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This paper proposes the asymmetric linear double autoregression, which jointly models the conditional mean and conditional heteroscedasticity characterized by asymmetric effects. A sufficient condition is established for the existence of a…
This paper investigates the asymptotic properties of quantile regression estimators in linear models, with a particular focus on polynomial regressors and robustness to heavy-tailed noise. Under independent and identically distributed…
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and…
We deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. Previous works by several authors have shown that the error structure of the method is characterized by…
For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a…
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…
In this paper, we are concerned with nonparametric estimation of the multivariate regression function in the presence of right censored data. More precisely, we propose a statistic that is shown to be asymptotically normally distributed…
In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…
In this paper, we first investigate the monotonicity and limit problem of the fractional integral functions. By fixed point theorem and these new results of the fractional integral functions, we present that the Riemann-Liouville fractional…
The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and…