Related papers: A fifth order expansion for the distribution funct…
We prove simple theorems concerning the maximal order of a large class of multiplicative functions. As an application, we determine the maximal orders of certain functions of the type $\sigma_A(n)= \sum_{d\in A(n)} d$, where A(n) is a…
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric…
Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large…
Particle Flow Filters perform the measurement update by moving particles to a different location rather than modifying the particles' weight based on the likelihood. Their movement (flow) is dictated by a drift term, which continuously…
We obtain asymptotic expansions for local probabilities of partial sums for uniformly bounded independent but not necessarily identically distributed integer-valued random variables. The expansions involve products of polynomials and…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood (MSL) estimators,…
The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this…
In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
Recently, we have proposed a maximum likelihood iterative algorithm for estimation of the parameters of the Nakagami-m distribution. This technique performs better than state of art estimation techniques for this distribution. This could be…
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
In this paper, we establish the second-order distributional expansions of normalized maxima of n independent observations, where the ith observation follows from a normal copula with its correlation coefficient being a monotone continuous…