Related papers: Minimax adaptive tests for the Functional Linear m…
Multivariate functional data has received considerable attention but testing for equality of mean surfaces and its profile has limited progress. The existing literature has tested equality of either mean curves of univariate functional…
This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…
Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
Posterior drift refers to changes in the relationship between responses and covariates while the distributions of the covariates remain unchanged. In this work, we explore functional linear regression under posterior drift with transfer…
We consider the problem of sequential (online) estimation of a single change point in a piecewise linear regression model under a Gaussian setup. We demonstrate that certain CUSUM-type statistics attain the minimax optimal rates for…
We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in $\mathbb{L}^2$ norm over classical Besov bodies and weak Besov…
We consider estimation of a functional parameter of a realistically modeled data distribution based on observing independent and identically distributed observations. We define an $m$-th order Spline Highly Adaptive Lasso Minimum Loss…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
Modeling functions that are sequentially observed as functional time series is becoming increasingly common. In such models, it is often crucial to ensure data homogeneity. We investigate the sensitivity of graph-based change point…
We consider the problem of optimizing an approximately convex function over a bounded convex set in $\mathbb{R}^n$ using only function evaluations. The problem is reduced to sampling from an \emph{approximately} log-concave distribution…
We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. In a statistical context in which such functions measure loss, this says that the least favourable…
This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
In massive data analysis, training and testing data often come from very different sources, and their probability distributions are not necessarily identical. A feature example is nonparametric classification in posterior drift model where…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…