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The Nature of Statistical Learning Theory
, 1999
"... Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the deve ..."
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Cited by 12992 (32 self)
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algorithmic approaches to function estimation problems. A more
Quantile Regression
 JOURNAL OF ECONOMIC PERSPECTIVES—VOLUME 15, NUMBER 4—FALL 2001—PAGES 143–156
, 2001
"... We say that a student scores at the fifth quantile of a standardized exam if he performs better than the proportion � of the reference group of students and worse than the proportion (1–�). Thus, half of students perform better than the median student and half perform worse. Similarly, the quartiles ..."
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Cited by 949 (10 self)
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as introduced by Koenker and Bassett (1978) seeks to extend these ideas to the estimation of conditional quantile functions—models in which quantiles of the conditional distribution of the response variable are expressed as functions of observed covariates. In Figure 1, we illustrate one approach to this task
Multivariate adaptive regression splines
 The Annals of Statistics
, 1991
"... A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automaticall ..."
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Cited by 678 (2 self)
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A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations
Projection Pursuit Regression
 Journal of the American Statistical Association
, 1981
"... A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, ..."
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Cited by 548 (6 self)
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A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures
A tutorial on support vector regression
, 2004
"... In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing ..."
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Cited by 838 (3 self)
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In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing
Instrumental Variables Regression with Weak Instruments
 ECONOMETRICA
, 1997
"... ... The theory suggests concrete guidelines for applied work, including using nonstandard methods for construction of confidence regions. These results are used to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approac ..."
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Cited by 1643 (14 self)
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approach the OLS estimate of 6%, the more reliable LIML estimates with fewer instruments fall between 8% and 10%, with a typical 95% confidence interval of (5%,15%).
Regression Shrinkage and Selection Via the Lasso
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1994
"... We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactl ..."
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Cited by 4061 (48 self)
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an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and treebased models are briefly described.
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 962 (12 self)
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for additive expansions based on any tting criterion. Specic algorithms are presented for least{squares, least{absolute{deviation, and Huber{M loss functions for regression, and multi{class logistic likelihood for classication. Special enhancements are derived for the particular case where the individual
Evaluating the Accuracy of SamplingBased Approaches to the Calculation of Posterior Moments
 IN BAYESIAN STATISTICS
, 1992
"... Data augmentation and Gibbs sampling are two closely related, samplingbased approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accurac ..."
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Cited by 582 (12 self)
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Data augmentation and Gibbs sampling are two closely related, samplingbased approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical
Mean shift: A robust approach toward feature space analysis
 In PAMI
, 2002
"... A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence ..."
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Cited by 2370 (37 self)
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the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and thus its utility in detecting the modes of the density. The equivalence of the mean shift procedure to the Nadaraya–Watson estimator from kernel regression and the robust M
Results 1  10
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3,912,213