1983, ISBN 9780817631574, Volume 6., xiv, 349

Book

Biometrika, ISSN 1464-3510, 2007, Volume 94, Issue 3, pp. 553 - 568

The penalized least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method...

Zero | Linear regression | Least squares | Linear models | Parametric models | Modeling | Estimators | Consistent estimators | Oracles | Estimation methods | Least absolute shrinkage and selection operator | Generalized crossvalidation | Smoothly clipped absolute deviation | AIC | BIC | smoothly clipped absolute deviation | MODEL SELECTION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STATISTICS & PROBABILITY | generalized crossvalidation | least absolute shrinkage and selection operator | LIKELIHOOD | Studies | Simulation | Regression analysis | aic | Generalised crossvalidation | bic

Zero | Linear regression | Least squares | Linear models | Parametric models | Modeling | Estimators | Consistent estimators | Oracles | Estimation methods | Least absolute shrinkage and selection operator | Generalized crossvalidation | Smoothly clipped absolute deviation | AIC | BIC | smoothly clipped absolute deviation | MODEL SELECTION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STATISTICS & PROBABILITY | generalized crossvalidation | least absolute shrinkage and selection operator | LIKELIHOOD | Studies | Simulation | Regression analysis | aic | Generalised crossvalidation | bic

Journal Article

Journal of combinatorial optimization, ISSN 1573-2886, 2017, Volume 34, Issue 3, pp. 781 - 797

.... For the univariate case, a robust version of the median is the Least Trimmed Absolute Deviation (LTAD) robust estimator introduced in Tableman...

Convex and Discrete Geometry | Operations Research/Decision Theory | Robust location estimation | Least trimmed absolute deviation | Outlier detection | Linear programming | Mixed integer programming | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COVARIANCE DETERMINANT ESTIMATOR | EQUIVARIANT | Algorithms | Information management | Mathematical optimization | Analysis | Methods

Convex and Discrete Geometry | Operations Research/Decision Theory | Robust location estimation | Least trimmed absolute deviation | Outlier detection | Linear programming | Mixed integer programming | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COVARIANCE DETERMINANT ESTIMATOR | EQUIVARIANT | Algorithms | Information management | Mathematical optimization | Analysis | Methods

Journal Article

1989, Cambridge tracts in mathematics, ISBN 9780521366502, Volume 93, x, 239

This monograph is concerned with the qualitative theory of best L1-approximation from finite-dimensional subspaces. It presents a survey of recent research...

Least absolute deviations (Statistics) | Approximation theory

Least absolute deviations (Statistics) | Approximation theory

Book

The Annals of statistics, ISSN 0090-5364, 2016, Volume 44, Issue 2, pp. 813 - 852

In the period 1991-2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450...

Datasets | Integers | Regression coefficients | Optimal solutions | Statistical properties | Linear regression | Threshing | Correlation coefficients | Least squares | Predictive modeling | Best subset selection | Global optimization | Algorithms | Lasso | Sparse linear regression | Least absolute deviation | Discrete optimization | Mixed integer programming | ℓ0-constrained minimization | l-constrained minimization | SPARSITY | algorithms | lasso | PERSISTENCE | STATISTICS & PROBABILITY | VARIABLE SELECTION | global optimization | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | least absolute deviation | mixed integer programming | discrete optimization | REGRESSION SHRINKAGE | best subset selection | 62J05 | 62J07 | 90C26 | 90C27 | ell_{0}-constrained minimization | 90C11 | 62G35

Datasets | Integers | Regression coefficients | Optimal solutions | Statistical properties | Linear regression | Threshing | Correlation coefficients | Least squares | Predictive modeling | Best subset selection | Global optimization | Algorithms | Lasso | Sparse linear regression | Least absolute deviation | Discrete optimization | Mixed integer programming | ℓ0-constrained minimization | l-constrained minimization | SPARSITY | algorithms | lasso | PERSISTENCE | STATISTICS & PROBABILITY | VARIABLE SELECTION | global optimization | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | least absolute deviation | mixed integer programming | discrete optimization | REGRESSION SHRINKAGE | best subset selection | 62J05 | 62J07 | 90C26 | 90C27 | ell_{0}-constrained minimization | 90C11 | 62G35

Journal Article

Neural Computing and Applications, ISSN 0941-0643, 3/2018, Volume 29, Issue 5, pp. 1455 - 1463

This paper proposes a simplified neural network for generalized least absolute deviation by transforming its optimization conditions into a system of double projection equations...

