Related papers: Asymptotic distribution of least square estimators…

In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…

In this paper, we consider the normalized least squares estimator of the parameter in a mildly-explosive first-order autoregressive model with dependent errors which are modeled as a mildly-explosive AR(1) process. We prove that the…

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory…

We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…

The limit distribution of the nonparametric maximum likelihood estimator for interval censored data with more than one observation time per unobservable observation, is still unknown in general. For the so-called separated case, where one…

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

A consistent kernel estimator of the limiting spectral distribution of general sample covariance matrices was introduced in Jing, Pan, Shao and Zhou (2010). The central limit theorem of the kernel estimator is proved in this paper.

We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…

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…

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…

In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…

This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…

We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully adaptive, in the sense that the attained…