Related papers: On low-sampling-rate Kramers-Moyal coefficients
The classical Cram\'er-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using…
Longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas. The within cluster correlation structure plays a very important role in longitudinal data analysis. This is because not only can an…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…
We consider the large deviations associated with the empirical mean of independent and identically distributed random variables under a subexponential moment condition. We show that non-trivial deviations are observable at a subexponential…
When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
Importance-weighting is a popular and well-researched technique for dealing with sample selection bias and covariate shift. It has desirable characteristics such as unbiasedness, consistency and low computational complexity. However,…
In prevalent cohort studies where subjects are recruited at a cross-section, the time to an event may be subject to length-biased sampling, with the observed data being either the forward recurrence time, or the backward recurrence time, or…
A probabilistic approach for estimating sample qualities for stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the distance between the invariant probability measure of a…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977)…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
The Koml\'os$\unicode{x2013}$Major$\unicode{x2013}$Tusn\'ady (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application has been hindered by a lack of practical constants.…
A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…
Assume that $X$ and $Y$ are independent random variables, each having a Cauchy distribution with a known median. Taking a random independent sample of size $n$ of each $X$ and $Y$, one can then compute their centralized empirical…
This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data…
A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…