Related papers: A Test Statistic for Weighted Runs
Based on the median and the median absolute deviation estimators, and the Hodges-Lehmann and Shamos estimators, robustified analogues of the conventional $t$-test statistic are proposed. The asymptotic distributions of these statistics are…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential…
Mathematical formulations and proofs for a wavelet based statistic employed in functional data analysis is elaborately discussed in this report. The propositions and derivations discussed here apply to a wavelet based statistic with hard…
We introduce several statistics on ordered partitions of sets, that is, set partitions where the blocks are permuted arbitrarily. The distribution of these statistics is closely related to the q-Stirling numbers of the second kind. Some of…
We consider goodness-of-fit tests with i.i.d. samples generated from a categorical distribution $(p_1,...,p_k)$. For a given $(q_1,...,q_k)$, we test the null hypothesis whether $p_j=q_{\pi(j)}$ for some label permutation $\pi$. The…
In this paper we analyse the behaviour of adaptive filters or detectors when they are trained with $t$-distributed samples rather than Gaussian distributed samples. More precisely we investigate the impact on the distribution of some…
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
Consider $k$ independent random samples from $p$-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of $k$ covariance…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
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…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
Consider the likelihood ratio test (LRT) statistics for the independence of sub-vectors from a $p$-variate normal random vector. We are devoted to deriving the limiting distributions of the LRT statistics based on a random sample of size…
We discuss the conditions under which Scan Statistics can be fruitfully implemented to signal a departure from the underlying probability model that describes the experimental data. It is shown that local perturbations (``bumps'' or…
We consider nonparametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We…
This paper is concerned with the problem of conditional independence testing for discrete data. In recent years, researchers have shed new light on this fundamental problem, emphasizing finite-sample optimality. The non-asymptotic viewpoint…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
The main purpose of this paper is to present new families of test statistics for studying the problem of goodness-of-fit of some data to a latent class model for binary data. The families of test statistics introduced are based on…