Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields

Parameter estimation based on cumulative Kullback-Leibler divergence

In this paper, we propose some estimators for the parameters of a statistical model based on Kullback-Leibler divergence of the survival function in continuous setting. We prove that the proposed estimators are subclass of "generalized estimating equations" estimators. The asymptotic properties of the estimators such as consistency, asymptotic normality, asymptotic confidence interval and asymptotic hypothesis testing are investigated.

Large Deviations of Factor Models with Regularly-Varying Tails: Asymptotics and Efficient Estimation

We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient sampling method for LDP estimation of this class is introduced and theoretically shown to exponentially outperform the crude Monte-Carlo estimator, in terms of the coverage probability and the confidence interval's length. The theoretical results are empirically validated through stochastic simulations on independent non-identically Pareto distributed factors. T…

Nonparametric estimation in a nonlinear cointegration type model

We derive an asymptotic theory of nonparametric estimation for a time series regression model $Z_t=f(X_t)+W_t$, where \ensuremath\{X_t\} and \ensuremath\{Z_t\} are observed nonstationary processes and $\{W_t\}$ is an unobserved stationary process. In econometrics, this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results are of wider interest. The class of nonstationary processes allowed for $\{X_t\}$ is a subclass of the class of null recurrent Markov chains. This subclass contains random walk, unit root processes and nonlinear processes. We deriv…

Asymptotic properties of AD(1, n) model and its maximum likelihood estimator

This paper deals with the problem of global parameter estimation of affine diffusions in $\mathbb{R}_+ \times \mathbb{R}^n$ denoted by $AD(1, n)$ where $n$ is a positive integer which is a subclass of affine diffusions introduced by Duffie et al in [14]. The $AD(1, n)$ model can be applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models. Our first result is about the classification of $AD(1, n)$ processes according to the subcritical, critical and supercritical cases. Then, we give the stationarity and the ergodicity theorems…

Efficient estimation for a subclass of shape invariant models

In this paper, we observe a fixed number of unknown $2π$-periodic functions differing from each other by both phases and amplitude. This semiparametric model appears in literature under the name "shape invariant model." While the common shape is unknown, we introduce an asymptotically efficient estimator of the finite-dimensional parameter (phases and amplitude) using the profile likelihood and the Fourier basis. Moreover, this estimation method leads to a consistent and asymptotically linear estimator for the common shape.

稀疏紧凑支持协方差模型在高斯超几何类中的研究：可识别性、重参数化和渐近性质

Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties

本文研究高斯超几何类协方差函数，推导了有效性条件并展示了模型在固定域渐近中的结构可识别性问题，提出稀疏紧凑支持子类并通过最大积分范围准则解决，并在固定域渐近中建立了最大似然估计的强一致性和渐近正态性。