259 research outputs found
Locally most powerful sequential tests of a simple hypothesis vs one-sided alternatives
Let be a discrete-time stochastic process with a distribution
, , where is an open subset of the real
line. We consider the problem of testing a simple hypothesis
versus a composite alternative ,
where is some fixed point. The main goal of this article is
to characterize the structure of locally most powerful sequential tests in this
problem.
For any sequential test with a (randomized) stopping rule
and a (randomized) decision rule let be the
type I error probability, the derivative, at
, of the power function, and an average
sample number of the test . Then we are concerned with the problem
of maximizing in the class of all sequential tests
such that where and are some
restrictions. It is supposed that is calculated under some
fixed (not necessarily coinciding with one of ) distribution of the
process .
The structure of optimal sequential tests is characterized.Comment: 30 page
Optimal sequential procedures with Bayes decision rules
In this article, a general problem of sequential statistical inference for
general discrete-time stochastic processes is considered. The problem is to
minimize an average sample number given that Bayesian risk due to incorrect
decision does not exceed some given bound. We characterize the form of optimal
sequential stopping rules in this problem. In particular, we have a
characterization of the form of optimal sequential decision procedures when the
Bayesian risk includes both the loss due to incorrect decision and the cost of
observations.Comment: Shortened version for print publication, 17 page
Optimal sequential multiple hypothesis tests
This work deals with a general problem of testing multiple hypotheses about
the distribution of a discrete-time stochastic process. Both the Bayesian and
the conditional settings are considered. The structure of optimal sequential
tests is characterized.Comment: To appear in Kybernetika (Prague
Optimal sequential tests for multiple hypotheses when sampling from a Bernoulli population
In this paper we deal with the problem of sequential testing of multiple
hypotheses. We are interested in minimising a weighted average sample number
under restrictions on the error probabilities. A computer-oriented method of
construction of optimal sequential tests is proposed. For the particular case
of sampling from a Bernoulli population we develop a whole set of computer
algorithms for optimal design and performance evaluation of sequential tests
and implement them in the form of computer code written in R programming
language.
The tests we obtain are exact (neither asymptotic nor approximate).
Extensions to other distribution families are discussed. A numerical comparison
with other known tests (of MSPRT type) is carried out.Comment: 14 pages, 2 table
Group sequential hypothesis tests with variable group sizes: optimal design and performance evaluation
In this paper, we propose a computer-oriented method of construction of
optimal group sequential hypothesis tests with variable group sizes. In
particular, for independent and identically distributed observations we obtain
the form of optimal group sequential tests which turn to be a particular case
of sequentially planned probability ratio tests (SPPRTs, Schmitz, 1993) .
Formulas are given for computing the numerical characteristics of general
SPPRTs, like error probabilities, average sampling cost, etc. A numerical
method of designing the optimal tests and evaluation of the performance
characteristics is proposed, and computer algorithms of its implementation are
developed. For a particular case of sampling from a Bernoulli population, the
proposed method is implemented in R programming language, the code is available
in a public GitHub repository. The proposed method is compared numerically with
other known sampling plans.Comment: 17 pages, 3 figures, 1 tabl
Sequential multiple hypothesis testing in presence of control variables
Suppose that at any stage of a statistical experiment a control variable
that affects the distribution of the observed data at this stage can be
used. The distribution of depends on some unknown parameter , and
we consider the problem of testing multiple hypotheses ,
, allowing the data to be
controlled by , in the following sequential context.
The experiment starts with assigning a value to the control variable
and observing as a response. After some analysis, another value for
the control variable is chosen, and as a response is observed, etc. It is
supposed that the experiment eventually stops, and at that moment a final
decision in favor of one of the hypotheses , is to be taken. In
this article, our aim is to characterize the structure of optimal sequential
testing procedures based on data obtained from an experiment of this type in
the case when the observations are independent, given
controls , .Comment: To appear in Kybernetik
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