dlg: The locally Gaussian density estimator (LGDE)
In lg: Locally Gaussian Distributions: Estimation and Methods

Description Usage Arguments Details Value References Examples

Estimate a multivariate density function using locally Gaussian approximations

1 2	dlg(lg_object, grid, level = 0.95, normalization_points = NULL, bootstrap = F, B = 500)

`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.

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.

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.

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

   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)