Related papers: Optimal Confidence Bands for Shape-Restricted Curv…
We study the approximation of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H>1/2$. For the mean-square error at a single point we derive the optimal rate of convergence that can be achieved…
We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test…
Isotonic regression (IR) is shape-constrained regression to maintain a univariate fitting curve non-decreasing, which has numerous applications including single-index models and probability calibration. When it comes to multi-output…
Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…
Statistical analyses of multipopulation studies often use the data to select a particular population as the target of inference. For example, a confidence interval may be constructed for a population only in the event that its sample mean…
For a general statistical model, we introduce the notion of data dependent measure (DDM) on the model parameter. Typical examples of DDM are the posterior distributions. Like for posteriors, the quality of a DDM is characterized by the…
The dimension function D_psi of a band-limited wavelet is bounded by n if the support of its Fourier transform is contained in the interval [-{2^(n+2)/3}pi, {2^(n+2)/3}pi]. For each positive integer n and for each epsilon > 0, we construct…
A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
We consider the problem of finding confidence intervals for the risk of forecasting the future of a stationary, ergodic stochastic process, using a model estimated from the past of the process. We show that a bootstrap procedure provides…
This paper develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on…
Recently, direct data-driven prediction has found important applications for controlling unknown systems, particularly in predictive control. Such an approach provides exact prediction using behavioral system theory when noise-free data are…
Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g.,…
The existence of flat bands is generally thought to be physically possible only for dimensions larger than one. However, by exciting a system with different orthogonal states this condition can be reformulated. In this work, we demonstrate…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
Starting from the observation of an R^n-Gaussian vector of mean f and covariance matrix \sigma^2 I_n (I_n is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of…
In the nonparametric Gaussian sequence space model an $\ell^2$-confidence ball $C_n$ is constructed that adapts to unknown smoothness and Sobolev-norm of the infinite-dimensional parameter to be estimated. The confidence ball has exact and…
A perturbative approach is used to quantify the effect of noise in data points on fitted parameters in a general homogeneous linear model, and the results applied to the case of conic sections. There is an optimal choice of normalisation…
We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…