Related papers: Confidence bands for a log-concave density
We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine…
We develop a new technique for proving distribution testing lower bounds for properties defined by inequalities involving the bin probabilities of the distribution in question. Using this technique we obtain new lower bounds for…
Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools with many applications. In this paper, we propose a novel criterion for comparing SCBs for percentiles, termed the Minimum Area Confidence Set…
Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample…
Nonparametric maximum likelihood estimation is intended to infer the unknown density distribution while making as few assumptions as possible. To alleviate the over parameterization in nonparametric data fitting, smoothing assumptions are…
We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…
We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to…
Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…
Nonparametric two-stage procedures to construct fixed-width confidence intervals are studied to quantify uncertainty. It is shown that the validity of the random central limit theorem (RCLT) accompanied by a consistent and asymptotically…
We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d.~observations. Our approach…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
We study and develop multilevel methods for the numerical approximation of a log-concave probability $\pi$ on $\mathbb{R}^d$, based on (over-damped) Langevin diffusion. In the continuity of \cite{art:egeapanloup2021multilevel} concentrated…
Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object, which…
The estimation of cumulative distribution functions (CDF) and probability density functions (PDF) is a fundamental practice in applied statistics. However, challenges often arise when dealing with data arranged in grouped intervals. In this…
In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…