# 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…

## References

SHOWING 1-10 OF 28 REFERENCES

Variable selection for high-dimensional generalized varying-coefficient models

- Mathematics, Computer ScienceStatistica Sinica
- 2012

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

- Mathematics, Computer ScienceJ. Mach. Learn. Res.
- 2012

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

- Mathematics, Computer Science
- 2013

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

- Mathematics
- 2015

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

- Computer Science
- 2019

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

- Computer Science
- 2007

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

- Mathematics
- 1998

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

- Computer Science, Mathematics
- 2014

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

- Mathematics
- 2011

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

- Mathematics
- 1998

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 ,…