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We consider a nonparametric version of the integer-valued GARCH(1,1) model for time series of counts. The link function in the recursion for the variances is not specified by finite-dimensional parameters, but we impose nonparametric smoothness conditions. We propose a least squares estimator for this function and show that it is consistent with a rate that we conjecture to be nearly optimal.
We study the parameter estimation problem of Vasicek Model driven by sub-fractional Brownian processes from discrete observations, and let {S_t^H,t>=0} denote a sub-fractional Brownian motion whose Hurst parameter 1/2<H<1 . The studies are as follows
The paper continues the authors work on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper it is shown that if the mean response function satisfies a condition of `saturated identifiability, which was introduced by Pron
We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ myvec{y} = myvec{X}myvec{theta}^* + myvec{omega},$$ and $myvec{X} in mathbb{R}^{N times D}$ which
In model selection, several types of cross-validation are commonly used and many variants have been introduced. While consistency of some of these methods has been proven, their rate of convergence to the oracle is generally still unknown. Until now,
We study the asymptotic properties of the SCAD-penalized least squares estimator in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We are particularly interested in the use of this