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A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…
We develop a novel asymptotic theory for local polynomial extremum estimators of time-varying parameters in a broad class of nonlinear time series models. We show the proposed estimators are consistent and follow normal distributions in…
In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…
This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We introduce a broad class of models called semiparametric spatial point process for making inference between spatial point patterns and spatial covariates. These models feature an intensity function with both parametric and nonparametric…
We introduce a new method for online parameter estimation in stochastic interacting particle systems, based on continuous observation of a small number of particles from the system. Our method recursively updates the model parameters using…
We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
This paper develops a general asymptotic theory of series estimators for spatial data collected at irregularly spaced locations within a sampling region $R_n \subset \mathbb{R}^d$. We employ a stochastic sampling design that can flexibly…
By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to…
In this paper, we develop nonparametric inference on spatial regression models as an extension of Lu and Tj\ostheim(2014), which develops nonparametric inference on density functions of stationary spatial processes under domain expanding…
Kimura and Yoshida treated a model in which the finite variation part of a two-dimensional semimartingale is expressed by time-integration of latent processes. They proposed a correlation estimator between the latent processes and proved…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…