Computational Biology/Bioinformatics | Stability | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Generalized least absolute deviation | Neural network | Computational Science and Engineering | Probability and Statistics in Computer Science | Convergence | IMAGE-RESTORATION | FINITE-TIME CONVERGENCE | CONVEX-OPTIMIZATION PROBLEMS | SIGNALS | L-1 ESTIMATION PROBLEMS | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VARIATIONAL-INEQUALITIES | DELAY ESTIMATION | LINEAR CONSTRAINTS | SYLVESTER EQUATION | Information science | Neurons | Neural networks | Analysis

Computational Biology/Bioinformatics | Stability | Computer Science | Data Mining and Knowledge Discovery | Image Processing and Computer Vision | Artificial Intelligence (incl. Robotics) | Generalized least absolute deviation | Neural network | Computational Science and Engineering | Probability and Statistics in Computer Science | Convergence | IMAGE-RESTORATION | FINITE-TIME CONVERGENCE | CONVEX-OPTIMIZATION PROBLEMS | SIGNALS | L-1 ESTIMATION PROBLEMS | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VARIATIONAL-INEQUALITIES | DELAY ESTIMATION | LINEAR CONSTRAINTS | SYLVESTER EQUATION | Information science | Neurons | Neural networks | Analysis

Journal Article

Statistical Papers, ISSN 0932-5026, 5/2011, Volume 52, Issue 2, pp. 371 - 390

This paper studies the asymptotic properties of a smoothed least absolute deviations estimator in a nonlinear parametric model with multiple change-points occurring at the unknown times...

Monte Carlo simulations | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 62F40 | SLAD estimator | Economic Theory | Probability Theory and Stochastic Processes | Change-point | 62F12 | Parametric nonlinear model | Statistics | 60J02 | MAXIMUM-LIKELIHOOD ESTIMATOR | REGRESSION | NUMBER | STATISTICS & PROBABILITY | ASYMPTOTICS | Monte Carlo method | Analysis | Models | Studies | Nonlinear equations | Mathematical models | Monte Carlo simulation | Monte Carlo methods | Approximation | Computer simulation | Least squares method | Nonlinearity | Deviation | Estimators | Statistics Theory | Mathematics

Monte Carlo simulations | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 62F40 | SLAD estimator | Economic Theory | Probability Theory and Stochastic Processes | Change-point | 62F12 | Parametric nonlinear model | Statistics | 60J02 | MAXIMUM-LIKELIHOOD ESTIMATOR | REGRESSION | NUMBER | STATISTICS & PROBABILITY | ASYMPTOTICS | Monte Carlo method | Analysis | Models | Studies | Nonlinear equations | Mathematical models | Monte Carlo simulation | Monte Carlo methods | Approximation | Computer simulation | Least squares method | Nonlinearity | Deviation | Estimators | Statistics Theory | Mathematics

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 02/2017, Volume 67, Issue 1, pp. 245 - 262

In this paper, we consider the problem of the existence of a least absolute deviations estimator for the Michaelis-Menten model function...

65C20 | 62J02 | 92C45 | weighted median | Michaelis-Menten reaction | 65D10 | least absolute deviations principle | MATHEMATICS | APPROXIMATION | KINETICS | Least absolute deviations (Statistics) | Functions | Research | Functional equations | Mathematical research | Performance evaluation | Mathematical models

65C20 | 62J02 | 92C45 | weighted median | Michaelis-Menten reaction | 65D10 | least absolute deviations principle | MATHEMATICS | APPROXIMATION | KINETICS | Least absolute deviations (Statistics) | Functions | Research | Functional equations | Mathematical research | Performance evaluation | Mathematical models

Journal Article

Journal of the American Statistical Association, ISSN 0162-1459, 09/2010, Volume 105, Issue 491, pp. 1104 - 1112

.... Least squares or least absolute deviation are among the most widely used criterions in statistical estimation for linear regression model...

