Related papers: Chernoff Index for Cox Test of Separate Parametric…
We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…
The problem of quickest detection of an anomalous process among M processes is considered. At each time, a subset of the processes can be observed, and the observations from each chosen process follow two different distributions, depending…
Active learning can reduce the number of samples needed to perform a hypothesis test and to estimate the parameters of a model. In this paper, we revisit the work of Chernoff that described an asymptotically optimal algorithm for performing…
We study the relative entropy of the empirical probability vector with respect to the true probability vector in multinomial sampling of $k$ categories, which, when multiplied by sample size $n$, is also the log-likelihood ratio statistic.…
Given a sequence of random variables $X^n=X_1,\ldots, X_n$, discriminating between two hypotheses on the underlying probability distribution is a key task in statistics and information theory. Of interest here is the Stein exponent, i.e.…
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for…
We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…
We consider the problem of testing multiple quantum hypotheses $\{\rho_1^{\otimes n},\ldots,\rho_r^{\otimes n}\}$, where an arbitrary prior distribution is given and each of the $r$ hypotheses is $n$ copies of a quantum state. It is known…
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…
We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR…
A profile likelihood ratio test is proposed for inferences on the index coefficients in generalized single-index models. Key features include its simplicity in implementation, invariance against parametrization, and exhibiting substantially…
Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks' theorem. This assumption breaks down…
Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…
Recently Liu and Wang derived the likelihood ratio test (LRT) statistic and its asymptotic distribution for testing equality of two multinomial distributions vs. the alternative that the second distribution is larger in terms of increasing…
Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the…
While analysing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest and they are said to be cured. When this feature of survival models is taken into account, the models are…
In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…
We consider a likelihood ratio method for testing whether a monotone baseline hazard function in the Cox model has a particular value at a fixed point. The characterization of the estimators involved is provided both in the nondecreasing…
Chernoff information upper bounds the probability of error of the optimal Bayesian decision rule for $2$-class classification problems. However, it turns out that in practice the Chernoff bound is hard to calculate or even approximate. In…