lr.test {RecordTest} | R Documentation |
Likelihood-Ratio Test for the Likelihood of the Record Indicators
Description
This function performs likelihood-ratio tests
for the likelihood of the record indicators to study the
hypothesis of the classical record model (i.e., of IID continuous RVs).
Usage
lr.test(
X,
record = c("upper", "lower"),
alternative = c("two.sided", "greater", "less"),
probabilities = c("different", "equal"),
simulate.p.value = FALSE,
B = 1000
)
Arguments
X |
A numeric vector, matrix (or data frame). |
record |
A character string indicating the type of record, "upper" or "lower". |
alternative |
A character indicating the alternative hypothesis
( |
probabilities |
A character indicating if the alternative hypothesis
assume all series with |
simulate.p.value |
Logical. Indicates whether to compute p-values by Monte Carlo simulation. |
B |
An integer specifying the number of replicates used in the Monte Carlo estimation. |
Details
The null hypothesis of the likelihood-ratio tests is that in every vector
(columns of the matrix X
), the probability of record at
time is
as in the classical record model, and
the alternative depends on the
alternative
and probabilities
arguments. The probability at time is any value, but equal in the
series if
probabilities = "equal"
or different in the
series if
probabilities = "different"
. The alternative
hypothesis is more specific in the first case than in the second one.
Furthermore, the "two.sided"
alternative
is tested with
the usual likelihood ratio statistic, while the one-sided
alternatives
use specific statistics based on likelihoods
(see Cebrián, Castillo-Mateo and Asín, 2022, for the details).
If alternative = "two.sided" & probabilities = "equal"
, under the
null, the likelihood ratio statistic has an asymptotic
distribution with
degrees of freedom. It has been seen that for
the approximation to be adequate
must be between 4 and 5 times
greater than
. Otherwise, a
simulate.p.value
is recommended.
If alternative = "two.sided" & probabilities = "different"
, the
asymptotic behaviour is not fulfilled, but the Monte Carlo approach to
simulate the p-value is applied. This statistic is the same as
below multiplied by a factor of 2, so the p-value is the same.
If alternative
is one-sided and probabilities = "equal"
,
the statistic of the test is
The p-value of this test is estimated with Monte Carlo simulations, because the computation of its exact distribution is very expensive.
If alternative
is one-sided and probabilities = "different"
,
the statistic of the test is
The p-value of this test is estimated with Monte Carlo simulations.
However, it is equivalent to the statistic of the weighted number of
records N.test
with weights
.
Value
A list of class "htest"
with the following elements:
statistic |
Value of the statistic. |
parameter |
Degrees of freedom of the approximate |
p.value |
(Estimated) P-value. |
method |
A character string indicating the type of test. |
data.name |
A character string giving the name of the data. |
alternative |
A character string indicating the alternative hypothesis. |
Author(s)
Jorge Castillo-Mateo
References
Cebrián AC, Castillo-Mateo J, Asín J (2022). “Record Tests to Detect Non Stationarity in the Tails with an Application to Climate Change.” Stochastic Environmental Research and Risk Assessment, 36(2): 313-330. doi:10.1007/s00477-021-02122-w.
See Also
Examples
set.seed(23)
# two-sided and different probabilities of record, always simulated the p-value
lr.test(ZaragozaSeries, probabilities = "different")
# equal probabilities
lr.test(ZaragozaSeries, probabilities = "equal")
# equal probabilities with simulated p-value
lr.test(ZaragozaSeries, probabilities = "equal", simulate.p.value = TRUE)
# one-sided and different probabilities of record
lr.test(ZaragozaSeries, alternative = "greater", probabilities = "different")
# different probabilities with simulated p-value
lr.test(ZaragozaSeries, alternative = "greater", probabilities = "different",
simulate.p.value = TRUE)
# equal probabilities, always simulated the p-value
lr.test(ZaragozaSeries, alternative = "greater", probabilities = "equal")