madem.density {mable}R Documentation

Minimum Approximate Distance Estimate of univariate Density Function with given model degree(s)

Description

Minimum Approximate Distance Estimate of univariate Density Function with given model degree(s)

Usage

madem.density(
  x,
  m,
  p = rep(1, prod(m + 1))/prod(m + 1),
  interval = NULL,
  method = c("qp", "em"),
  maxit = 10000,
  eps = 1e-07
)

Arguments

x

an n x d matrix or data.frame of multivariate sample of size n

m

a positive integer or a vector of d positive integers specify the given model degrees for the joint density.

p

initial guess of p

interval

a vector of two endpoints or a 2 x d matrix, each column containing the endpoints of support/truncation interval for each marginal density. If missing, the i-th column is assigned as c(min(x[,i]), max(x[,i])).

method

method for finding minimum distance estimate. "em": EM like method;

maxit

the maximum iterations

eps

the criterion for convergence

Details

A d-variate cdf F on a hyperrectangle [a, b] =[a_1, b_1] \times \cdots \times [a_d, b_d] can be approximated by a mixture of d-variate beta cdfs on [a, b], \beta_{mj}(x) = \prod_{i=1}^dB_{m_i,j_i}[(x_i-a_i)/(b_i-a_i)], with proportion p(j_1, \ldots, j_d), 0 \le j_i \le m_i, i = 1, \ldots, d. With a given model degree m, the parameters p, the mixing proportions of the beta distribution, are calculated as the minimizer of the approximate L_2 distance between the empirical distribution and the Bernstein polynomial model. The quadratic programming with linear constraints is used to solve the problem.

Value

An invisible mable object with components


[Package mable version 4.1.1 Index]