made.mvar {mable} | R Documentation |
Minimum Approximate Distance Estimate of Multivariate Density Function
Description
Minimum Approximate Distance Estimate of Multivariate Density Function
Usage
made.mvar(
x,
M0 = 1L,
M,
search = TRUE,
interval = NULL,
mar.deg = TRUE,
method = c("cd", "quadprog"),
controls = mable.ctrl(),
progress = TRUE
)
Arguments
x |
an |
M0 |
a positive integer or a vector of |
M |
a positive integer or a vector of |
search |
logical, whether to search optimal degrees between |
interval |
a vector of two endpoints or a |
mar.deg |
logical, if TRUE, the optimal degrees are selected based on marginal data, otherwise, the optimal degrees are chosen the joint data. See details. |
method |
method for finding minimum distance estimate. "cd": coordinate-descent; |
controls |
Object of class |
progress |
if TRUE a text progressbar is displayed |
Details
A d
-variate density 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 densities on [a, b]
,
\beta_{mj}(x) = \prod_{i=1}^d\beta_{m_i,j_i}[(x_i-a_i)/(b_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
.
If search=TRUE
then the model degrees are chosen using a method of change-point based on
the marginal data if mar.deg=TRUE
or the joint data if mar.deg=FALSE
.
If search=FALSE
, then the model degree is specified by M
.
For large data and multimodal density, the search for the model degrees is
very time-consuming. In this case, it is suggested that use method="cd"
and select the degrees based on marginal data using mable
or
optimable
.
Value
A list with components
-
m
a vector of the selected optimal degrees by the method of change-point -
p
a vector of the mixture proportionsp(j_1, \ldots, j_d)
, arranged in the column-major order ofj = (j_1, \ldots, j_d)
,0 \le j_i \le m_i, i = 1, \ldots, d
. -
minD
the minimum distance at an optimal degreem
-
pval
the p-values of change-points for choosing the optimal degrees for the marginal densities -
M
the vector(m1, m2, ... , md)
, wheremi
is the largest candidate degree when the search stoped for thei
-th marginal density -
interval
support hyperrectangle[a, b]=[a_1, b_1] \times \cdots \times [a_d, b_d]
-
convergence
An integer code. 0 indicates successful completion(the EM iteration is convergent). 1 indicates that the iteration limitmaxit
had been reached in the EM iteration;
Author(s)
Zhong Guan <zguan@iu.edu>
References
Guan, Z. (2016) Efficient and robust density estimation using Bernstein type polynomials. Journal of Nonparametric Statistics, 28(2):250-271.
Wang, T. and Guan, Z.,(2019) Bernstein Polynomial Model for Nonparametric Multivariate Density, Statistics, Vol. 53, no. 2, 321-338
See Also
Examples
## Old Faithful Data
library(mable)
a<-c(0, 40); b<-c(7, 110)
ans<- made.mvar(faithful, M = c(46,19), search =FALSE, method="quadprog",
interval = rbind(a,b), progress=FALSE)
plot(ans, which="density")
plot(ans, which="cumulative")