scholarly journals An integrated selection formulation for the best normal mean: the unequal and unknown variance case

2002 ◽  
Vol 6 (1) ◽  
pp. 23-42 ◽  
Author(s):  
Pinyuen Chen ◽  
Jun-Lue Zhang
Keyword(s):  
Sample Size ◽  
Parameter Space ◽  
Correct Selection ◽  
Indifference Zone ◽  
Unknown Variance ◽  
Normal Mean ◽  
Favorable Configuration ◽  
Preference Zone ◽  
Selected Subset ◽  
Least Favorable Configuration

This paper considers an integrated formulation in selecting the best normal mean in the case of unequal and unknown variances. The formulation separates the parameter space into two disjoint parts, the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best for a correct selection (CS1) but in the IZ we define any selected subset to be correct (CS2) if it contains the best population. We find the least favorable configuration (LFC) and the worst configuration (WC) respectively in PZ and IZ. We derive formulas for P(CS1|LFC), P(CS2|WC) and the bounds for the expected sample size E(N). We also give tables for the procedure parameters to implement the proposed procedure. An example is given to illustrate how to apply the procedure and how to use the table.

SELECTING THE MOST RELIABLE POPULATION UNDER STEP-STRESS ACCELERATED LIFE TEST

1999 ◽  
Vol 06 (04) ◽  
pp. 347-359 ◽  
Author(s):  
LOON CHING TANG ◽  
YESHENG SUN
Keyword(s):  
Selection Procedure ◽  
Approximate Expression ◽  
Accelerated Life Testing ◽  
Accelerated Life Test ◽  
Correct Selection ◽  
Test Results ◽  
Indifference Zone ◽  
Probability Of Correct Selection ◽  
Accelerated Life ◽  
Favorable Configuration

We present a method for selecting the most reliable population under step-stress accelerated life testing with type II censoring. We construct a new statistic, the transitional order statistic (TOS), and derive an approximate expression for its distribution. Using the TOS, a selection rule is formulated from the test results. For planning purposes, we establish the relation between sample size and the probability of correct selection by defining a nonlinear indifference zone under the least favorable configuration. Finally, a simulation study is performed to illustrate the selection procedure and to validate the associated probability of correct selection.

scholarly journals A two-stage procedure on comparing several experimental treatments and a control—the common and unknown variance case

2005 ◽  
Vol 2005 (1) ◽  
pp. 47-58
Author(s):  
John Zhang ◽  
Pinyuen Chen ◽  
Yue Fang
Keyword(s):  
Selection Rule ◽  
Selection Procedure ◽  
Experimental Treatment ◽  
Correct Decision ◽  
Two Stage ◽  
Sample Mean ◽  
Indifference Zone ◽  
Unknown Variance ◽  
Preference Zone ◽  
Experimental Treatments

This paper introduces a two-stage selection rule to compare several experimental treatments with a control when the variances are common and unknown. The selection rule integrates the indifference zone approach and the subset selection approach in multiple-decision theory. Two mutually exclusive subsets of the parameter space are defined, one is called the preference zone (PZ) and the other, the indifference zone (IZ). The best experimental treatment is defined to be the experimental treatment with the largest population mean. The selection procedure opts to select only the experimental treatment which corresponds to the largest sample mean when the parameters are in the PZ, and selects a subset of the experimental treatments and the control when the parameters fall in the IZ. The concept of a correct decision is defined differently in these two zones. A correct decision in the preference zone (CD1) is defined to be the event that the best experimental treatment is selected. In the indifference zone, a selection is called correct (CD2) if the selected subset contains the best experimental treatment. Theoretical results on the lower bounds for P(CD1) in PZ and P(CD2) in IZ are developed. A table is computed for the implementation of the selection procedure.

scholarly journals Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

2020 ◽  
Vol 8 (2) ◽  
pp. 507-520
Author(s):  
Abdenour Hamdaoui ◽  
Abdelkader Benkhaled ◽  
Nadia Mezouar
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Unknown Variance ◽  
Multivariate Normal Mean ◽  
Normal Mean

In this article, we consider two forms of shrinkage estimators of a multivariate normal mean with unknown variance. We take the prior law as a normal multivariate distribution and we construct a Modified Bayes estimator and an Empirical Modified Bayes estimator. We are interested instudying the minimaxity and the behavior of risks ratios of these estimators to the maximum likelihood estimator, when the dimension of the parameters space and the sample size tend to infinity.

Selecting the Best Alternative Based on Its Quantile

2020 ◽  
Author(s):  
Demet Batur ◽  
F. Fred Choobineh
Keyword(s):  
Value At Risk ◽  
Decision Makers ◽  
Correct Selection ◽  
Zone Size ◽  
Indifference Zone ◽  
Probability Of Correct Selection ◽  
A Value ◽  
Conscious Decision ◽  
Target Probability ◽  
Sequential Procedures

A value-at-risk, or quantile, is widely used as an appropriate investment selection measure for risk-conscious decision makers. We present two quantile-based sequential procedures—with and without consideration of equivalency between alternatives—for selecting the best alternative from a set of simulated alternatives. These procedures asymptotically guarantee a user-defined target probability of correct selection within a prespecified indifference zone. Experimental results demonstrate the trade-off between the indifference-zone size and the number of simulation iterations needed to render a correct selection while satisfying a desired probability of correct selection.

scholarly journals Power in High‐Dimensional Testing Problems

Econometrica ◽  
2019 ◽  
Vol 87 (3) ◽  
pp. 1055-1069 ◽  
Author(s):  
Anders Bredahl Kock ◽  
David Preinerstorfer
Keyword(s):  
Asymptotic Normality ◽  
Sample Size ◽  
Parameter Space ◽  
Sufficient Conditions ◽  
High Dimensional ◽  
Local Asymptotic Normality ◽  
Asymptotic Power ◽  
Asymptotic Size ◽  
Power Of Tests ◽  
Power Enhancement

Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high‐dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non‐inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that cannot be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than 1 can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case.

Sign in / Sign up

Export Citation Format

Share Document