Random weighting | Logarithm transformation | Multiplicative regression model | Human error | Error rates | Density estimation | Theory and Methods | Linear regression | Least squares | Regression analysis | Modeling | Estimators | Estimation methods | Term weighting | DEVIATION | REGRESSION-ESTIMATORS | STATISTICS & PROBABILITY | PREDICTION | Usage | Models | Logarithmic functions | Weighting (Statistics) | Relative error

Random weighting | Logarithm transformation | Multiplicative regression model | Human error | Error rates | Density estimation | Theory and Methods | Linear regression | Least squares | Regression analysis | Modeling | Estimators | Estimation methods | Term weighting | DEVIATION | REGRESSION-ESTIMATORS | STATISTICS & PROBABILITY | PREDICTION | Usage | Models | Logarithmic functions | Weighting (Statistics) | Relative error

Journal Article

Journal of the Royal Statistical Society. Series B (Statistical Methodology), ISSN 1369-7412, 1/2005, Volume 67, Issue 3, pp. 381 - 393

.... To solve this problem, we propose a self-weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded...

Statistical variance | Economic models | Statistical inferences | Autoregressive models | Hydrological modeling | Statistical theories | Time series | Standard deviation | Traffic estimation | Estimators | Self‐weighted least absolute deviation | Autoregressive model | Least absolute deviation estimation | Infinite variance | Heavy‐tailed time series | Heavy-tailed time series | Self-weighted least absolute deviation | ERRORS | PARAMETER-ESTIMATION | RETURNS | ARCH | infinite variance | STATISTICS & PROBABILITY | heavy-tailed time series | least absolute deviation estimation | LIMIT THEORY | self-weighted least absolute deviation | REGRESSION QUANTILES | MOVING AVERAGES | autoregressive model | ARMA MODELS

Statistical variance | Economic models | Statistical inferences | Autoregressive models | Hydrological modeling | Statistical theories | Time series | Standard deviation | Traffic estimation | Estimators | Self‐weighted least absolute deviation | Autoregressive model | Least absolute deviation estimation | Infinite variance | Heavy‐tailed time series | Heavy-tailed time series | Self-weighted least absolute deviation | ERRORS | PARAMETER-ESTIMATION | RETURNS | ARCH | infinite variance | STATISTICS & PROBABILITY | heavy-tailed time series | least absolute deviation estimation | LIMIT THEORY | self-weighted least absolute deviation | REGRESSION QUANTILES | MOVING AVERAGES | autoregressive model | ARMA MODELS

Journal Article

Journal of Mathematics and Statistics, ISSN 1549-3644, 2014, Volume 10, Issue 3, pp. 331 - 338

Journal Article

Statistics, ISSN 0233-1888, 03/2014, Volume 48, Issue 2, pp. 405 - 420

It is well known that the least absolute deviation (LAD) estimators are more robust than the least squares estimators particularly in presence of heavy tail errors...

strong consistency | asymptotic distribution | chirp signals | least absolute deviation estimators | PARAMETER-ESTIMATION | ASYMPTOTIC PROPERTIES | SIGNALS | NON-LINEAR REGRESSION | STATISTICS & PROBABILITY | SQUARES ESTIMATORS

strong consistency | asymptotic distribution | chirp signals | least absolute deviation estimators | PARAMETER-ESTIMATION | ASYMPTOTIC PROPERTIES | SIGNALS | NON-LINEAR REGRESSION | STATISTICS & PROBABILITY | SQUARES ESTIMATORS

Journal Article

Journal of the Royal Statistical Society. Series B, Statistical methodology, ISSN 1467-9868, 2008, Volume 70, Issue 5, pp. 849 - 911

... representation. Sparsity comes frequently with high dimensional data, which is a growing feature in many areas of contemporary statistics. The problems arise frequently...

