Related papers: Hypothesis Testing for High-Dimensional Multinomia…
For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more…
The randomized $p$-value, (nonrandomized) mid-$p$-value and abstract randomized $p$-value have all been recommended for testing a null hypothesis whenever the test statistic has a discrete distribution. This paper provides a unifying…
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…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
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…
Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a P-value, we construct a…
The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
In this paper, we propose a new scalar and shift transform invariant test statistic for the high-dimensional two-sample location test. The expectation of our test is exactly zero under the null hypothesis. And we allow the dimension could…
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…
We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider…
The development of high-dimensional white noise test is important in both statistical theories and applications, where the dimension of the time series can be comparable to or exceed the length of the time series. This paper proposes…
In this paper, we have developed new multistage tests which guarantee prescribed level of power and are more efficient than previous tests in terms of average sampling number and the number of sampling operations. Without truncation, the…
We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…
We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated…
Rare and Weak models for multiple hypothesis testing assume that only a small proportion of the tested hypotheses concern non-null effects and the individual effects are only moderately large, so they generally do not stand out…
We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called $\phi$-divergence measures. By taking into account the…