PARTIALLY LINEAR MODELS WITH UNIT ROOTS

Partially Linear Models

Sparse Partially Linear Additive Models

The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing them to have either a linear or nonlinear effect on the response. However, the assignment of features to the linear and nonlinear groups is typically assumed known. Thus, to make a GPLAM a viable approach in situatio...

Analysis of Models with Complex Roots on the Unit Circle

This paper deals with nonstationary autoregressive (AR) models with complex roots on the unit circle. We examine the asymptotic properties of the least squares estimators (LSEs) in the model. We also extend the model to the case where the error term follows a stationary linear process. We show that the limiting distribution of the LSE of the unit root parameter has a property comparable to that...

Generalized Partially Linear Single-Index Models

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...

Wavelet estimation of partially linear models

A wavelet approach is presented for estimating a partially linear model (PLM). We find an estimator of the PLM by minimizing the square of the l2 norm of the residual vector with penalizing the l1 norm of the wavelet coefficients of the nonparametric component. This approach, an extension of the wavelet approach for nonparametric regression problems, avoids the restrictive smoothness requiremen...