Related papers: On low-sampling-rate Kramers-Moyal coefficients
The sample correlation coefficient $R$ plays an important role in many statistical analyses. We study the moments of $R$ under the bivariate Gaussian model assumption, provide a novel approximation for its finite sample mean and connect it…
We present a sample path dependent measure of causal influence between two time series. The proposed measure is a random variable whose expected sum is the directed information. A realization of the proposed measure may be used to identify…
We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate…
Case-deleted analysis is a popular method for evaluating the influence of a subset of cases on inference. The use of Monte Carlo estimation strategies in complicated Bayesian settings leads naturally to the use of importance sampling…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…
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…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…
A method is proposed to reconstruct a cyclic time-inhomogeneous Markov pro- cess from measured data. First, a time-inhomogeneous Markov model is fit to the data, taken here from measurements on a wind turbine. From the time-dependent…
We explore the effect of sampling rates when measuring data given by $Mf$ for special operators $M$ arising in Thermoacoustic Tomography. We start with sampling requirements on $Mf$ given $f$ satisfying certain conditions. After this we…
We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In this way one is able to define separately the marginal distribution and the…
This paper deals with parameter estimation from extreme measurements. While being a special case of parameter estimation from partial data, in scenarios where only one sample from a given set of K measurements can be extracted, choosing…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by…
We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…
This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at different time lags are investigated in the topology of their…
We prove the limiting absorption principle on the non-compact interval $I$, on which the uniformly positive Mourre estimate holds. We reveal that such a result yields so-called smoothing estimates.
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…