179 research outputs found
Estimation of the Selected Treatment Mean in Two-Stage Drop-the-Losers Design
A common problem faced in clinical studies is that of estimating the effect
of the most effective (e.g., the one having the largest mean) treatment among
available treatments. The most effective treatment is adjudged
based on numerical values of some statistic corresponding to the
treatments. A proper design for such problems is the so-called "Drop-the-Losers
Design (DLD)". We consider two treatments whose effects are described by
independent Gaussian distributions having different unknown means and a common
known variance. To select the more effective treatment, the two treatments are
independently administered to subjects each and the treatment
corresponding to the larger sample mean is selected. To study the effect of the
adjudged more effective treatment (i.e., estimating its mean), we consider the
two-stage DLD in which subjects are further administered the adjudged
more effective treatment in the second stage of the design. We obtain some
admissibility and minimaxity results for estimating the mean effect of the
adjudged more effective treatment. The maximum likelihood estimator is shown to
be minimax and admissible. We show that the uniformly minimum variance
conditionally unbiased estimator (UMVCUE) of the selected treatment mean is
inadmissible and obtain an improved estimator. In this process, we also derive
a sufficient condition for inadmissibility of an arbitrary location and
permutation equivariant estimator and provide dominating estimators in cases
where this sufficient condition is satisfied. The mean squared error and the
bias performances of various competing estimators are compared via a simulation
study. A real data example is also provided for illustration purposes
On Estimating the Selected Treatment Mean under a Two-Stage Adaptive Design
Adaptive designs are commonly used in clinical and drug development studies
for optimum utilization of available resources. In this article, we consider
the problem of estimating the effect of the selected (better) treatment using a
two-stage adaptive design. Consider two treatments with their effectiveness
characterized by two normal distributions having different unknown means and a
common unknown variance. The treatment associated with the larger mean effect
is labeled as the better treatment. In the first stage of the design, each of
the two treatments is independently administered to different sets of
subjects, and the treatment with the larger sample mean is chosen as the better
treatment. In the second stage, the selected treatment is further administered
to additional subjects. In this article, we deal with the problem of
estimating the mean of the selected treatment using the above adaptive design.
We extend the result of \cite{cohen1989two} by obtaining the uniformly minimum
variance conditionally unbiased estimator (UMVCUE) of the mean effect of the
selected treatment when multiple observations are available in the second
stage. We show that the maximum likelihood estimator (a weighted sample average
based on the first and the second stage data) is minimax and admissible for
estimating the mean effect of the selected treatment. We also propose some
plug-in estimators obtained by plugging in the pooled sample variance in place
of the common variance , in some of the estimators proposed by
\cite{misra2022estimation} for the situations where is known. The
performances of various estimators of the mean effect of the selected treatment
are compared via a simulation study. For the illustration purpose, we also
provide a real-data application
A Note On Simultaneous Estimation of Order Restricted Location Parameters of a General Bivariate Symmetric Distribution Under a General Loss Function
The problem of simultaneous estimation of order restricted location
parameters and ()
of a bivariate location symmetric distribution, under a general loss function,
is being considered. In the literature, many authors have studied this problem
for specific probability models and specific loss functions. In this paper, we
unify these results by considering a general bivariate symmetric model and a
quite general loss function. We use the Stein and the Kubokawa (or IERD)
techniques to derive improved estimators over any location equivariant
estimator under a general loss function. We see that the improved Stein type
estimator is robust with respect to the choice of a bivariate symmetric
distribution and the loss function, as it only requires the loss function to
satisfy some generic conditions. A simulation study is carried out to validate
the findings of the paper. A real-life data analysis is also provided
A unified study for estimation of order restricted location/scale parameters under the generalized Pitman nearness criterion
We consider component-wise estimation of order restricted location/scale
parameters of a general bivariate location/scale distribution under the
generalized Pitman nearness criterion (GPN). We develop some general results
that, in many situations, are useful in finding improvements over
location/scale equivariant estimators. In particular, under certain conditions,
these general results provide improvements over the unrestricted Pitman nearest
location/scale equivariant estimators and restricted maximum likelihood
estimators. The usefulness of the obtained results is illustrated through their
applications to specific probability models. A simulation study has been
considered to compare how well different estimators perform under the GPN
criterion with a specific loss function
Estimation of Order Restricted Location/Scale Parameters of a General Bivariate Distribution Under General Loss function: Some Unified results
We consider component-wise equivariant estimation of order restricted
location/scale parameters of a general bivariate distribution under quite
general conditions on underlying distributions and the loss function. This
paper unifies various results in the literature dealing with sufficient
conditions for finding improvments over arbitrary location/scale equivariant
estimators. The usefulness of these results is illustrated through various
examples. A simulation study is considered to compare risk performances of
various estimators under bivariate normal and independent gamma probability
models. A real-life data analysis is also performed to demonstrate
applicability of the derived results
Componentwise Equivariant Estimation of Order Restricted Location and Scale Parameters In Bivariate Models: A Unified Study
The problem of estimating location (scale) parameters and
of two distributions when the ordering between them is known apriori
(say, ) has been extensively studied in the literature.
Many of these studies are centered around deriving estimators that dominate the
best location (scale) equivariant estimators, for the unrestricted case, by
exploiting the prior information that . Several of
these studies consider specific distributions such that the associated random
variables are statistically independent. This paper considers a general
bivariate model and general loss function and unifies various results proved in
the literature. We also consider applications of these results to a bivariate
normal and a Cheriyan and Ramabhadran's bivariate gamma model. A simulation
study is also considered to compare the risk performances of various estimators
under bivariate normal and Cheriyan and Ramabhadran's bivariate gamma models
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