The nature of statistical learning theory
The nature of statistical learning theory
SIAM Review
Least Squares Support Vector Machine Classifiers
Neural Processing Letters
Large Scale Kernel Regression via Linear Programming
Machine Learning
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
A tutorial on support vector regression
Statistics and Computing
Primal-Dual Monotone Kernel Regression
Neural Processing Letters
Neural Computation
Nonparametric Quantile Estimation
The Journal of Machine Learning Research
Incorporating prior knowledge in support vector regression
Machine Learning
Cutting plane method for continuously constrained kernel-based regression
IEEE Transactions on Neural Networks
Measuring financial risk with generalized asymmetric least squares regression
Applied Soft Computing
Multivariate convex support vector regression with semidefinite programming
Knowledge-Based Systems
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In frontier analysis, most of nonparametric approaches produce a full frontier that envelopes all observations. Its sensitivity to extreme values and outliers can be overcome by @a-frontier, which is defined as the @a-quantile of the output conditional on a given input. The @a-frontier can be regarded as the benchmark output whether a specified firm achieves top @a efficiency. This paper proposes a nonparametric smooth multivariate estimation for @a-frontier based on shape-restricted kernel quantile regression. This method explicitly appends the classical kernel quantile regression with two shape restrictions: nondecreasing and concave, which are necessary conditions for production functions. Its training is a semi-infinite programming and can be discretized to a semidefinite programming problem, which is computationally tractable. Theoretical analysis shows that the rate of exceedance in the samples will converge to @a as the size of training data increases. Experimental results on two toy data sets clearly show that this exploitation of these prior shape knowledge can greatly improve learning performance. Experimental results on a data set from the NBER-CES Manufacturing Industry Database clearly show that the shaped restricted kernel quantile regression can achieve better out-of-sample performance than those of two benchmark methods.