Simulations | Dimensionality | Sample size | Linear regression | Correlations | Least squares | Induced substructures | Modeling | Estimators | Oracles | Adaptive lasso | Dimensionality reduction | Oracle estimator | Sure independence screening | Lasso | Sure screening | Smoothly clipped absolute deviation | Dantzig selector | Variable selection | PERSISTENCE | REPRESENTATION | STATISTICS & PROBABILITY | LIMIT | MODEL | CANCER | NONCONCAVE PENALIZED LIKELIHOOD | SMALLEST EIGENVALUE | Management science | Studies | Variables | Statistical methods | Models

Simulations | Dimensionality | Sample size | Linear regression | Correlations | Least squares | Induced substructures | Modeling | Estimators | Oracles | Adaptive lasso | Dimensionality reduction | Oracle estimator | Sure independence screening | Lasso | Sure screening | Smoothly clipped absolute deviation | Dantzig selector | Variable selection | PERSISTENCE | REPRESENTATION | STATISTICS & PROBABILITY | LIMIT | MODEL | CANCER | NONCONCAVE PENALIZED LIKELIHOOD | SMALLEST EIGENVALUE | Management science | Studies | Variables | Statistical methods | Models

Journal Article

Journal of the American Statistical Association, ISSN 1537-274X, 2010, Volume 105, Issue 489, pp. 312 - 323

We apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators. This approach relies heavily on the choice...

Least absolute shrinkage and selection operator | Akaike information criterion | Smoothly clipped absolute deviation | Nonconcave penalized likelihood | Bayesian information criterion | Deadweight loss | Generalized linear model | Sample size | Theory and Methods | Linear regression | Least squares | Regression analysis | Parametric models | Modeling | Estimators | Oracles | NUMBER | STATISTICS & PROBABILITY | VARIABLE SELECTION | ORACLE PROPERTIES | REGRESSION VARIABLES | ORDER | PROPORTIONAL HAZARDS MODEL | SHRINKAGE | CROSS-VALIDATION | ADAPTIVE LASSO | Usage | Parameter estimation | GIC | AIC | SCAD | BIC | LASSO

Least absolute shrinkage and selection operator | Akaike information criterion | Smoothly clipped absolute deviation | Nonconcave penalized likelihood | Bayesian information criterion | Deadweight loss | Generalized linear model | Sample size | Theory and Methods | Linear regression | Least squares | Regression analysis | Parametric models | Modeling | Estimators | Oracles | NUMBER | STATISTICS & PROBABILITY | VARIABLE SELECTION | ORACLE PROPERTIES | REGRESSION VARIABLES | ORDER | PROPORTIONAL HAZARDS MODEL | SHRINKAGE | CROSS-VALIDATION | ADAPTIVE LASSO | Usage | Parameter estimation | GIC | AIC | SCAD | BIC | LASSO

Journal Article

Computational Statistics and Data Analysis, ISSN 0167-9473, 03/2014, Volume 71, pp. 128 - 137

A robust estimation procedure for mixture linear regression models is proposed by assuming that the error terms follow a Laplace distribution. Using the fact...

Mixture regression model | Laplace distribution | Normal mixture | EM algorithm | Least absolute deviation | ABSOLUTE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHM | STATISTICS & PROBABILITY | ESTIMATOR | Analysis | Models | Algorithms

Mixture regression model | Laplace distribution | Normal mixture | EM algorithm | Least absolute deviation | ABSOLUTE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHM | STATISTICS & PROBABILITY | ESTIMATOR | Analysis | Models | Algorithms

Journal Article

Test (Madrid, Spain), ISSN 1863-8260, 2018, Volume 28, Issue 3, pp. 785 - 803

... · Functional data analysis · Least absolute deviation · Robust statistics Mathematics Subject Classiﬁcation 62G08 · 62G35 1 Introduction Advancements in modern technology...

