hcnm: Hierarchical Constrained Newton method

In nspmix: Nonparametric and Semiparametric Mixture Estimation

Hierarchical Constrained Newton method

Description

Function hcnm can be used to compute the MLE of a finite discrete mixing distribution, given the component density values of each observation. It implements the hierarchical CNM algorithm of Wang and Taylor (2013).

Usage

hcnm(
  D,
  p0 = NULL,
  w = 1,
  maxit = 1000,
  tol = 1e-06,
  blockpar = NULL,
  recurs.maxit = 2,
  compact = TRUE,
  depth = 1,
  verbose = 0
)

Arguments

D	A numeric matrix, each row of which stores the component density values of an observation.
p0	Initial mixture component proportions.
w	Duplicity of each row in matrix D (i.e., that of a corresponding observation).
maxit	Maximum number of iterations.
tol	A tolerance value to terminate the algorithm. Specifically, the algorithm is terminated, if the increase of the log-likelihood value after an iteration is less than tol.
blockpar	Block partitioning parameter. If > 1, the number of blocks is roughly nrol(D)/blockpar. If < 1, the number of blocks is roughly nrol(D)^blockpar.
recurs.maxit	Maximum number of iterations in recursions.
compact	Whether iteratively select and use a compact subset (which guarantees convergence), or not (if already done so before calling the function).
depth	Depth of recursion/hierarchy.
verbose	Verbosity level for printing intermediate results.

Value

p	Computed probability vector.
convergence	convergence code. =0 means a success, and =1 reaching the maximum number of iterations
ll	log-likelihood value at convergence
maxgrad	Maximum gradient value.
numiter	number of iterations required by the algorithm

Author(s)

Yong Wang <[e-mail]>

References

Wang, Y. (2007). On fast computation of the non-parametric maximum likelihood estimate of a mixing distribution. Journal of the Royal Statistical Society, Ser. B, 69, 185-198.

Wang, Y. and Taylor, S. M. (2013). Efficient computation of nonparametric survival functions via a hierarchical mixture formulation. Statistics and Computing, 23, 713-725.

See Also

cnm, nppois, disc.

Examples

x = rnppois(1000, disc(0:50))    # Poisson mixture
D = outer(x$v, 0:1000/10, dpois)
(r = hcnm(D, w=x$w))
disc(0:1000/10, r$p, collapse=TRUE)

cnm(x, init=list(mix=disc(0:1000/10)), model="p")

nspmix documentation built on June 8, 2025, 12:29 p.m.