An Invitation to Operator-Based Statistics

Mapping Intimacies ◽

10.1093/oxfordhb/9780199568444.013.16 ◽

2018 ◽

Author(s):

Yves Romain

Keyword(s):

Multivariate Analysis ◽

Toeplitz Operators ◽

Quantum Statistics ◽

Classical Statistics ◽

Covariance Operators ◽

Associated Operators ◽

Tensor Operators

This article deals with operator-based statistics and its advantages. It first provides an overview of the historical and pedagogical aspects of operator-based statistics before explaining the underlying practical and theoretical motivations, along with synthetic and conceptual arguments. In particular, it develops the operator-based approach for factor multivariate analysis (and for their asymptotic studies) and offers several examples that show the value of operators in statistics. The discussion focuses on covariance operators, Hankel and Toeplitz operators, regression operators, measure-associated operators, tensor operators, and some other important categories. The article also describes noncommutative or quantum statistics and concludes with some reflections on the key notions and formulations of a "unified statistics" and projectors in (classical) statistics.

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Multivariate Analysis under Indeterminacy: An Application to Chemical Content Data

Journal of Analytical Methods in Chemistry ◽

10.1155/2020/1406028 ◽

2020 ◽

Vol 2020 ◽

pp. 1-6 ◽

Cited By ~ 2

Author(s):

Muhammad Aslam ◽

Osama H. Arif

Keyword(s):

Multivariate Analysis ◽

Multivariate Data ◽

Classical Statistics ◽

Chemical Content ◽

Neutrosophic Statistics ◽

Uncertainty Environment

The Hotelling T-squared statistic has been widely used for the testing of differences in means for the multivariate data. The existing statistic under classical statistics is applied when observations in multivariate data are determined, precise, and exact. In practice, it is not necessary that all observations in the data are determined and precise due to measurement in complex situations and under uncertainty environment. In this paper, we will introduce the Hotelling T-squared statistic under neutrosophic statistics (NS) which is the generalization of classical statistics and applied under uncertainty environment. We will discuss the application and advantage of the neutrosophic Hotelling T-squared statistic with the aid of data. From the comparison, we will conclude that the proposed statistic is more adequate and effective in uncertainty.

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Statistical analysis of classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053420 ◽

1966 ◽

Vol 24 ◽

pp. 188-189

Author(s):

T. J. Deeming

Keyword(s):

Multivariate Analysis ◽

Statistical Analysis ◽

Classification Scheme ◽

Analytical Procedure ◽

Narrow Band ◽

Scientific Research ◽

Maximum Amount ◽

Amount Of Information

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

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