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Least absolute deviations estimation for the censored regression model
 Journal of Econometrics
, 1984
"... This paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression (or censored ‘Tobit’) model. The proposed estimator is a generalization of least absolute deviations estimation for the standard linear model, and, unlike estimation methods based on the ..."
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Cited by 277 (6 self)
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This paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression (or censored ‘Tobit’) model. The proposed estimator is a generalization of least absolute deviations estimation for the standard linear model, and, unlike estimation methods based
Analysis of least absolute deviation
"... The least absolute deviation or L1 method is a widely known alternative to the classical least squares or L2 method for statistical analysis of linear regression models. Instead of minimizing the sum of squared errors, it minimizes the sum of absolute values of errors. Despite its long history and m ..."
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Cited by 4 (1 self)
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The least absolute deviation or L1 method is a widely known alternative to the classical least squares or L2 method for statistical analysis of linear regression models. Instead of minimizing the sum of squared errors, it minimizes the sum of absolute values of errors. Despite its long history
Estimation Noise in Portfolio Optimization with Absolute Deviation
, 2004
"... Portfolio selection has a central role in finance theory and practical applications. The classical approach uses the standard deviation (variance) as risk measure, while several other alternatives have also been introduced in the literature. Due to its computational advantages, portfolio optimizat ..."
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optimization based on absolute deviation looks particularly interesting and it is widely used in practice. For the practical implementation of any variant, however, one needs to estimate the parameters from finite return series, which inevitably introduces measurement noise that in turn affects the portfolio
Fuzzy linear regression based on least absolute deviations
 Iranian J. fuzzy system
, 2012
"... Abstract. This study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which can ..."
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Cited by 2 (0 self)
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Abstract. This study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which
Bahadur Representations for the Median Absolute Deviation and Its Modifications
, 2009
"... The median absolute deviation about the median (MAD) is an important univariate spread measure having wide appeal due to its highly robust sample version. A powerful tool in treating the asymptotics of a statistic is a linearization, i.e., a Bahadur representation. Here we establish both strong and ..."
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Cited by 2 (1 self)
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The median absolute deviation about the median (MAD) is an important univariate spread measure having wide appeal due to its highly robust sample version. A powerful tool in treating the asymptotics of a statistic is a linearization, i.e., a Bahadur representation. Here we establish both strong
2007b). Tuning parameter selectors for the smoothly clipped absolute deviation method
 Biometrika
"... The penalised least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method. It not only automatically and consistently selects the important variables, but also produces estimators which are ..."
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Cited by 71 (9 self)
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The penalised least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method. It not only automatically and consistently selects the important variables, but also produces estimators which
Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution
"... Abstract: Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA). T ..."
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Abstract: Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA
Instrumental Variable Estimation Based on Mean Absolute Deviation
, 2001
"... this paper. 2 An estimator based on this approach can be defined as the maximizer of the sample analogue of Q. We can form various estimators by taking various dispersion measures in Q. A leading example of the dispersion measure is the standard deviation. The function Q with the standard deviation ..."
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Cited by 5 (3 self)
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this paper. 2 An estimator based on this approach can be defined as the maximizer of the sample analogue of Q. We can form various estimators by taking various dispersion measures in Q. A leading example of the dispersion measure is the standard deviation. The function Q with the standard deviation
Printed in Great Britain Analysis of least absolute deviation
"... We develop a unified L1based analysisofvariancetype method for testing linear hypotheses. Like the classical L2based analysis of variance, the method is coordinatefree in the sense that it is invariant under any linear transformation of the covariates or regression parameters. Moreover, it all ..."
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We develop a unified L1based analysisofvariancetype method for testing linear hypotheses. Like the classical L2based analysis of variance, the method is coordinatefree in the sense that it is invariant under any linear transformation of the covariates or regression parameters. Moreover, it allows singular design matrices and heterogeneous error terms. A simple approximation using stochastic perturbation is proposed to obtain cutoff values for the resulting test statistics. Both test statistics and distributional approximations can be computed using standard linear programming. An asymptotic theory is derived for the method. Special cases of one and multiway analysis of variance and analysis of covariance models are worked out in detail. The main results of this paper can be extended to general quantile regression. Extensive simulations show that the method works well in practical settings. The method is also applied to a dataset from General Social Surveys.
Mean absolute deviation portfolio optimization model and its application to Tokyo Stock Market
 Management Science
, 1991
"... Abstract We will propose a branch and bound algorithm for solving, a portfolio optimization model under nonconvex transaction costs. It is well known that the unit transaction cost is larger when the amount of transaction is small while it remains stable up to a certain point and then increases due ..."
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Cited by 182 (2 self)
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aside due to its computational difficulty. In fact, there are only a few studies which treated nonconvex costs in a rigorous manner. In this paper, we will propose a branch and bound algorithm for solving a meanabsolute deviation portfolio optimization model assuming that the cost function is concave
Results 1  10
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