Confidence intervals for high-dimensional partially linear single-index models
نویسندگان
چکیده
منابع مشابه
Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates.
We study the heteroscedastic partially linear single-index model with an unspecified error variance function, which allows for high dimensional covariates in both the linear and the single-index components of the mean function. We propose a class of consistent estimators of the parameters by using a proper weighting strategy. An interesting finding is that the linearity condition which is widel...
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The typical generalized linear model for a regression of a response Y on predictors (X;Z) has conditional mean function based upon a linear combination of (X;Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0( T 0 X) + T 0 Z, where 0( ) is an unknown function. We call these generalized partially linear single-index models (GPLSI...
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We consider heteroscedastic regression models where the mean function is a partially linear single-index model and the variance function depends on a generalized partially linear single-index model.We do not insist that the variance function depends only on the mean function, as happens in the classical generalized partially linear single-index model.We develop efficient and practical estimatio...
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Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the parameter estimates. This in turn implies that it is extremely challenging to quantify the uncertainty associated with a certain parameter estimate. Concretely, no...
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This paper addresses the problem of fitting nonlinear regression models in high-dimensional situations, where the number of predictors, p, is large relative to the number of observations, n. Most of the research in this area has been conducted under the assumption that the regression function has a simple additive structure. This paper focuses instead on single index models, which are becoming ...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2016
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2016.03.007