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Fuzzy linear regression based on least absolutes deviations
2012Summary: This study is an investigation of fuzzy linear regression models for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such models is developed by introducing and applying a new metric on the space of fuzzy numbers.
Taheri, S. M., Kelkinnama, M.
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Least Absolute Deviation Estimation for Regression with ARMA Errors
Journal of Theoretical Probability, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davis, Richard A. +1 more
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A descent method for least absolute deviation lasso problems
Optimization Letters, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yue Shi, Zhiguo Feng, Ka Fai Cedric Yiu
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Least absolute deviation estimates in stable autoregression
1977We consider an L_1 analogue of the least squares estimator for the parameters of a stationary, finite order autoregressive scheme based on stable random variables. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. Finally, the sampling properties are compared to those
Gross, S., Steiger, William L.
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SEQUENTIAL EXTRACTION OF FUZZY REGRESSION MODELS: LEAST SQUARES AND LEAST ABSOLUTE DEVIATIONS
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2011Fuzzy c-regression models are known to be useful in real applications, but there are two drawbacks: strong dependency on the predefined number of clusters and sensitiveness against outliers or noises. To avoid these drawbacks, we propose sequential fuzzy regression models based on least absolute deviations which we call SFCRMLAD.
Tang, Hengjin, Miyamoto, Sadaaki
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Linear fuzzy clustering based on least absolute deviations
Proceedings of the 41st SICE Annual Conference. SICE 2002., 2003This paper proposes a technique of linear fuzzy clustering based on least absolute deviations. The least absolute deviations adopted in the method provide robust clustering results that are free from the influence of outliers. The simplicity of the proposed objective function makes it possible to handle missing values by simply ignoring only the ...
K. Honda, N. Togo, H. Ichihashi
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Least Absolute Deviation Estimation of a Shift
Econometric Theory, 1995This paper develops the asymptotic theory for least absolute deviation estimation of a shift in linear regressions. Rates of convergence and asymptotic distributions for the estimated regression parameters and the estimated shift point are derived.
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Asymptotics for Least Absolute Deviation Regression Estimators
Econometric Theory, 1991The LAD estimator of the vector parameter in a linear regression is defined by minimizing the sum of the absolute values of the residuals. This paper provides a direct proof of asymptotic normality for the LAD estimator. The main theorem assumes deterministic carriers.
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The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators
Econometrica, 1983In a recent paper \textit{T. Amemiya} [ibid. 50, 689-711 (1982; Zbl 0493.62098)] introduced a class of estimators, termed two-stage least absolute deviations (2SLAD) estimators, for the parameters of a structural equation in a simultaneous equations model; the estimators are defined to minimize a sum of absolute values of residual terms which depend ...
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