points used to approximate the integral of the density estimate, in order to normalize?

• normalization_constant If approximated, the integral of the non-normalized density estimate. NA if not normalized.

• density_normalized Logical, indicates whether the final density estimate (contained in f_est) has been approximately normalized to have unit integral.

• loc_cor_sd Estimated asymptotic standard deviation for the local correlations.

• loc_cor_lower Lower confidence limit based on the asymptotic standard deviation.

• loc_cor_upper Upper confidence limit based on the asymptotic standard deviation.

References

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

Examples

   x <- cbind(rnorm(100), rnorm(100), rnorm(100))
   lg_object <- lg_main(x)  # Put all the running parameters in here.
   grid <- cbind(seq(-4, 4, 1), seq(-4, 4, 1), seq(-4, 4, 1))
   density_estimate <- dlg(lg_object, grid = grid)