Optimum Testing Time of Software using Size-Biased Concepts

Testing Biased Randomization Assumptions and Quantifying Imperfect Matching and Residual Confounding in Matched Observational Studies

One central goal of design of observational studies is to embed non-experimental data into an approximate randomized controlled trial using statistical matching. Despite empirical researchers' best intention and effort to create high-quality matched samples, residual imbalance due to observed covariates not being well matched often persists. Although statistical tests have been developed to test the randomization assumption and its implications, few provide a means to quantify the level of residual confounding due to observed covariates not being well matched in matched samples. In this articl…

应用于条件分布检验的去偏两样本U统计量

De-Biased Two-Sample U-Statistics With Application To Conditional Distribution Testing

针对含冗余参数的两样本U统计量推断问题，提出带交叉拟合的一步估计框架以消除一阶偏差，并将其应用于条件分布检验，揭示两类冗余参数对共形秩和检验有效性的不同影响。

Bayesian adjustment for preferential testing in estimating the COVID-19 infection fatality rate

A key challenge in estimating the infection fatality rate (IFR) -- and its relation with various factors of interest -- is determining the total number of cases. The total number of cases is not known because not everyone is tested, but also, more importantly, because tested individuals are not representative of the population at large. We refer to the phenomenon whereby infected individuals are more likely to be tested than non-infected individuals, as "preferential testing." An open question is whether or not it is possible to reliably estimate the IFR without any specific knowledge about th…

Testing Independence under Biased Sampling

Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from the population. An important example is truncation models, in which observed pairs are restricted to a specific subset of the X-Y plane. Standard tests for independence are not suitable in such cases, and alternative tests that take the selection bias into account are required. To deal with this issue, we generalize the notion of quasi-independence with res…

Decentralized Sequential Hypothesis Testing using Asynchronous Communication

We present a test for the problem of decentralized sequential hypothesis testing, which is asymptotically optimum. By selecting a suitable sampling mechanism at each sensor, communication between sensors and fusion center is asynchronous and limited to 1-bit data. The proposed SPRT-like test turns out to be order-2 asymptotically optimum in the case of continuous time and continuous path signals, while in discrete time this strong asymptotic optimality property is preserved under proper conditions. If these conditions do not hold, then we can show optimality of order-1. Simulations corroborate…

De-biased sparse PCA: Inference and testing for eigenstructure of large covariance matrices

Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the population covariance matrix, provided that only a certain number of loadings are non-zero. In this paper, we propose confidence intervals for individual loadings and for the largest eigenvalue of the population covariance matrix. Given an independent sample $X^i \in\mathbb R^p, i = 1,...,n,$ generated from an unknown distribution with an unknown covariance ma…