compute.stream {TopKLists} | R Documentation |
Calculates point of degeneration j0 into noise of the Idata, applying moderate deviation-based inference
Description
The estimation of is achieved via a moderate deviation-based approach. The probability that an estimator, computed from a pilot sample size
, exceeds a value z, the deviation above z is said to be a moderate deviation if its associated probability is polynomially small as a function of
, and to be a large deviation if the probability is exponentially small in
. The values of
that are associated with moderate deviations are
, where
. The null hypothesis that
for
consecutive values of k, versus the alternative hypothesis that
for at least one of the values of k, is rejected when
. The probabilities
and
are estimates of
computed from the
data pairs
for which
lies immediately to the right of j, or immediately to the left of j, respectively.
The iterative algorithm consists of an ordered sequence of "test stages" In stage
an integer
is estimated, which is a potential lower bound to
(when
is odd), or a potential upper bound to
(when
is even).
Usage
compute.stream(Idata, const=0.251, v, r=1.2)
Arguments
Idata |
Input data is a vector of 0s and 1s (see |
const |
Denotes the constant C of the moderate deviation bound, needs to be larger than 0.25 (default is 0.251) |
v |
Denotes the pilot sample size |
r |
Denotes a technical constant determining the starting point from which the probability for |
Value
A named list containing:
j0_est |
Is the estimated index for which the |
k |
|
reason.break |
The reason why the computation has ended - convergence or break condition |
js |
Is the sequence of estimated |
v |
Is the preselected value of the parameter |
Author(s)
Eva Budinska <budinska@iba.muni.cz>, Michael G. Schimek <michael.schimek@medunigraz.at>
See Also
Examples
set.seed(465)
myhead <- rbinom(20, 1, 0.8)
mytail <- rbinom(20, 1, 0.5)
mydata <- c(myhead, mytail)
compute.stream(mydata, v=10)