Related papers: Power Enhancement in High Dimensional Cross-Sectio…
Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
Given $p$-dimensional Gaussian vectors $X_i \stackrel{iid}{\sim} N(0, \Sigma)$, $1 \leq i \leq n$, where $p \geq n$, we are interested in testing a null hypothesis where $\Sigma = I_p$ against an alternative hypothesis where all eigenvalues…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
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…
Testing high-dimensional quantile regression coefficients is crucial, as tail quantiles often reveal more than the mean in many practical applications. Nevertheless, the sparsity pattern of the alternative hypothesis is typically unknown in…
We study methods for identifying heterogeneous parameter components in distributed M-estimation with minimal data transmission. One is based on a re-normalized Wald test, which is shown to be consistent as long as the number of distributed…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates…
In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…
A Partial Conjunction Hypothesis (PCH) test combines information across a set of base hypotheses to determine whether some subset is non-null. PCH tests arise in a diverse array of fields, but standard PCH testing methods can be highly…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…
The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample…
We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…
This paper develops a new framework for alpha testing in high-dimensional factor pricing models with time-varying coefficients. To detect sparse alternatives, we propose a spatial-sign-based max-type test and derive its limiting null…
This paper proposes an overidentifying restriction test for high-dimensional linear instrumental variable models. The novelty of the proposed test is that it allows the number of covariates and instruments to be larger than the sample size.…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
In testing of hypothesis the robustness of the tests is an important concern. Generally, the maximum likelihood based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations…
Wald's sequential probability ratio test (SPRT) is a cornerstone of sequential analysis. Based on desired type-I, II error levels $\alpha, \beta$, it stops when the likelihood ratio crosses certain thresholds, guaranteeing optimality of the…
Structured multiple-testing problems (gatekeeping trials, dose-finding, multi-tissue eQTL mapping, bundled-challenger A/B experiments) organize hypotheses into design-imposed blocks and demand strong family-wise error rate (FWER) control…