Results 1  10
of
29
Locally weighted learning
 ARTIFICIAL INTELLIGENCE REVIEW
, 1997
"... This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, ass ..."
Abstract

Cited by 594 (53 self)
 Add to MetaCart
This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning t parameters, interference between old and new data, implementing locally weighted learning e ciently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.
Prediction From Randomly Right Censored Data
, 1999
"... Let X be a random vector taking values in IR d , let Y be a bounded random variable, and let C be a right censoring random variable operating on Y . It is assumed that C is independent of (X; Y ), the distribution function of C is continuous and the support of the distribution of Y is a proper sub ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
Let X be a random vector taking values in IR d , let Y be a bounded random variable, and let C be a right censoring random variable operating on Y . It is assumed that C is independent of (X; Y ), the distribution function of C is continuous and the support of the distribution of Y is a proper subset of the support of the distribution of C. Given a sample fX i ; minfY i ; C i g; I [Y i C i ] g and a vector of covariates X , we want to construct an estimate of Y such that the mean squared error is minimized. Without censoring, i.e. for C = 1 almost surely, it is wellknown that the mean squared error of suitably defined kernel, partitioning, nearest neighbor, least squares and smoothing spline estimates converges for every distribution of (X; Y ) to the optimal value almost surely, if the sample size tends to infinity. In this paper, we modify the above estimates and show that in the right random censoring model described above the same is true for the modified estimates. AMS classif...
Dimension reduction for censored regression data
 Ann. Stat
, 1999
"... Without parametric assumptions, highdimensional regression analysis is already complex. This is made even harder when data are subject to censoring. In this article, we seek ways of reducing the dimensionality of the regressor before applying nonparametric smoothing techniques. If the censoring ti ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
Without parametric assumptions, highdimensional regression analysis is already complex. This is made even harder when data are subject to censoring. In this article, we seek ways of reducing the dimensionality of the regressor before applying nonparametric smoothing techniques. If the censoring time is independent of the lifetime, then the method of sliced inverse regression can be applied directly. Otherwise, modification is needed to adjust for the censoring bias. A key identity leading to the bias correction is derived and the rootn consistency of the modified estimate is established. Patterns of censoring can also be studied under a similar dimension reduction framework. Some simulation results and an application to a real data set are reported.
Adaptive nonparametric regression estimation in presence of right censoring, working paper
"... Abstract. In this paper, we consider the problem of estimating a regression function when the outcome is censored. Two strategies of estimation are proposed: a twostep strategy where the ratio of two projection estimators is used to estimate the regression function; a direct strategy based on a sta ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we consider the problem of estimating a regression function when the outcome is censored. Two strategies of estimation are proposed: a twostep strategy where the ratio of two projection estimators is used to estimate the regression function; a direct strategy based on a standard meansquare contrast for censored data. For both estimators, nonasymptotic bounds for the integrated meansquare risk are provided and datadriven model selection is performed. In most cases, asymptotically optimal minimax rates of convergence are obtained, when the regression function belongs to a class of Besov functions.
Estimation in nonparametric locationscale regression models with censored data
, 2010
"... Abstract Consider the random vector (X, Y), where X is completely observed and Y is subject to random right censoring. It is well known that the completely nonparametric kernel estimator of the conditional distribution F(·x) of Y given X = x suffers from inconsistency problems in the right tail (B ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract Consider the random vector (X, Y), where X is completely observed and Y is subject to random right censoring. It is well known that the completely nonparametric kernel estimator of the conditional distribution F(·x) of Y given X = x suffers from inconsistency problems in the right tail (Beran 1981, Technical Report, University of California, Berkeley), and hence any location function m(x) that involves the right tail of F(·x) (like the conditional mean) cannot be estimated consistently in a completely nonparametric way. In this paper, we propose an alternative estimator of m(x), that, under certain conditions, does not share the above inconsistency problems. The estimator is constructed under the model Y = m(X) + σ(X)ε, where σ(·) is an unknown scale function and ε (with location zero and scale one) is independent of X. We obtain the asymptotic properties of the proposed estimator of m(x), we compare it with the completely nonparametric estimator via simulations and apply it to a study of quasars in astronomy.
Estimation of the covariance matrix of random effects in longitudinal studies
 Ann. Statist
, 2007
"... Longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas. The within cluster correlation structure plays a very important role in longitudinal data analysis. This is because not only can an estimator be improved by incorporating the within cluster corre ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas. The within cluster correlation structure plays a very important role in longitudinal data analysis. This is because not only can an estimator be improved by incorporating the within cluster correlation structure into the estimation procedure, but also the within cluster correlation structure can sometimes provide valuable insights in practical problems. For example, it can reveal the correlation strengths among the impacts of various factors. Motivated by data typified by a set from Bangladesh pertinent to the use of contraceptives, we propose a random effect varyingcoefficient model, and an estimation procedure for the within cluster correlation structure of the proposed model. The estimation procedure is optimizationfree and the proposed estimators enjoy asymptotic normality under mild conditions. Simulations suggest that the proposed estimation is practicable for finite samples and resistent against mild
Global Partial Likelihood for Nonparametric Proportional Hazards Models (Supplemental Technical Report)
"... A global partial likelihood method, in contrast to the local partial likelihood method ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
A global partial likelihood method, in contrast to the local partial likelihood method
MODEL SELECTION FOR ADDITIVE REGRESSION IN PRESENCE OF RIGHT CENSORING
"... Abstract. In this paper, we explain how works a nonparametric algorithm for estimating a regression function when the response is censored. The strategy is based on an adequate transformation of the data in order to take the censoring into account and on a standard meansquare contrast for the estim ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. In this paper, we explain how works a nonparametric algorithm for estimating a regression function when the response is censored. The strategy is based on an adequate transformation of the data in order to take the censoring into account and on a standard meansquare contrast for the estimation of the regression function. We illustrate the method through several empirical experiments, in particular in the bivariate setting of an additive regression function and also on real data sets. 1.