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This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we…
Confidence bounds are an essential tool for rigorously quantifying the uncertainty of predictions. They are a core component in many sequential learning and decision-making algorithms, with tighter confidence bounds giving rise to…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…
Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating…
Our aim is to estimate the largest community (a.k.a., mode) in a population composed of multiple disjoint communities. This estimation is performed in a fixed confidence setting via sequential sampling of individuals with replacement. We…
An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold…
In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…
A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…
Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…
Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…
The problem of probabilistic verification of a neural network investigates the probability of satisfying the safe constraints in the output space when the input is given by a probability distribution. It is significant to answer this…
The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more…
Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. The existing methods often require correct model specifications for both outcome and response models. However, due to…
We study a likelihood ratio test for the location of the mode of a log-concave density. Our test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…
Bayesian inference for spatial point patterns is often hindered computationally by intractable likelihoods. In the frequentist literature, estimating equations utilizing pseudolikelihoods have long been used for simulation-free parameter…