Riesz estimators

Aliprantis, Charalambos D.; Harris, David; Tourky, Rabee

doi:10.1016/j.jeconom.2005.11.005

Cited by 4 publications

(7 citation statements)

References 27 publications

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“…The background of the paper [1] about Riesz estimators is [2]. In the present paper, we determine the projection operator, which is necessary to fit the Riesz estimator regression.…”

Section: Motivationmentioning

confidence: 99%

Non-Parametric Regression and Riesz Estimators

Kountzakis

Tsachouridou-Papadatou

2023

Axioms

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In this paper, we consider a non-parametric regression model relying on Riesz estimators. This linear regression model is similar to the usual linear regression model since they both rely on projection operators. We indicate that Riesz estimator regression relies on the positive basis elements of the finite-dimensional sub-lattice generated by the rows of some design matrix. A strong motivation for using the Riesz estimator model is that the data of explanatory variables may come from categorical variables. Calculations related to Riesz estimator regression are very easy since they arise from the measurability in finite-dimensional probability spaces. Moreover, we show that the fitted model of Riesz estimators is an ordinary least squares model. Any vector of some Euclidean space is supposed to be a rendom variable under the objective probability values, being used in expected utility theory and its applications. Finally, the reader may notice that goodness-of-fit measures are similar to those defined for the usual linear regression. Due to the fact that this model is non-parametric, it may include samples relevant to finance and actuarial science variables.

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“…The background of the paper [1] about Riesz estimators is [2]. In the present paper, we determine the projection operator, which is necessary to fit the Riesz estimator regression.…”

Section: Motivationmentioning

confidence: 99%

Non-Parametric Regression and Riesz Estimators

Kountzakis

Tsachouridou-Papadatou

2023

Axioms

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“…The objective of this section is to present a brief discussion of the basic mathematical background in Riesz space theory needed for the present work and to study the Riesz estimators in Aliprantis, Harris, and Tourky (2006). The mathematics behind the theory of Riesz estimators are those of Riesz spaces and Banach lattices.…”

Section: Riesz Spaces and Banach Latticesmentioning

confidence: 99%

“…, f p }, we can enumerate through a finite combination of Max-Min operations the finite family of continuous piecewise linear functions generated by the set F . This third property is exploited in Aliprantis, Harris, and Tourky (2006).…”

Section: ( )mentioning

confidence: 99%

“…The purpose of this paper is twofold: first, to study the function space of continuous piecewise linear functions in the space of continuous functions; and second, to provide the necessary mathematical background to our paper, Aliprantis, Harris, and Tourky (2006), which studies statistical estimators that we dub Riesz estimators. In that paper, we envisage a situation in which we seek to estimate a random variable Y based on some observed random vector X = (X 1 , X 2 , .…”

Section: Introductionmentioning

confidence: 99%

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Continuous Piecewise Linear Functions

2005

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The paper studies the function space of continuous piecewise linear functions in the space of continuous functions on the m-dimensional Euclidean space. It also studies the special case of one dimensional continuous piecewise linear functions. The study is based on the theory of Riesz spaces that has many applications in economics. The work also provides the mathematical background to its sister paper Aliprantis, Harris, and Tourky (2006), in which we estimate multivariate continuous piecewise linear regressions by means of Riesz estimators, that is, by estimators of the the Boolean formwhere X = (X 1 , X 2 , . . . , X m ) is some random vector, {E j } j ∈J is a finite family of finite sets.

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Piecewise affine functions on subsets of R m were studied in [11,7,8,9]. In this paper we study a more general concept of a locally piecewise affine function.

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confidence: 99%

Locally piecewise affine functions and their order structure

Adeeb

Troitsky

2016

Positivity

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Abstract. Piecewise affine functions on subsets of R m were studied in [11,7,8,9]. In this paper we study a more general concept of a locally piecewise affine function. We characterize locally piecewise affine functions in terms of components and regions. We prove that a positive function is locally piecewise affine iff it is the supremum of a locally finite sequence of piecewise affine functions. We prove that locally piecewise affine functions are uniformly dense in C(R m ), while piecewise affine functions are sequentially order dense in C(R m ). This paper is partially based on [3]. Piecewise affine functionsWe start with a brief overview of affine and piecewise affine functions; we refer the reader to [11,7] and [9, Chapter 7] for details.Fix m ∈ N. By an affine function we mean a function f : R m → R of form f (x) = v, x +b for some v ∈ R m and b ∈ R. Its kernel {f = 0} is an affine hyperplane in R m . It is easy to see that any two affine functions which agree on a non-empty open set are equal. We write A for the vector space of all affine functions on R m . Clearly, A is a subspace of C(R m ), the space of all real-valued continuous functions on R m .Let Ω be a convex closed subset of R m with non-empty interior. Following [9], we call such a set a solid domain. A continuous function f : Ω → R is called piecewise affine if it agrees with finitely many

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Riesz estimators

Cited by 4 publications

References 27 publications

Non-Parametric Regression and Riesz Estimators

Non-Parametric Regression and Riesz Estimators

Continuous Piecewise Linear Functions

Locally piecewise affine functions and their order structure

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