Related papers: Uniform mean estimation via generic chaining
There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…
This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…
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…
We study here weighted polynomial multiple ergodic averages. A sequence of weights is called universally good if any polynomial multiple ergodic average with this sequence of weights converges in $L^{2}$. We find a necessary condition and…
In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the…
Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of…
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an…
In the framework of supervised classification (discrimination) for functional data, it is shown that the optimal classification rule can be explicitly obtained for a class of Gaussian processes with "triangular" covariance functions. This…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual…
We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs $\inf_{(\epsilon_i)}{\sup_{f\in F}}|{\sum_{i=1}^k\epsilon_i}f(X_i)|$ is asymptotically smaller than the expectation over signs as a…
A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the…
Most existing methods for testing equality of means of functional data from multiple populations rely on assumptions of equal covariance and/or Gaussianity. In this work we provide a new testing method based on a statistic that is…
The article presents a systematic study of the problem of conditioning a Gaussian random variable $\xi$ on nonlinear observations of the form $F \circ \phi(\xi)$ where $\phi: \mathcal{X} \to \mathbb{R}^N$ is a bounded linear operator and…
Suppose that $X_1,X_2,\ldots$ are a stream of independent, identically distributed Poisson random variables with mean $\mu$. This work presents a new estimate $\mu_k$ for $\mu$ with the property that the distribution of the relative error…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…