Related papers: An estimation method for the chi-square divergence…
The complexity underlying real-world systems implies that standard statistical hypothesis testing methods may not be adequate for these peculiar applications. Specifically, we show that the likelihood-ratio test's null-distribution needs to…
I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find…
We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…
Statistical methodology plays a crucial role in drug regulation. Decisions by the FDA or EMA are typically made based on multiple primary studies testing the same medical product, where the two-trials rule is the standard requirement,…
We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained which can be used for parameter estimations and goodness-of-fit testing when adjusting curves…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne a well posed problem when applied to the model; secondly the…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the…
Chi-squared tests for lack of fit are traditionally employed to find evidence against a hypothesized model, with the model accepted if the Karl Pearson statistic comparing observed and expected numbers of observations falling within cells…
It is often necessary to compare the power spectra of two or more time series: one may, for instance, wish to estimate what the power spectrum of the combined data sets might have been, or one may wish to estimate the significance of a…
In this paper we use a well know method in statistics, the $\delta$-method, to provide an asymptotic distribution for the Mutual Information, and construct and independence test based on it. Interesting connections are found with the…
This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the $ Z $-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve…
In this paper, we develop new test statistics for private hypothesis testing. These statistics are designed specifically so that their asymptotic distributions, after accounting for noise added for privacy concerns, match the asymptotics of…
We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…
We propose a new concept of codivergence, which quantifies the similarity between two probability measures $P_1, P_2$ relative to a reference probability measure $P_0$. In the neighborhood of the reference measure $P_0$, a codivergence…
The Gaussian mixture distribution is important in various statistical problems. In particular it is used in the Gaussian-sum filter and smoother for linear state-space model with non-Gaussian noise inputs. However, for this method to be…
We explore properties of the $\chi^2$ and more general R\'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using…