Related papers: On prediction errors in regression models with non…
We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…
Nested error regression models are commonly used to incorporate observational unit specific auxiliary variables to improve small area estimates. When the mean structure of this model is misspecified, there is generally an increase in the…
We study the asymptotic behaviour of least squares estimators in regression models for long-range dependent random fields observed on spheres. The least squares estimator can be given as a weighted functional of long-range dependent random…
We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in…
This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodicvector autoregressive time series models (hereafter PVAR) with uncorrelated but dependent innovations. When theinnovations…
We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…
This paper introduces R-OLS, an estimator for the average partial effect (APE) of a continuous treatment variable on an outcome variable in the presence of non-linear and non-additively separable confounding of unknown form. Identification…
We establish a negative moment bound for the sample autocovariance matrix of a stationary process driven by conditional heteroscedastic errors. This moment bound enables us to asymptotically express the mean squared prediction error (MSPE)…
We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve…
We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…
In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear)…
The statistical analysis of Randomized Numerical Linear Algebra (RandNLA) algorithms within the past few years has mostly focused on their performance as point estimators. However, this is insufficient for conducting statistical inference,…
In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least squares estimator under…
A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve…
The model averaging problem is to average multiple models to achieve a prediction accuracy not much worse than that of the best single model in terms of mean squared error. It is known that if the models are misspecified, model averaging is…
We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$-distribution with parameter in the range $1/2 \leq \nu \leq 5$.…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
Estimating characteristics of domains (referred to as small areas) within a population from sample surveys of the population is an important problem in survey statistics. In this paper, we consider model-based small area estimation under…
Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…
This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.)…