An objective general index for multivariate ordered data

Sei, Tomonari

doi:10.1016/j.jmva.2016.02.005

Cited by 9 publications

(12 citation statements)

References 12 publications

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“…For Gaussian random variables, we obtain the following lemma. We denote the expectation by E. Lemma 1 (Theorem 5 of [33]) Let μ denote the d-dimensional normal distribution with mean zero and covariance matrix S = (S i j ). Then, μ is Stein-type if and only if j S i j = 1 for each i.…”

Section: Definition Of Stein-type Distributions and Transformationsmentioning

confidence: 99%

“…In this section, we briefly describe an application of Stein-type transformations. We first explain a linear rating method of multivariate data according to [33]. Let S be a covariance matrix of an R d -valued random vector x = (x i ).…”

Section: Application To a Rating Problemmentioning

confidence: 99%

“…This property is not attained in general for other methods of weighting. The quantity j w j x j is called the objective general index (OGI) in [33], which reflects the d scores in this sense. In a similar manner, we can define a nonlinear version of the objective general index via Stein-type transformations.…”

Section: Application To a Rating Problemmentioning

confidence: 99%

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Coordinate-wise transformation of probability distributions to achieve a Stein-type identity

Sei

2021

Info. Geo.

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It is shown that for any given multi-dimensional probability distribution with regularity conditions, there exists a unique coordinate-wise transformation such that the transformed distribution satisfies a Stein-type identity. A sufficient condition for the existence is referred to as copositivity of distributions. The proof is based on an energy minimization problem over a totally geodesic subset of the Wasserstein space. The result is considered as an alternative to Sklar’s theorem regarding copulas, and is also interpreted as a generalization of a diagonal scaling theorem. The Stein-type identity is applied to a rating problem of multivariate data. A numerical procedure for piece-wise uniform densities is provided. Some open problems are also discussed.

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Section: Definition Of Stein-type Distributions and Transformationsmentioning

confidence: 99%

Section: Application To a Rating Problemmentioning

confidence: 99%

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Coordinate-wise transformation of probability distributions to achieve a Stein-type identity

Sei

2021

Info. Geo.

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“…Nevertheless, one of the undesirable features of such approaches is that these indices can be negatively correlated with some of the variates. To tackle such shortcomings, Sei (2016) proposed an OGI that is always positively correlated with each of the variates. We apply the notion of OGI under a two-stage framework to study the competitiveness of the regions.…”

Section: A Two-stage Objective General Index Approach To Regional Competitivenessmentioning

confidence: 99%

“…A naive algorithm to obtain the weights is to solve the quadratic equation (1) with respect to w i > 0 given { w j } j ≠ i for each i , and repeat this process until convergence. Refer to Sei (2016) for more details.…”

Section: A Two-stage Objective General Index Approach To Regional Competitivenessmentioning

confidence: 99%

A two-stage OGI approach to compute the regional competitiveness index

Charles

Sei

2019

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Purpose Regional competitiveness refers to the capacity of a region to manage its resources and competencies to increase the well-being of its people. Measuring regional competitiveness is, thus, a major consideration for policymakers, businesses and the academic community in their endeavour to improve the same. This paper aims to demonstrate a novel way to calculate the regional competitiveness index under a two-stage objective general index (OGI) framework. Design/methodology/approach The authors compute the regional competitiveness index under a two-stage OGI framework. In the first stage, they aggregate the sub-factor level information into a factor level index; in the second stage, they use the factor level index to obtain a regional competitiveness index. Findings The authors discuss the properties of the proposed index in detail. They further analyse five periods of regional competitiveness of Peru spanning the period 2008-2015. Among others, the results reveal the existence of the resource curse of the mining regions of Peru. Practical implications The paper is a contribution to the practical measurement of competitiveness. Social implications The calculation of a regional competitiveness index is vital for improving the competitiveness of the countries and for reducing regional inequalities. Originality/value When compared to the existent methods available in the literature, the advantage of the proposed method resides in the fact that the derived index has a positive correlation with the factor-level indices and the factor-level indices have a positive correlation with the sub-factor-level information.

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A Novel Two-Phase Approach to Computing a Regional Social Progress Index

Charles

Gherman

Tsolas

2020

International Series in Operations Research &Amp; Management Science

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In recent decades, concerns have emerged regarding the fact that standard macro-economic statistics (such as gross domestic product) do not provide a sufficiently detailed and accurate picture of societal progress and wellbeing and of people's true quality of life. This has further translated into concerns regarding the design of related public policies and whether these actually have the intended impact in practice. One of the first steps in bridging the gap between wellbeing metrics and policy intervention is the developement of improved wellbeing measures. The calculation of a regional Social Progress Index (SPI) has been on the policymakers' agenda for quite some time, as it is used to assist in the proposal of strategies that would create the conditions for all individuals in a society to reach their full potential, enhancing and sustaining the quality of their lives, while reducing regional inequalities. In this manuscript, we show a novel way to calculate a regional SPI under a two-phase approach. In the first phase, we aggregate the item-level information into subfactor-level indices and the sub-factor-level indices into a factor-level index using an Objective General Index (OGI); in the second phase, we use the factor-level indices to obtain the regional SPI through a pure data envelopment analysis (DEA) approach. We further apply the method developed to analyse a single period of social progress in Peru. The manuscript is a contribution to the practical measurement of social progress.

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An objective general index for multivariate ordered data

Cited by 9 publications

References 12 publications

Coordinate-wise transformation of probability distributions to achieve a Stein-type identity

Coordinate-wise transformation of probability distributions to achieve a Stein-type identity

A two-stage OGI approach to compute the regional competitiveness index

A Novel Two-Phase Approach to Computing a Regional Social Progress Index

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