Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing

In this paper, we develop fuzzy, possibilistic hypothesis tests for testing crisp hypotheses for a distribution parameter from crisp data. In these tests, fuzzy statistics are used, which are produced by the possibility distribution of the estimated parameter, constructed by the known from crisp statistics confidence intervals. The results of these tests are in much better agreement with crisp statistics than the ones produced by the respective tests of a popular book on fuzzy statistics, which uses fuzzy critical values. We also present an error that we found in the implementation of the unbiased fuzzy estimator of the variance in this book, due to a poor interpretation of its mathematical content, which leads to disagreement of some fuzzy hypotheses tests with their respective crisp ones. Implementing correctly this estimator, we produce test statistics that achieve results in hypotheses tests that are in much better agreement with the results of the respective crisp ones.

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Fuzzy hypothesis testing for a population proportion based on set-valued information

Fuzzy Sets and Systems ◽

10.1016/j.fss.2019.02.017 ◽

2020 ◽

Vol 387 ◽

pp. 127-157 ◽

Cited By ~ 2

Author(s):

Nataliya Chukhrova ◽

Arne Johannssen

Keyword(s):

Hypothesis Testing ◽

Population Proportion ◽

Fuzzy Hypothesis

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An artificial neural network-based critical values for multiple hypothesis testing: data-snooping case

Survey Review ◽

10.1080/00396265.2021.1968176 ◽

2021 ◽

pp. 1-16

Author(s):

Vinicius Francisco Rofatto ◽

Marcelo Tomio Matsuoka ◽

Ivandro Klein ◽

Maria Luísa Silva Bonimani ◽

Bruno Póvoa Rodrigues ◽

...

Keyword(s):

Neural Network ◽

Artificial Neural Network ◽

Hypothesis Testing ◽

Multiple Hypothesis Testing ◽

Critical Values ◽

Data Snooping ◽

Multiple Hypothesis ◽

Testing Data ◽

Artificial Neural

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Uncertainty and Inference for Verification Measures

Weather and Forecasting ◽

10.1175/waf989.1 ◽

2007 ◽

Vol 22 (3) ◽

pp. 637-650 ◽

Cited By ~ 74

Author(s):

Ian T. Jolliffe

Keyword(s):

Hypothesis Testing ◽

Confidence Intervals ◽

Multiple Testing ◽

Prediction Intervals ◽

Hypothesis Tests ◽

Statistical Inferences ◽

The Difference ◽

Main Ideas

Abstract When a forecast is assessed, a single value for a verification measure is often quoted. This is of limited use, as it needs to be complemented by some idea of the uncertainty associated with the value. If this uncertainty can be quantified, it is then possible to make statistical inferences based on the value observed. There are two main types of inference: confidence intervals can be constructed for an underlying “population” value of the measure, or hypotheses can be tested regarding the underlying value. This paper will review the main ideas of confidence intervals and hypothesis tests, together with the less well known “prediction intervals,” concentrating on aspects that are often poorly understood. Comparisons will be made between different methods of constructing confidence intervals—exact, asymptotic, bootstrap, and Bayesian—and the difference between prediction intervals and confidence intervals will be explained. For hypothesis testing, multiple testing will be briefly discussed, together with connections between hypothesis testing, prediction intervals, and confidence intervals.

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