scholarly journals On Multiple Hypotheses LAO Testing With Rejection of Decision for Two Dependent Objects

2018 ◽  
pp. 110-114
Author(s):  
Evgueni Haroutunian ◽  
Aram Yesayan ◽  
Narine Harutyunyan
Keyword(s):  
Hypotheses Testing ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Multiple Hypotheses ◽  
Optimal Tests ◽  
The Matrix ◽  
Statistical Hypotheses ◽  
Asymptotically Optimal Tests ◽  
Error Probabilities ◽  
Statistical Hypotheses Testing

Multiple statistical hypotheses testing with possibility of rejecting of decisionis considered for model consisting of two dependent objects characterized by joint discrete probability distribution. The matrix of error probabilities exponents (reliabilities) of asymptotically optimal tests is studied.

scholarly journals A Neyman-Pearson Proper Way to Universal Testing of Multiple Hypotheses Formed by Groups of Distributions

2020 ◽  
pp. 18-33
Author(s):  
Evgueni Haroutunian ◽  
Aram Yesayan
Keyword(s):  
Error Probability ◽  
Probability Distributions ◽  
Single Letter ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Multiple Hypotheses ◽  
Universal Testing ◽  
Error Probabilities ◽  
Discrete Probability Distributions ◽  
The Given

The asymptotically optimal Neyman-Pearson procedures of detection for models characterized by M discrete probability distributions arranged into K, 2 ≤ K ≤ M groups considered as hypotheses are investigated. The sequence of tests based on a growing number of observations is logarithmically asymptotically optimal (LAO) when a certain part of the given error probability exponents (reliabilities) provides positives values for all other reliabilities. LAO tests sequences for some models of objects, including cases, when rejection of decision may be permitted, and when part, or all given error probabilities decrease subexponentially with an increase in the of number of experiments, are desined. For all reliabilities of such tests single-letter characterizations are obtained. A simple case with three distributions and two hypotheses is considered.

Two-stage test with possibility of rejection of decision

2016 ◽  
Vol 09 (03) ◽  
pp. 1650050
Author(s):  
Farshin Hormozinejad
Keyword(s):  
Error Probability ◽  
Probability Distributions ◽  
Functional Relation ◽  
Hypotheses Testing ◽  
Two Stage ◽  
Asymptotically Optimal ◽  
Second Stage ◽  
One Stage ◽  
The Matrix ◽  
Statistical Hypotheses

The multiple statistical hypotheses two-stage testing with possibility of rejecting of decision to make choice between hypotheses concerning the pair of groups of probability distributions is considered such that in the first stage one group of distributions is distinguished and then in the second stage, the true distribution is denoted between mentioned group of probability distributions. Description of characteristics of logarithmically asymptotically optimal (LAO) hypotheses testing with possibility of decision rejection and the matrix of optimal asymptotically interdependencies of all pairs of the error probability exponents or reliabilities are studied. The goal of research is to express the optimal functional relation between the reliabilities of LAO hypotheses testing by a pair of stages and to compare with the case of similar one-stage testing.

GENERALIZATION OF BAYESIAN RULE OF MANY SIMPLE HYPOTHESES TESTING

2003 ◽  
Vol 02 (01) ◽  
pp. 41-70 ◽  
Author(s):  
K. J. KACHIASHVILI
Keyword(s):  
Unconstrained Optimization ◽  
Bayesian Approach ◽  
Optimization Problem ◽  
Classical Case ◽  
Hypotheses Testing ◽  
Unconstrained Optimization Problem ◽  
Finite Set ◽  
Statistical Hypotheses ◽  
Space Point ◽  
Statistical Hypotheses Testing

There are different methods of statistical hypotheses testing.1–4 Among them, is Bayesian approach. A generalization of Bayesian rule of many hypotheses testing is given below. It consists of decision rule dimensionality with respect to the number of tested hypotheses, which allows to make decisions more differentiated than in the classical case and to state, instead of unconstrained optimization problem, constrained one that enables to make guaranteed decisions concerning errors of true decisions rejection, which is the key point when solving a number of practical problems. These generalizations are given both for a set of simple hypotheses, each containing one space point, and hypotheses containing a finite set of separated space points.

scholarly journals The role of benchmark technology in sustainable value analysis

2008 ◽  
pp. 1-6
Author(s):  
Timo Kuosmanen ◽  
Natalia Kuosmanen
Keyword(s):  
Production Technology ◽  
Empirical Data ◽  
Hypotheses Testing ◽  
Direct Link ◽  
Value Analysis ◽  
Sustainability Performance ◽  
Sustainable Value ◽  
Statistical Hypotheses ◽  
Statistical Hypotheses Testing

Sustainable Value Analysis (SVA) [F. Figge, T. Hahn, Ecol. Econ. 48(2004) 173-187] is a method formeasuring sustainability performance consistent with the constant capital rule and strongsustainability. SVA compares eco-efficiency of a firm relative to some benchmark. The choice of thebenchmark implies some assumptions regarding the underlying production technology. This paperpresents a rigorous examination of the role of benchmark technology in SVA. We show that Figge andHahn’s formula for calculating sustainable value implies a peculiar linear benchmark technology. Wepresent a generalized formulation of sustainable value that is not restricted to any particular functionalform and allows for estimating benchmark technology from empirical data. Our generalized SVAformulation reveals a direct link between SVA and frontier approaches to environmental performancemeasurement and facilitates statistical hypotheses testing concerning the benchmark.

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