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The Wilcoxon signed-rank test and the Wilcoxon-Mann-Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic…
This paper presents new families of Rao-type test statistics based on the minimum density power divergence estimators which provide robust generalizations for testing simple and composite null hypotheses. The asymptotic null distributions…
A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…
Rank-based approaches are among the most popular nonparametric methods for univariate data in tackling statistical problems such as hypothesis testing due to their robustness and effectiveness. However, they are unsatisfactory for more…
The r largest order statistics approach is widely used in extreme value analysis because it may use more information from the data than just the block maxima. In practice, the choice of r is critical. If r is too large, bias can occur; if…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
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…
In genetic studies of complex diseases, the underlying mode of inheritance is often not known. Thus, the most powerful test or other optimal procedure for one model, e.g. recessive, may be quite inefficient if another model, e.g. dominant,…
Tests based on sample mean vectors and sample spatial signs have been studied in the recent literature for high dimensional data with the dimension larger than the sample size. For suitable sequences of alternatives, we show that the powers…
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…
Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples…
As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of…
We prove that the largest and smallest root in modulus of random Kac polynomials have a non-universal behavior. They do not converge towards the edge of the support of the limiting distribution of the zeros. This non-universality is…
Random Forests (RF) is a popular machine learning method for classification and regression problems. It involves a bagging application to decision tree models. One of the primary advantages of the Random Forests model is the reduction in…
Learning a parametric model of a data distribution is a well-known statistical problem that has seen renewed interest as it is brought to scale in deep learning. Framing the problem as a self-supervised task, where data samples are…
Low-rank approximation is a popular strategy to tackle the "big n problem" associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified.…
We consider the problem of ranking a set of objects based on their performance when the measurement of said performance is subject to noise. In this scenario, the performance is measured repeatedly, resulting in a range of measurements for…
Relying on random matrix theory (RMT), this paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of (Lim, 2005), we show that the analysis of the…
One of the most widely applied unit root test, Phillips-Perron test, enjoys in general highpowers, but suffers from size distortions when moving average noise exists. As a remedy, thispaper proposes a nonparametric bootstrap unit root test…