Related papers: A bootstrap approximation to Lp_statistic of kerne…
A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…
Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…
We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an $n\times p$ data matrix $X$. We focus on the modern framework where $p/n$ is not close to 0 but…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue…
In this paper we consider the construction of simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for classical lag-window spectral density estimators evaluated at the set of all…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
In the spatial point process context, kernel intensity estimation has been mainly restricted to exploratory analysis due to its lack of consistency. Different methods have been analysed to overcome this problem, and the inclusion of…
This paper considers a new bootstrap procedure to estimate the distribution of high-dimensional $\ell_p$-statistics, i.e. the $\ell_p$-norms of the sum of $n$ independent $d$-dimensional random vectors with $d \gg n$ and $p \in [1,…
This paper studies the Gaussian and bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when the dimension $d$ is large. A two-step Gaussian approximation…
Structural equation models and Bayesian networks have been widely used to study causal relationships between continuous variables. Recently, a non-Gaussian method called LiNGAM was proposed to discover such causal models and has been…
The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
Non-asymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
This paper is concerned with testing global null hypotheses about population mean vectors of high-dimensional data. Current tests require either strong mixing (independence) conditions on the individual components of the high-dimensional…
We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing…
Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] proposed the Adaptive LASSO (ALASSO) method for simultaneous variable selection and estimation of the regression parameters, and established its oracle property. In this paper, we…