Related papers: Uniformly most powerful tests in linear models
Model selection for Gaussian concentration graph is based on multiple testing of pairwise conditional independence. In practical applications partial correlation tests are widely used. However it is not known whether partial correlation…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the…
Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…
In this paper, we investigate score function-based tests to check the significance of an ultrahigh-dimensional sub-vector of the model coefficients when the nuisance parameter vector is also ultrahigh-dimensional in linear models. We first…
We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis…
This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…
In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…
We address the following question in this paper: "What are the most robust statistical methods for social choice?'' By leveraging the theory of uniformly least favorable distributions in the Neyman-Pearson framework to finite models and…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Generalized linear models are often misspecified due to overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood methods for testing in misspecified models often do not provide satisfactory type-I error…
Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17…
This paper considers inference in a linear instrumental variable regression model with many potentially weak instruments, in the presence of heterogeneous treatment effects. I first show that existing test procedures, including those that…
Hotelling's $T^2$-test for the mean of a multivariate normal distribution is one of the triumphs of classical multivariate analysis. It is uniformly most powerful among invariant tests, and admissible, proper Bayes, and locally and…
Under a multinormal distribution with an arbitrary unknown covariance matrix, the main purpose of this paper is to propose a framework to achieve the goal of reconciliation of Bayesian, frequentist, and Fisher's reporting $p$-values,…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…
In this paper, after a discussion of general properties of statistical tests, we present the construction of the most powerful hypothesis test for determining the existence of a new phenomenon in counting-type experiments where the observed…
We develop a new permutation test for inference on a subvector of coefficients in linear models. The test is exact when the regressors and the error terms are independent. Then, we show that the test is asymptotically of correct level,…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…