Related papers: Inference for the mode of a log-concave density
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…
We investigate the likelihood ratio test for a large block-diagonal covariance matrix with an increasing number of blocks under the null hypothesis. While so far the likelihood ratio statistic has only been studied for normal populations,…
Bi-log-concavity of probability measures is a univariate extension of the notion of log-concavity that has been recently proposed in a statistical literature. Among other things, it has the nice property from a modelisation perspective to…
Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…
Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…
Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…
This study aims to evaluate the performance of power in the likelihood ratio test for changepoint detection by bootstrap sampling, and proposes a hypothesis test based on bootstrapped confidence interval lengths. Assuming i.i.d normally…
In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…
Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum…
We study the transformed hazards model with time-dependent covariates observed intermittently for the censored outcome. Existing work assumes the availability of the whole trajectory of the time-dependent covariates, which is unrealistic.…
To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic. We also study confidence regions based on the likelihood…
This paper utilizes the modified signed log-likelihood ratio method for the problem of inference about the common coefficient of variation in several independent normal populations. This method is applicable for both the problem of…
The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC) distributions.…
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…
AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…
We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…