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We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of…
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…
We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
We consider the moderate deviations behaviors for two (co-) volatility estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The results are obtained by using a new result about the moderate deviations principle for…
A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, nearly non-stationary process, unit root process, mildly…
Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires…
The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
Covariate-adaptive randomization is widely used in clinical trials to balance prognostic factors, and regression adjustments are often adopted to further enhance the estimation and inference efficiency. In practice, the covariates may…
Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional…
This paper investigates asymptotic properties of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the…
In this paper, we give a tutorial on asymptotic properties of the Least Square (LS) and Regularized Least Squares (RLS) estimators for the finite impulse response model with filtered white noise inputs. We provide three perspectives: the…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…