Confidence sets in a linear regression model for interval data

Blanco-Fernández, Angela; Colubi, Ana; González‐Rodríguez, Gil

doi:10.1016/j.jspi.2011.09.017

Cited by 24 publications

(11 citation statements)

References 15 publications

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“…In some cases, for instance in statistics of particles (see Stoyan & Stoyan 1994) and in partially identified models in econometrics (see Molchanov & Molinari 2018), the data consist of convex sets, which is the setting of this paper. In the simplest one-dimensional case, observations are given by intervals, for example, data on daily price ranges in finance, imprecise measurements, salary brackets in econometrics, to name a few sources, see Beresteanu & Molinari (2008), Blanco-Fernández, Colubi & González-Rodríguez (2012), Blanco-Fernández, Corral & González-Rodríguez (2011), Manski & Tamer (2002) and Yang et al (2016) and references therein. A substantial body of these works focuses on regression with interval responses and sometimes also interval regressors.…”

Section: Introductionmentioning

confidence: 99%

Depth and outliers for samples of sets and random sets distributions

Cascos

Molchanov

2021

Aus NZ J of Statistics

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We suggest several constructions suitable to define the depth of set-valued observations with respect to a sample of convex sets or with respect to the distribution of a random closed convex set. With the concept of a depth, it is possible to determine if a given convex set should be regarded an outlier with respect to a sample of convex closed sets. Some of our constructions are motivated by the known concepts of half-space depth and band depth for function-valued data. A novel construction derives the depth from a family of non-linear expectations of random sets. Furthermore, we address the role of positions of sets for evaluation of their depth. Two case studies concern interval regression for Greek wine data and detection of outliers in a sample of particles.

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Section: Introductionmentioning

confidence: 99%

Depth and outliers for samples of sets and random sets distributions

Cascos

Molchanov

2021

Aus NZ J of Statistics

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“…() and Blanco‐Fernández et al. () develop inferential methods for these models within the realm of random set theory. Because of their versatility and their virtues of making full use of the whole information given by the intervals in a coherent way, we will use the model of Blanco‐Fernández et al.…”

Section: Motivation and Related Workmentioning

confidence: 99%

“…In addition, an interval prediction that is always well-defined can be directly obtained through interval arithmetic in the linear model setup involving interval-valued variables. Gil et al (2007) and Blanco-Fernández et al (2012) develop inferential methods for these models within the realm of random set theory. Because of their versatility and their virtues of making full use of the whole information given by the intervals in a coherent way, we will use the model of Blanco-Fernández et al (2011) and an even more flexible model recently introduced in Blanco-Fernández et al (2015) in our empirical analysis.…”

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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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“…They proposed a least square estimation of model coefficients under the d 2 metric of intervals. Blanco-Fernandez et al [5] studied strong consistency and asymptotic distribution of the least square estimate. Gonzalez-Rivera and Lin [14] introduced a constrained condition for the regression models of upper and lower bounds of intervals, which guarantees the nature order of interval in the forecast problem.…”

Section: Introductionmentioning

confidence: 99%

Set-valued and interval-valued stationary time series

Wang

Zhang

2016

Journal of Multivariate Analysis

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International audienceStationarity is a key tool in classical time series. In order to analyze the set-valued time series, it must be extended to the set-valued case. In this paper, stationary set-valued time series is defined via DpDp metric of set-valued random variables. Then, estimation methods of expectation and auto-covariance function of stationary set-valued time series are proposed. Unbiasedness and consistency of the expectation estimator and asymptotic unbiasedness of the auto-covariance function estimator are justified. After that, a special case of the set-valued time series, known as interval-valued time series, is considered. Two forecast methods of the stationary interval-valued time series are explicitly presented. Furthermore, the interval-valued time series is contextualized in the Box–Jenkins framework: an interval-valued autoregression model, along with its parameter estimation method, is introduced. Finally, experiments on both simulated and real data are presented to justify the efficiency of the parameters estimation method and the availability of the proposed model

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Confidence sets in a linear regression model for interval data

Cited by 24 publications

References 15 publications

Depth and outliers for samples of sets and random sets distributions

Depth and outliers for samples of sets and random sets distributions

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

Set-valued and interval-valued stationary time series

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