Related papers: A smooth ROC curve estimator based on log-concave …
In Statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the…
We propose a method for estimating a log-concave density on $\mathbb R^d$ from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave…
We study the smoothed log-concave maximum likelihood estimator of a probability distribution on $\mathbb{R}^d$. This is a fully automatic nonparametric density estimator, obtained as a canonical smoothing of the log-concave maximum…
In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one…
A novel computational approach to log-concave density estimation is proposed. Previous approaches utilize the piecewise-affine parametrization of the density induced by the given sample set. The number of parameters as well as non-smooth…
The Receiver Operating Characteristic (ROC) curve is a useful tool that measures the discriminating power of a continuous variable or the accuracy of a pharmaceutical or medical test to distinguish between two conditions or classes. In…
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…
We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…
In this paper, we present three estimators of the ROC curve when missing observations arise among the biomarkers. Two of the procedures assume that we have covariates that allow to estimate the propensity and the estimators are obtained…
Diagnostic tests are of critical importance in health care and medical research. Motivated by the impact that atypical and outlying test outcomes might have on the assessment of the discriminatory ability of a diagnostic test, we develop a…
Receiver Operating Characteristic (ROC) curves have recently been used to evaluate the performance of models for spatial presence-absence or presence-only data. Applications include species distribution modelling and mineral prospectivity…
We expect that some observers in perceptual signal detection experiments, such as radiologists, will make rational decisions, and therefore ratings from those observers are expected to form a convex ROC curve. However, measured and…
Receiver operating characteristic (ROC) curves are used ubiquitously to evaluate covariates, markers, or features as potential predictors in binary problems. We distinguish raw ROC diagnostics and ROC curves, elucidate the special role of…
Let X_1, ..., X_n be independent and identically distributed random vectors with a log-concave (Lebesgue) density f. We first prove that, with probability one, there exists a unique maximum likelihood estimator of f. The use of this…
We consider the nonparametric maximum likelihood estimation for the underlying event time based on mixed-case interval-censored data, under a log-concavity assumption on its distribution function. This generalized framework relaxes the…
We present a new approach for inference about a log-concave distribution: Instead of using the method of maximum likelihood, we propose to incorporate the log-concavity constraint in an appropriate nonparametric confidence set for the cdf…
Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…
We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
Pooled logistic regression models are commonly applied in survival analysis. However, the standard implementation can be computationally demanding, which is further exacerbated when using the nonparametric bootstrap for inference. To ease…