adestr (version 1.0.0)

PointEstimator-class: Point estimators

Description

This is the parent class for all point estimators implemented in this package. Currently, only estimators for the parameter \(\mu\) of a normal distribution are implemented.

Usage

PointEstimator(g1, g2, label)
SampleMean()
FirstStageSampleMean()
WeightedSampleMean(w1 = 0.5)
AdaptivelyWeightedSampleMean(w1 = 1/sqrt(2))
MinimizePeakVariance()
BiasReduced(iterations = 1L)
RaoBlackwell()
PseudoRaoBlackwell()
MidpointStagewiseCombinationFunctionOrderingCI()
MidpointMLEOrderingCI()
MidpointLikelihoodRatioOrderingCI()
MidpointScoreTestOrderingCI()
MidpointNeymanPearsonOrderingCI()
MedianUnbiasedStagewiseCombinationFunctionOrdering()
MedianUnbiasedMLEOrdering()
MedianUnbiasedLikelihoodRatioOrdering()
MedianUnbiasedScoreTestOrdering()
MedianUnbiasedNeymanPearsonOrdering(mu0 = 0, mu1 = 0.4)

Value

an object of class PointEstimator. This class signals that an object can be supplied to the evaluate_estimator and the analyze functions.

Arguments

g1

functional representation of the estimator in the early futility and efficacy regions.

g2

functional representation of the estimator in the continuation region.

label

name of the estimator. Used in printing methods.

w1

weight of the first-stage data.

iterations

number of bias reduction iterations. Defaults to 1.

mu0

expected value of the normal distribution under the null hypothesis.

mu1

expected value of the normal distribution under the null hypothesis.

Details

Details about the point estimators can be found in (our upcoming paper).

Sample Mean (SampleMean())

The sample mean is the maximum likelihood estimator for the mean and probably the 'most straightforward' of the implemented estimators.

Fixed weighted sample means (WeightedSampleMean())

The first- and second-stage (if available) sample means are combined via fixed, predefined weights. See brannath2006estimationadestr and @Section 8.3.2 in @wassmer2016groupadestr.

Adaptively weighted sample means (AdaptivelyWeightedSampleMean())

The first- and second-stage (if available) sample means are combined via a combination of fixed and adaptively modified weights that depend on the standard error. See @Section 8.3.4 in @wassmer2016groupadestr.

Minimizing peak variance in adaptively weighted sample means (MinimizePeakVariance())

For this estimator, the weights of the adaptively weighted sample mean are chosen to minimize the variance of the estimator for the value of \(\mu\) which maximizes the expected sample size.

(Pseudo) Rao-Blackwell estimators (RaoBlackwell and PseudoRaoBlackwell)

The conditional expectation of the first-stage sample mean given the overall sample mean and the second-stage sample size. See emerson1997computationallyadestr.

A bias-reduced estimator (BiasReduced())

This estimator is calculated by subtracting an estimate of the bias from the MLE. See whitehead1986biasadestr.

Median-unbiased estimators

The implemented median-unbiased estimators are:

• MedianUnbiasedMLEOrdering()

• MedianUnbiasedLikelihoodRatioOrdering()

• MedianUnbiasedScoreTestOrdering()

• MedianUnbiasedStagewiseCombinationFunctionOrdering()

These estimators are constructed by specifying an ordering of the sample space and finding the value of \(\mu\), such that the observed sample is the median of the sample space according to the chosen ordering. Some of the implemented orderings are based on the work presented in emerson1990parameteradestr, @Sections 8.4 in @jennison1999groupadestr, and @Sections 4.1.1 and 8.2.1 in @wassmer2016groupadestr.

References

See Also

evaluate_estimator

Examples

PointEstimator(g1 = \(smean1, ...) smean1,g2 = \(smean2, ...) smean2, label="My custom estimator")