Related papers: Non-Regular Likelihood Inference for Seasonally Pe…
Assume that we observe a stochastic process $(X(t))_{t\in[-r,T]}$, which satisfies the linear stochastic delay differential equation \[ \mathrm{d} X(t) = \vartheta \int_{[-r,0]} X(t + u) \, a(\mathrm{d} u) \, \mathrm{d} t + \mathrm{d} W(t)…
We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena…
This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
This paper proposes feasible asymptotically efficient estimators for a certain class of Gaussian noises with self-similar and stationary properties, which includes the fractional Gaussian noise, under high frequency observations. In this…
Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…
The spatial structure of fluctuations in spatially inhomogeneous processes can be modeled in terms of Gibbs random fields. A local low energy estimator (LLEE) is proposed for the interpolation (prediction) of such processes at points where…
We consider a doubly stochastic Poisson process with stochastic intensity $\lambda_t =n q\left(X_t\right)$ where $X$ is a continuous It\^o semimartingale and $n$ is an integer. Both processes are observed continuously over a fixed period…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence…
Profile likelihood intervals of large quantiles in Extreme Value distributions provide a good way to estimate these parameters of interest since they take into account the asymmetry of the likelihood surface in the case of small and…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
We propose a novel estimation procedure for certain spectral distributions associated with a class of high dimensional linear time series. The processes under consideration are of the form $X_t = \sum_{\ell=0}^\infty \mathbf{A}_\ell…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…
Locally stationary (LSPs) constitute an essential modeling paradigm for capturing the nuanced dynamics inherent in time series data whose statistical characteristics, including mean and variance, evolve smoothly across time. In this paper,…
Ocean buoy data in the form of high frequency multivariate time series are routinely recorded at many locations in the world's oceans. Such data can be used to characterise the ocean wavefield, which is important for numerous socio-economic…
We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…