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Adaptive Optimal Nonparametric Regression and Density Estimation Based on Fourier-Legendre Expansion
Adaptive estimations regression density martingale confidence interval Legend repolynomials
2010/4/29
Motivated by finance and technical applications, the objective of this paper
is to consider adaptive estimation of regression and density distribution based
on Fourier-Legendre expansion, and constr...
We consider the least angle regression and forward stagewise algorithms
for solving penalized least squares regression problems. In Efron,
Hastie, Johnstone & Tibshirani (2004) it is proved that the...
“Pre-conditioning” for feature selection and regression in high-dimensional problems
Pre-conditioning feature selection regression high-dimensional problems
2010/4/27
The primary method used for this initial regression is supervised principal components. Then we
apply a standard procedure such as forward stepwise selection or the
LASSO to the pre-conditioned resp...
Anomalies in the Foundations of Ridge Regression
Constrained optimization incomplete use of LaGrange’s method nonsingular distributions alternative foundations
2010/4/27
Anomalies persist in the foundations of ridge regression as set forth in Hoerl
and Kennard (1970) and subsequently. Conventional ridge estimators and their properties
do not follow on constraining l...
Large and moderate deviations principles for kernel estimators of the multivariate regression
Nadaraya-Watson estimator Recursive kernel estimator Large deviations principle Moderatedeviations principle
2010/4/27
In this paper, we prove large deviations principle for the
Nadaraya-Watson estimator and for the semi-recursive kernel
estimator of the regression in the multidimensional case.
Under suitable condi...
Quantile regression when the covariates are functions
Functional data analysis conditional quantiles B-spline functions roughness penalty
2010/4/27
This paper deals with a linear model of regression on quantiles
when the explanatory variable takes values in some functional space and the
response is scalar. We propose a spline estimator of the f...
On prediction errors in regression models with nonstationary regressors
accumulated prediction errors final prediction error least squares estimators random walk models
2010/4/27
In this article asymptotic expressions for the final prediction error
(FPE) and the accumulated prediction error (APE) of the least squares
predictor are obtained in regression models with nonstatio...
Kernel matrix regression
Kernel matrix regression kernel Hilbert space information geometry
2010/4/27
We address the problem of filling missing entries in a kernel Gram matrix, given a related full Gram matrix.We attack this problem from the viewpoint of regression, assuming that the two kernel matric...
Posterior consistency of Gaussian process prior for nonparametric binary regression
Binary regression Gaussian process Karhunen–Loeve expansion maximal inequality posterior consistency
2010/4/26
Consider binary observations whose response probability is an
unknown smooth function of a set of covariates. Suppose that a prior
on the response probability function is induced by a Gaussian proce...
Prediction in functional linear regression
Bootstrap covariance dimension reduction eigenfunction eigenvalue eigenvector functional data analysis
2010/4/26
There has been substantial recent work on methods for estimating
the slope function in linear regression for functional data analysis.
However, as in the case of more conventional finite-dimensional...
Component selection and smoothing in multivariate nonparametric regression
Smoothing spline ANOVA method of regularization nonparametricregression nonparametric classification model selection
2010/4/26
We propose a new method for model selection and model fitting
in multivariate nonparametric regression models, in the framework
of smoothing spline ANOVA. The “COSSO” is a method of
regularization ...
Bayesian shrinkage prediction for the regression problem
Bayesian prediction shrinkage estimation Normal regression superharmonic function minimaxity Kullback-Leibler divergence
2010/4/26
We consider Bayesian shrinkage predictions for the Normal regression problem
under the frequentist Kullback-Leibler risk function.
Firstly, we consider the multivariate Normal model with an unknown ...