A robust method for linear regression of symbolic interval data

Domingues, Marco A. O.; Souza, Renata M. C. R. de; Cysneiros, Francisco José A.

doi:10.1016/j.patrec.2010.06.008

Cited by 53 publications

(11 citation statements)

References 11 publications

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“…Furthermore, since the width of the resulting interval predictions is found to be too small throughout, it is adjusted upwards by the authors in a rather ad hoc fashion to match the average width of the intervals in the sample. 11 Domingues et al (2010), following the 'center-and-range' method, make independent probabilistic assumptions for two basic interval characteristics. In an attempt to remedy the robustness problems of using OLS when (midpoint) outliers are present, they assume the Student-t distribution for the midpoints' errors and the normal distribution for the errors in the equation of the interval ranges when estimating each model's parameters by maximum likelihood.…”

Section: Model Specificationsmentioning

confidence: 99%

Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

Fischer

Blanco-Fernández

Winker

2015

Journal of Forecasting

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We study the performance of recently developed linear regression models for interval data when it comes to forecasting the uncertainty surrounding future stock returns. These interval data models use easy-to-compute daily return intervals during the modeling, estimation and forecasting stage. They have to stand up to comparable point-data models of the well-known capital asset pricing model type-which employ single daily returns based on successive closing prices and might allow for GARCH effects-in a comprehensive out-of-sample forecasting competition. The latter comprises roughly 1000 daily observations on all 30 stocks that constitute the DAX, Germany's main stock index, for a period covering both the calm market phase before and the more turbulent times during the recent financial crisis. The interval data models clearly outperform simple random walk benchmarks as well as the point-data competitors in the great majority of cases. This result does not only hold when one-day-ahead forecasts of the conditional variance are considered, but is even more evident when the focus is on forecasting the width or the exact location of the next day's return interval. Regression models based on interval arithmetic thus prove to be a promising alternative to established point-data volatility forecasting tools.

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Section: Model Specificationsmentioning

confidence: 99%

Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

Fischer

Blanco-Fernández

Winker

2015

Journal of Forecasting

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“…In this method, the upper and lower values are regarded as two features, but it ignores the internal distribution of IVD. (3) Midpoint and radius method takes location information into account on the basis of boundary values [7], [8]. Reference [7] used the traditional regression method to generate regression equations for the midpoint and radius respectively, then predicted the upper and lower bounds of IVD with generated equations.…”

Section: Introductionmentioning

confidence: 99%

An Interval-Valued Data Classification Method Based on the Unified Representation Frame

Qi¹,

Guo²,

Artem³

et al. 2020

IEEE Access

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Interval-valued data (IVD) is a kind of data where each feature is an interval. The midpoint and boundary are the two commonly used methods for representing IVD. However, their structure information (such as location, size) may be incomplete because only midpoint or endpoint is adopted which will lead to poor results of data processing. To better depict the structural information of IVD, a unified representation frame (URF) for IVD is proposed. It not only takes into account the size and location information, but the relationship between them as well. This frame can also represent the midpoint and boundary methods in a unified way. Besides, symmetrical uncertainty (SU) is adopted to measure the relationship between features and classes quantitatively, and irrelevant features will be eliminated based on SU. The proposed URF_ SU is applied in some traditional classifiers like LIBSVM, CART Tree and KNN. The experimental results on synthetic and real-world datasets demonstrate that the proposed approach is more effective than other representation methods of IVD in classification tasks. INDEX TERMS Interval-valued data, unified representation frame, symmetrical uncertainty, feature selection.

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“…Where interest in the outcome of an analysis exists at the level of a group, rather than at an individual level, interval-valued data provide a convenient group-level aggregation device (Neto & de Carvalho, 2010;Noirhomme-Fraiture & Brito, 2011). Similarly, aggregation of individual observations within an interval structure allows for some preservation of privacy for the individual (Domingues, de Souza, & Cysneiros, 2010).…”

Section: Introductionmentioning

confidence: 99%

Constructing likelihood functions for interval‐valued random variables

Zhang

Beranger

Sisson

2019

Scandinavian J Statistics

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There is a growing need for flexible methods to analyze interval‐valued data, which can provide efficient data representations for very large data sets. However, the existing descriptive frameworks to achieve this ignore the process by which interval‐valued data are typically constructed, namely, by the aggregation of real‐valued data generated from some underlying process. In this paper, we develop the foundations of likelihood‐based statistical inference for intervals that directly incorporates the underlying data generating procedure into the analysis. That is, it permits the direct fitting of models for the underlying real‐valued data given only the interval‐valued summaries. This generative approach overcomes several problems associated with existing methods, including the rarely satisfied assumption of within‐interval uniformity. The new methods are illustrated by simulated and real data analyses.

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A robust method for linear regression of symbolic interval data

Cited by 53 publications

References 11 publications

Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

An Interval-Valued Data Classification Method Based on the Unified Representation Frame

Constructing likelihood functions for interval‐valued random variables

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