Multivariate binary discrimination by the kernel method

Aitchison, J.; Aitken, Colin

doi:10.1093/biomet/63.3.413

Cited by 478 publications

(267 citation statements)

References 16 publications

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“…Such linearizing techniques still require the choice of a kernel function and the determination of a bandwidth. In this research, we used the following kernel function proposed by [33] for the environmental variables (which are "unordered" categorical variables) instead of K ppz´Z i q {hq (which is used for continuous variables):…”

Section: Conditional and Unconditional Efficiency Scoresmentioning

confidence: 99%

Computing Economies of Scope Using Robust Partial Frontier Nonparametric Methods

Carvalho

Marques

2016

Water

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This paper proposes a methodology to examine economies of scope using the recent order-α nonparametric method. It allows us to investigate economies of scope by comparing the efficient order-α frontiers of firms that produce two or more goods with the efficient order-α frontiers of firms that produce only one good. To accomplish this, and because the order-α frontiers are irregular, we suggest to linearize them by the DEA estimator. The proposed methodology uses partial frontier nonparametric methods that are more robust than the traditional full frontier methods. By using a sample of 67 Portuguese water utilities for the period 2002-2008 and, also, a simulated sample, we prove the usefulness of the approach adopted and show that if only the full frontier methods were used, they would lead to different results. We found evidence of economies of scope in the provision of water supply and wastewater services simultaneously by water utilities in Portugal.

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Section: Conditional and Unconditional Efficiency Scoresmentioning

confidence: 99%

Computing Economies of Scope Using Robust Partial Frontier Nonparametric Methods

Carvalho

Marques

2016

Water

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“…The two λ values, λ = 1 and λ = 0.5, lead to two extreme forms of density estimations: uniform distribution and relative frequencies of appearance of the given discrete data, respectively. Thus these two values of λ are ignored-that is, 0.5 ≤ λ ≤ 1 becomes 0.5 < λ < 1 (see Aitchison & Aitken, 1976).…”

Section: The Aa-kernel and Positive Definite Kernel Function (Pdkf)mentioning

confidence: 99%

“…In a seminal paper Aitchison and Aitken (1976) proposed a kernel function defined on discrete descriptor/input spaces. These authors introduced this kernel function, which is henceforth referred to as the AA-kernel, for estimating density functions in binary input spaces (Aitchison & Aitken, 1976).…”

Section: Introductionmentioning

confidence: 99%

“…These authors introduced this kernel function, which is henceforth referred to as the AA-kernel, for estimating density functions in binary input spaces (Aitchison & Aitken, 1976). Its simple non-parametric nature together with its consistency properties have made the AA-kernel a useful tool for generating discriminant functions.…”

Section: Introductionmentioning

confidence: 99%

“…The AA-kernel, which is defined on a discrete metric space, is not a Gaussian function in this space, but it can be viewed as the counterpart of a Gaussian kernel function defined on an Euclidean ("standard") metric space (Aitchison & Aitken, 1976). It is well documented that a Gaussian kernel function is PDKF on standard metric spaces (Berg, 1998), but the same cannot be said for the AA-kernel on its discrete metric space.…”

Section: Introductionmentioning

confidence: 99%

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The Aitchison and Aitken Kernel Function Revisited

Mussa¹

2013

JMR

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Over three decades ago Aitchison and Aitken proposed a novel kernel function for estimating the density functions of underlying distributions in discrete input spaces. To the best of our knowledge, it has not been shown whether this kernel function is positive definite (i.e., a reproducing kernel function) on these spaces. Its positive definiteness would have enriched and enlarged its applicability domain: a positive definite kernel function has an associated Reproducing Kernel Hilbert Space, a framework on which a variety of powerful statistical and machine learning schemes can be developed.This paper aims to demonstrate that Aitchison and Aitken's kernel function is indeed positive definite on discrete metric spaces. We also touch on possible applications of the proposed theorem.

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Binary Data, Multivariate

Johnson¹

2004

Encyclopedia of Statistical Sciences

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Multivariate binary discrimination by the kernel method

Cited by 478 publications

References 16 publications

Computing Economies of Scope Using Robust Partial Frontier Nonparametric Methods

Computing Economies of Scope Using Robust Partial Frontier Nonparametric Methods

The Aitchison and Aitken Kernel Function Revisited

Binary Data, Multivariate

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