Related papers: Asymptotic Statistical Theory for the Samples Prob…
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
Although variable selection is one of the most popular areas of modern statistical research, much of its development has taken place in the classical paradigm compared to the Bayesian counterpart. Somewhat surprisingly, both the paradigms…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
The empirical distribution function assigns mass $1/n$ to each of the $n$ observations in a sample. As these are highly variable, estimation error may be reduced by replacing them with estimated observations that are asymptotically less…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting,…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
An observation of a cumulative distribution function $F$ with finite variance is said to be contaminated according to the inflated variance model if it has a large probability of coming from the original target distribution $F$, but a small…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to…
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…
In this paper, a class of resampling techniques for finite populations under complex sampling design is introduced. The basic idea on which it rests is a two-step procedure consisting in : (i) constructing a pseudo-population on the basis…