View source: R/mable-multivar.r
mable.mvar | R Documentation |
Maximum Approximate Bernstein Likelihood Estimate of Multivariate Density Function
mable.mvar(
x,
M0 = 1,
M,
search = TRUE,
interval = NULL,
mar.deg = TRUE,
high.dim = FALSE,
criterion = c("cdf", "pdf"),
controls = mable.ctrl(),
progress = TRUE
)
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 those minimize the maximum L2 distance between marginal cdf or pdf estimated based on marginal data and the joint data. See details. |
high.dim |
logical, data are high dimensional/large sample or not if TRUE, run a slower version procedure which requires less memory |
criterion |
either cdf or pdf should be used for selecting optimal degrees. Default is "cdf" |
controls |
Object of class |
progress |
if TRUE a text progressbar is displayed |
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
.
Let \tilde F_i
(\tilde f_i
) be an estimate with degree \tilde m_i
of
the i-th marginal cdf (pdf) based on marginal data x[,i]
, i=1, \ldots, d
.
If search=TRUE
and use.marginal=TRUE
, then the optimal degrees
are (\tilde m_1,\ldots,\tilde m_d)
. If search=TRUE
and
use.marginal=FALSE
, then the optimal degrees (\hat m_1,\ldots,\hat m_d)
are those that minimize the maximum of L_2
-distance between
\tilde F_i
(\tilde f_i
) and the estimate of F_i
(f_i
)
based on the joint data with degrees m=(m_1,\ldots,m_d)
for all m
between M_0
and M
if criterion
="cdf" (criterion
="pdf").
For large data and multimodal density, the search for the model degrees is
very time-consuming. In this case, it is suggested that the degrees are selected
based on marginal data using mable
or optimable
.
A list with components
m
a vector of the selected optimal degrees by the method of change-point
p
a vector of the mixture proportions p(j_1, \ldots, j_d)
, arranged in the
column-major order of j = (j_1, \ldots, j_d)
, 0 \le j_i \le m_i, i = 1, \ldots, d
.
mloglik
the maximum log-likelihood at an optimal degree m
pval
the p-values of change-points for choosing the optimal degrees for the
marginal densities
M
the vector (m1, m2, ... , md)
, where mi
is the largest candidate
degree when the search stoped for the i
-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 limit maxit
had been reached in the EM iteration;
Zhong Guan <zguan@iusb.edu>
Wang, T. and Guan, Z.,(2019) Bernstein Polynomial Model for Nonparametric Multivariate Density, Statistics, Vol. 53, no. 2, 321-338
mable
, optimable
## Old Faithful Data
a<-c(0, 40); b<-c(7, 110)
ans<- mable.mvar(faithful, M = c(46,19), search =FALSE,
interval = rbind(a,b), progress=FALSE)
plot(ans, which="density")
plot(ans, which="cumulative")
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