IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i9p2568-2578.html
   My bibliography  Save this article

Estimation of a flexible simple linear model for interval data based on set arithmetic

Author

Listed:
  • Blanco-Fernández, Angela
  • Corral, Norberto
  • González-Rodríguez, Gil

Abstract

The estimation of a simple linear regression model when both the independent and dependent variable are interval valued is addressed. The regression model is defined by using the interval arithmetic, it considers the possibility of interval-valued disturbances, and it is less restrictive than existing models. After the theoretical formalization, the least-squares (LS) estimation of the linear model with respect to a suitable distance in the space of intervals is developed. The LS approach leads to a constrained minimization problem that is solved analytically. The strong consistency of the obtained estimators is proven. The estimation procedure is reinforced by a real-life application and some simulation studies.

Suggested Citation

  • Blanco-Fernández, Angela & Corral, Norberto & González-Rodríguez, Gil, 2011. "Estimation of a flexible simple linear model for interval data based on set arithmetic," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2568-2578, September.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2568-2578
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311000843
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ham, John & Hsiao, Cheng, 1984. "Two-stage estimation of structural labor supply parameters using interval data from the 1971 canadian census," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 133-158.
    2. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    3. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 71(3), pages 905-932, May.
    4. Giordani, Paolo & Kiers, Henk A.L., 2006. "A comparison of three methods for principal component analysis of fuzzy interval data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 379-397, November.
    5. Chesher, Andrew & Irish, Margaret, 1987. "Residual analysis in the grouped and censored normal linear model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 33-61.
    6. Lima Neto, Eufrasio de A. & de Carvalho, Francisco de A.T., 2008. "Centre and Range method for fitting a linear regression model to symbolic interval data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1500-1515, January.
    7. Gil, Maria Angeles & Gonzalez-Rodriguez, Gil & Colubi, Ana & Montenegro, Manuel, 2007. "Testing linear independence in linear models with interval-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3002-3015, March.
    8. Rivero, Carlos & Valdes, Teofilo, 2008. "An algorithm for robust linear estimation with grouped data," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 255-271, December.
    9. Zhang, Xinyan & Sun, Jianguo, 2010. "Regression analysis of clustered interval-censored failure time data with informative cluster size," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1817-1823, July.
    10. Lima Neto, Eufrásio de A. & de Carvalho, Francisco de A.T., 2010. "Constrained linear regression models for symbolic interval-valued variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 333-347, February.
    11. Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Paula, Gilberto A. & Barreto, Mauricio L., 2011. "Regression models for grouped survival data: Estimation and sensitivity analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 993-1007, February.
    12. M. Gil & M. López-García & M. Lubiano & Manuel Montenegro, 2001. "Regression and correlation analyses of a linear relation between random intervals," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 183-201, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Paolo Giordani, 2015. "Lasso-constrained regression analysis for interval-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(1), pages 5-19, March.
    2. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    3. Eufr�sio de A. Lima Neto & Ulisses U. dos Anjos, 2015. "Regression model for interval-valued variables based on copulas," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 2010-2029, September.
    4. Henning Fischer & Marta García-Bárzana & Peter Tillmann & Peter Winker, 2014. "Evaluating FOMC forecast ranges: an interval data approach," Empirical Economics, Springer, vol. 47(1), pages 365-388, August.
    5. Angela Blanco-Fernández & Peter Winker, 2016. "Data generation processes and statistical management of interval data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 475-494, October.
    6. Yan Sun & Guanghua Lian & Zudi Lu & Jennifer Loveland & Isaac Blackhurst, 2020. "Modeling the Variance of Return Intervals Toward Volatility Prediction," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 492-519, July.
    7. Hao, Peng & Guo, Junpeng, 2017. "Constrained center and range joint model for interval-valued symbolic data regression," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 106-138.
    8. Yoichi Tsuchiya, 2021. "The value added of the Bank of Japan's range forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 817-833, August.
