Estimating the Index of Increase via Balancing Deterministic and Random Data

Chen, Lingzhi; Davydov, Youri; Gribkova, Nadezhda; Zitikis, Ričardas

doi:10.3103/s1066530718020011

Cited by 14 publications

(11 citation statements)

References 32 publications

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“…one of the most important conditions for their quality education [7], which is a weighty argument for using tasks of all existing types in teaching stochastics. Note that, at present, the role of stochastics in school and after-school education in mathematics is only increasing, which is confirmed by contemporary publications [6]. Therefore, studying the essence of stochastic problems and their significance in the mathematical education is relevant and timely.…”

Section: Resultsmentioning

confidence: 88%

Specific Diversity of School Stochastic Problems

Aksenov¹,

Selutin²

2018

Proceedings of the International Conference on the Development of Education in Russia and the CIS Member States (ICEDER 2018)

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：In the modern theory and methodology of teaching mathematics, the theoretical basis for the application of problems in the learning process is developing. In particular, the traditional view on the species composition of tasks is also changing. Their new species are proposed. A few years ago, elements of the theory of probability and mathematical statistics were strongly included in the school course of mathematics, a significant part in the study of which consists of stochastic problems. These tasks should be not only an integral part of the stochastic educational material, but also get a full description in the general theory of school math problems. In particular, this article shows that stochastic problems fully satisfy the species diversity of problems in a school mathematics course.

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Section: Resultsmentioning

confidence: 88%

Specific Diversity of School Stochastic Problems

Aksenov¹,

Selutin²

2018

Proceedings of the International Conference on the Development of Education in Russia and the CIS Member States (ICEDER 2018)

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“…as closely as desired by choosing a sufficiently large n. Namely, we have the statement I 0 n (g) → I(g) when n → ∞, (1.4) whose numerical explorations can be found in Chen and Zitikis (2017), and Chen et al (2018).…”

Section: Introductionmentioning

confidence: 98%

“…In this case, the index I 0 n (g) turns into the random index I ε n (g) defined by with P → denoting convergence in probability. To circumvent the issue, Chen et al (2018) have proposed a method based on averaging a certain number of outputs to mitigate the influence of random errors on the non-contaminated outputs g(t i,n ). In the current paper we further advance the understanding of this research area.…”

Section: Introductionmentioning

confidence: 99%

Assessing Transfer Functions in Control Systems

Gribkova

Zitikis

2019

J Stat Theory Pract

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When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be even monotonic. In addition, they may have structural breaks and other abberations that require monitoring and quantification to aid decision making. The present paper develops such a methodology, which is based on an index of increase that naturally arises as the solution to an optimization problem. We show theoretically and illustrate numerically that the empirical counterpart of the index needs to be used with great care and indepth knowledge of the problem at hand in order to achieve desired large-sample properties, such as consistency.

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“…From the conceptual point of view, broadly speaking, two scenarios arise. First, if it is suspected that the outputs are affected, then testing whether or not this is indeed the case falls, in a sense, within the context of regression analysis, though additional statistical challenges arise (e.g., Perote and Perote-Peña 2004;Perote et al 2015.;Chen et al 2018;Gribkova and Zitikis 2018). The second scenario, which is the main topic of the present paper, deals with the case when it is the inputs that are possibly affected by risks.…”

Section: Introductionmentioning

confidence: 99%

“…where δ is an exogenous risk, sometimes called input-reading error, that directly affects the input X and thus, indirectly, the output variable as well. We note that Chen et al (2018) consider model (1) with deterministic inputs, like those to be defined in Equation 3below. Gribkova and Zitikis (2018) explore risk-free model (1), which can be viewed as the "null hypothesis" in the context of the present paper.…”

Section: Introductionmentioning

confidence: 99%

A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model

Gribkova

Zitikis

2018

Risks

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Background, or systematic, risks are integral parts of many systems and models in insurance and finance. These risks can, for example, be economic in nature, or they can carry more technical connotations, such as errors or intrusions, which could be intentional or unintentional. A most natural question arises from the practical point of view: is the given system really affected by these risks? In this paper we offer an algorithm for answering this question, given input-output data and appropriately constructed statistics, which rely on the order statistics of inputs and the concomitants of outputs. Even though the idea is rooted in complex statistical and probabilistic considerations, the algorithm is easy to implement and use in practice, as illustrated using simulated data.

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Estimating the Index of Increase via Balancing Deterministic and Random Data

Cited by 14 publications

References 32 publications

Specific Diversity of School Stochastic Problems

Specific Diversity of School Stochastic Problems

Assessing Transfer Functions in Control Systems

A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model

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