Related papers: Estimating odds and log odds with guaranteed accur…

We obtain the best possible upper bounds for the moments of a single order statistic from independent, non-negative random variables, in terms of the population mean. The main result covers the independent identically distributed case.…

The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…

Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…

This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…

Many proper scoring rules such as the Brier and log scoring rules implicitly reward a probability forecaster relative to a uniform baseline distribution. Recent work has motivated weighted proper scoring rules, which have an additional…

In this paper we consider the problem of estimating a Bernoulli parameter using finite memory. Let $X_1,X_2,\ldots$ be a sequence of independent identically distributed Bernoulli random variables with expectation $\theta$, where $\theta \in…

Let $M(n, k, p)$ denote the maximum probability of the event $X_1 = X_2 = \cdots = X_n=1$ under a $k$-wise independent distribution whose marginals are Bernoulli random variables with mean $p$. A long-standing question is to calculate $M(n,…

Consider the problem of maximizing the probability of stopping with one of the two highest values in a Bernoulli random walk with arbitrary parameter $p$ and finite time horizon $n$. Allaart \cite{Allaart} proved that the optimal strategy…

The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…

Let $X$ be a random variable distributed according to the binomial distribution with parameters $n$ and $p$. It is shown that $P(X>EX)\ge1/4$ if $1>p\ge c/n$, where $c:=\ln(4/3)$, the best possible constant factor.

We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…

The restricted maximum likelihood method enhances popularity of maximum likelihood methods for variance component analysis on large scale unbalanced data. As the high throughput biological data sets and the emerged science on uncertainty…

The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…

We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…

We propose simple randomized strategies for sequential prediction under imperfect monitoring, that is, when the forecaster does not have access to the past outcomes but rather to a feedback signal. The proposed strategies are consistent in…

We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the…

In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and…

We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random…