    9. Dias, Sónia & Brito, Paula, 2017. "Off the beaten track: A new linear model for interval data," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1118-1130.
    10. Marta García-Bárzana & Ana Belén Ramos-Guajardo & Ana Colubi & Erricos J. Kontoghiorghes, 2020. "Multiple linear regression models for random intervals: a set arithmetic approach," Computational Statistics, Springer, vol. 35(2), pages 755-773, June.
    11. Henning Fischer & Ángela Blanco‐FERNÁndez & Peter Winker, 2016. "Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(2), pages 113-146, March.
    12. Wang, Xun & Zhang, Zhongzhan & Li, Shoumei, 2016. "Set-valued and interval-valued stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 208-223.
    13. Jian Li & Ping Qing & Wuyang Hu & Minglai Li, 2022. "Contract farming, community effect, and farmer valuation of biofortified crop varieties in China: The case of high‐zinc wheat," Review of Development Economics, Wiley Blackwell, vol. 26(2), pages 1035-1055, May.
    14. Wenhua Li & Junpeng Guo & Ying Chen & Minglu Wang, 2016. "A New Representation of Interval Symbolic Data and Its Application in Dynamic Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 149-165, April.
    15. Wei Yang & Ai Han & Yongmiao Hong & Shouyang Wang, 2016. "Analysis of crisis impact on crude oil prices: a new approach with interval time series modelling," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1917-1928, December.
    16. Ana Belén Ramos-Guajardo, 2022. "A hierarchical clustering method for random intervals based on a similarity measure," Computational Statistics, Springer, vol. 37(1), pages 229-261, March.
    17. Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2016. "An exploratory data analysis in scale-space for interval-valued data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2643-2660, October.
    18. Ai Han & Yanan He & Yongmiao Hong & Shouyang Wang, 2013. "Forecasting Interval-valued Crude Oil Prices via Autoregressive Conditional Interval Models," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yan Sun & Guanghua Lian & Zudi Lu & Jennifer Loveland & Isaac Blackhurst, 2020. "Modeling the Variance of Return Intervals Toward Volatility Prediction," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 492-519, July.
    2. Karel Hron & Paula Brito & Peter Filzmoser, 2017. "Exploratory data analysis for interval compositional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 223-241, June.
    3. Giulia Bettin & Riccardo Lucchetti, 2012. "Interval regression models with endogenous explanatory variables," Empirical Economics, Springer, vol. 43(2), pages 475-498, October.
    4. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    5. Angela Blanco-Fernández & Peter Winker, 2016. "Data generation processes and statistical management of interval data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 475-494, October.
    6. Henning Fischer & Ángela Blanco‐FERNÁndez & Peter Winker, 2016. "Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(2), pages 113-146, March.
    7. Gloria Gonzalez-Rivera & Javier Arroyo & Carlos Mate, 2011. "Forecasting with Interval and Histogram Data. Some Financial Applications," Working Papers 201438, University of California at Riverside, Department of Economics.
    8. Eufr�sio de A. Lima Neto & Ulisses U. dos Anjos, 2015. "Regression model for interval-valued variables based on copulas," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 2010-2029, September.
    9. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    11. Sun, Yuying & Han, Ai & Hong, Yongmiao & Wang, Shouyang, 2018. "Threshold autoregressive models for interval-valued time series data," Journal of Econometrics, Elsevier, vol. 206(2), pages 414-446.
    12. Paolo Giordani, 2015. "Lasso-constrained regression analysis for interval-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(1), pages 5-19, March.
    13. Sun, Yuying & Zhang, Xinyu & Wan, Alan T.K. & Wang, Shouyang, 2022. "Model averaging for interval-valued data," European Journal of Operational Research, Elsevier, vol. 301(2), pages 772-784.
    14. Maia, André Luis Santiago & de Carvalho, Francisco de A.T., 2011. "Holt’s exponential smoothing and neural network models for forecasting interval-valued time series," International Journal of Forecasting, Elsevier, vol. 27(3), pages 740-759.
    15. Lin, Wei & González-Rivera, Gloria, 2016. "Interval-valued time series models: Estimation based on order statistics exploring the Agriculture Marketing Service data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 694-711.
    16. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957, arXiv.org.
    18. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    19. Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2016. "An exploratory data analysis in scale-space for interval-valued data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2643-2660, October.
    20. Antonio Calcagnì & Luigi Lombardi & Lorenzo Avanzi & Eduardo Pascali, 2020. "Multiple mediation analysis for interval-valued data," Statistical Papers, Springer, vol. 61(1), pages 347-369, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2568-2578. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.