Related papers: Asymptotic Statistical Theory for the Samples Prob…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and…
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…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…
In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…
The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…
The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range…
Let X be a second order random process indexed by a compact interval [0,T]. Assume that n independent realizations of X are observed on a fixed grid of p time points. Under mild regularity assumptions on the sample paths of X, we show the…
The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…
A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning…
The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…