Robust statistics | Statistics for Business, Management, Economics, Finance, Insurance | 62G08 | Confidence band | Least absolute deviation | Statistical Theory and Methods | Statistics, general | Statistics | 62G35 | Functional data analysis | REGRESSION | ESTIMATORS | STATISTICS & PROBABILITY | PRINCIPAL COMPONENTS | DEPTH | Mathematical analysis | Robustness | Regression analysis | Polynomials

Robust statistics | Statistics for Business, Management, Economics, Finance, Insurance | 62G08 | Confidence band | Least absolute deviation | Statistical Theory and Methods | Statistics, general | Statistics | 62G35 | Functional data analysis | REGRESSION | ESTIMATORS | STATISTICS & PROBABILITY | PRINCIPAL COMPONENTS | DEPTH | Mathematical analysis | Robustness | Regression analysis | Polynomials

Journal Article

Journal of Business & Economic Statistics, ISSN 1537-2707, 2007, Volume 25, Issue 3, pp. 347 - 355

The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso...

LAD-lasso | Oracle property | Lasso | LAD | Outliers | Datasets | Linear regression | Mathematical independent variables | Modeling | Stock markets | Estimators | Consistent estimators | Oracles | Estimation methods | SMALL SAMPLES | ASYMPTOTIC THEORY | oracle property | ARCH | STATISTICS & PROBABILITY | MODEL SELECTION | ESTIMATORS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | LIKELIHOOD | Least absolute deviations (Statistics) | Usage | Regression analysis | Analysis | Analysis of variance | Methods

LAD-lasso | Oracle property | Lasso | LAD | Outliers | Datasets | Linear regression | Mathematical independent variables | Modeling | Stock markets | Estimators | Consistent estimators | Oracles | Estimation methods | SMALL SAMPLES | ASYMPTOTIC THEORY | oracle property | ARCH | STATISTICS & PROBABILITY | MODEL SELECTION | ESTIMATORS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | LIKELIHOOD | Least absolute deviations (Statistics) | Usage | Regression analysis | Analysis | Analysis of variance | Methods

Journal Article

Communications in Statistics - Simulation and Computation: International Conference on Advances in Interdisciplinary Statistics and Combinatorics, ISSN 0361-0918, 10/2015, Volume 44, Issue 9, pp. 2442 - 2462

Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods...

Characteristic function | Index | Estimation | Stable distribution | LAWS | STATISTICS & PROBABILITY | PARAMETERS | Economic models | Regression analysis | Mean square values | Least squares method | Mathematical analysis | Samples | Regression | Mathematical models | Deviation | Recognition

Characteristic function | Index | Estimation | Stable distribution | LAWS | STATISTICS & PROBABILITY | PARAMETERS | Economic models | Regression analysis | Mean square values | Least squares method | Mathematical analysis | Samples | Regression | Mathematical models | Deviation | Recognition

Journal Article

Statistica Sinica, ISSN 1017-0405, 10/2007, Volume 17, Issue 4, pp. 1533 - 1548

.... We propose a robust weighted least-absolute-deviations (LAD) method for estimation in the AFT model with right-censored data...

Censored data | Kaplan Meier estimator | Linear regression | Least squares | General | Censorship | Regression analysis | Logarithms | Estimators | Consistent estimators | Distribution functions | Kaplan-Meier weights | Least absolute deviations | Robust regression | Asymptotic normality | Right censored data | asymptotic normality | LINEAR-REGRESSION | least absolute deviations | CENSORED REGRESSION | SURVIVAL ANALYSIS | robust regression | COVARIABLES | STATISTICS & PROBABILITY | right censored data | MEDIAN REGRESSION | RANK-TESTS

Censored data | Kaplan Meier estimator | Linear regression | Least squares | General | Censorship | Regression analysis | Logarithms | Estimators | Consistent estimators | Distribution functions | Kaplan-Meier weights | Least absolute deviations | Robust regression | Asymptotic normality | Right censored data | asymptotic normality | LINEAR-REGRESSION | least absolute deviations | CENSORED REGRESSION | SURVIVAL ANALYSIS | robust regression | COVARIABLES | STATISTICS & PROBABILITY | right censored data | MEDIAN REGRESSION | RANK-TESTS

Journal Article

2011, ISBN 1405183691, xvi, 375

"A Probability Metrics Approach to Financial Risk Measures relates the field of probability metrics and risk measures to one another and applies them to...

Financial risk management | Probabilities

Financial risk management | Probabilities

Book