clg: The locally Gaussian conditional density estimator
In lg: Locally Gaussian Distributions: Estimation and Methods

Description Usage Arguments Details Value References Examples

Estimate a conditional density function using locally Gaussian approximations.

1 2	clg(lg_object, grid = NULL, condition = NULL, normalization_points = NULL, fixed_grid = NULL)

`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. Number of columns must be the same as number of variables in X1.
`condition`	A vector with conditions for the variables that we condition upon. Length of this vector must be the same as the number of variables in X2. The function will throw an error of there is any discrepancy in the dimensions of the `grid`, `condition` and data set.
`normalization_points`	How many grid points for approximating the integral of the density estimate, to use for normalization?
`fixed_grid`	Not used presently.

This function is the conditional version of the locally Gaussian density estimator (LGDE), described in Otneim & Tjøstheim (2018). The function takes as arguments an lg-object as produced by the main lg_main- function, a grid of points where the density estimate should be estimated, and a set of conditions.

The variables must be sorted before they are supplied to this function. It will always assume that the free variables come before the conditioning variables.

Assume that X is a stochastic vector with two components X1 and X2. This function will thus estimate the conditional density of X1 given a specified value of X2.

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

f_est: The estimated conditional density.
c_mean: The estimated local conditional means as defined in equation (10) of Otneim & Tjøstheim (2017).
c_cov: The estimated local conditional covariance matrices as defined in equation (11) of Otneim & Tjøstheim (2017).
x: The data set.
bw: The bandwidth object.
transformed_data: The data transformed to approximate marginal standard normality (if selected).
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) (if selected).
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.

Otneim, Håkon, and Dag Tjøstheim. "Conditional density estimation using the local Gaussian correlation" Statistics and Computing 28, no. 2 (2018): 303-321.

  # A 3 variate example
  x <- cbind(rnorm(100), rnorm(100), rnorm(100))

  # Generate the lg-object with default settings
  lg_object <- lg_main(x)

  # Estimate the conditional density of X1|X2 = 0, X3 = 1 on a small grid
  cond_dens <- clg(lg_object, grid = matrix(-4:4, ncol = 1), condition = c(0, 1))