• Corpus ID: 238744091

High-Dimensional Varying Coefficient Models with Functional Random Effects

@inproceedings{Law2021HighDimensionalVC,
  title={High-Dimensional Varying Coefficient Models with Functional Random Effects},
  author={Michael Law and Yaacov Ritov},
  year={2021}
}
We consider a sparse high-dimensional varying coefficients model with random effects, a flexible linear model allowing covariates and coefficients to have a functional dependence with time. For each individual, we observe discretely sampled responses and covariates as a function of time as well as time invariant covariates. Under sampling times that are either fixed and common or random and independent amongst individuals, we propose a projection procedure for the empirical estimation of all… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 28 REFERENCES
Variable selection for high-dimensional generalized varying-coefficient models
  • H. Lian
  • Mathematics, Computer Science
    Statistica Sinica
  • 2012
TLDR
This paper proposes a polynomial-spline based procedure that simultaneously eliminates irrelevant predictors and estimates the nonzero coefficients and uses the extended Bayesian information cri- terion (eBIC) to automatically choose the regularization parameters.
Variable Selection in High-dimensional Varying-coefficient Models with Global Optimality
  • L. Xue, A. Qu
  • Mathematics, Computer Science
    J. Mach. Learn. Res.
  • 2012
TLDR
This work considers model selection in the high-dimensional setting and adopts difference convex programming to approximate the L0 penalty, and investigates the global optimality properties of the varying-coefficient estimator.
Sparse high-dimensional varying coefficient model: Nonasymptotic minimax study
TLDR
The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting and construct an adaptive estimator which attains those lower bounds within a constant or logarithmic factor of the number of observations.
Inference of high-dimensional linear models with time-varying coefficients
We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing
Fast Algorithms and Theory for High-Dimensional Bayesian Varying Coefficient Models
TLDR
The nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian estimation and variable selection in NVC models is introduced and a simple method is introduced to make the model robust to misspecification of the temporal correlation structure.
Sparse additive models
TLDR
An algorithm for fitting the models is derived that is practical and effective even when the number of covariates is larger than the sample size, and empirical results show that they can be effective in fitting sparse non‐parametric models in high dimensional data.
Asymptotic Confidence Regions for Kernel Smoothing of a Varying-Coefficient Model With Longitudinal Data
Abstract We consider the estimation of the k + 1-dimensional nonparametric component β(t) of the varying-coefficient model Y(t) = X T (t)β(t) + e(t) based on longitudinal observations (Yij , X i (tij
On asymptotically optimal confidence regions and tests for high-dimensional models
TLDR
A general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model and develops the corresponding theory which includes a careful analysis for Gaussian, sub-Gaussian and bounded correlated designs.
Scaled sparse linear regression
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating
Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data
This paper considers nonparametric estimation in a varying coefficient model with repeated measurements (Y ij , X ij , t ij ), for i = 1 n and j = 1 n i , where X ij = (X ij .,,X ijk ) T and (Y ij ,
...
1
2
3
...