Related papers: On the optimality of likelihood ratio test for pro…
The classical likelihood ratio test (LRT) based on the asymptotic chi-squared distribution of the log likelihood is one of the fundamental tools of statistical inference. A recent universal LRT approach based on sample splitting provides…
We establish the asymptotic distribution of likelihood ratio tests (LRTs) in settings where some of the nuisance parameters are unidentifiable under the null hypothesis, parameters of interest lie on the boundary of the parameter space, and…
Prospect Theory (PT) models human decision-making behaviour under uncertainty, among which linguistic uncertainty is commonly adopted in real-world scenarios. Although recent studies have developed some frameworks to test PT parameters for…
This paper considers the asymptotic power of likelihood ratio test (LRT) for the identity test when the dimension p is large compared to the sample size n. The asymptotic distribution of LRT under alternatives is given and an explicit…
Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…
We study sequential testing for a binary disease outcome when risk follows an unknown logistic model. At each round, the decision maker may either pay for a test revealing the true label or predict the outcome based on patient features and…
Challenge Theory (CT), a new approach to decision under risk departs significantly from expected utility, and is based on firmly psychological, rather than economic, assumptions. The paper demonstrates that a purely cognitive-psychological…
In this paper, the Gaussian quasi likelihood ratio test (GQLRT) for non-Bayesian binary hypothesis testing is generalized by applying a transform to the probability distribution of the data. The proposed generalization, called…
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…
Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent…
This paper revisits the classical problem of determining the bias of a weighted coin, where the bias is known to be either $p = 1/2 + \varepsilon$ or $p = 1/2 - \varepsilon$, while minimizing the expected number of coin tosses and the error…
The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile…
This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…
Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how…
This paper extends my research applying statistical decision theory to treatment choice with sample data, using maximum regret to evaluate the performance of treatment rules. The specific new contribution is to study as-if optimization…
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…
Likelihood ratio tests are widely used to test statistical hypotheses about parametric families of probability distributions. If interest is restricted to a subfamily of distributions, then it is natural to inquire if the restricted LRT is…
Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman--Pearson…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
Understanding how humans respond to uncertainty is critical for designing safe and effective physical human-robot interaction (pHRI), as physically working with robots introduces multiple sources of uncertainty, including trust, comfort,…