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We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
We aim to develop simultaneous inference tools for the mean function of functional data from sparse to dense. First, we derive a unified Gaussian approximation to construct simultaneous confidence bands of mean functions based on the…
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived…
In this article, we consider change point inference for high dimensional linear models. For change point detection, given any subgroup of variables, we propose a new method for testing the homogeneity of corresponding regression…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the…
In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
We propose a method to infer the presence and location of change-points in the distribution of a sequence of independent data taking values in a general metric space, where change-points are viewed as locations at which the distribution of…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
We establish the convergence rates and asymptotic distributions of the common break change-point estimators, obtained by least squares and maximum likelihood in panel data models and compare their asymptotic variances. Our model assumptions…
In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…
We investigate the online detection of changepoints in the distribution of a sequence of observations using degenerate U-statistic-type processes. We study weighted versions of: an ordinary, CUSUM-type scheme, a Page-CUSUM-type scheme, and…
In this work, we establish some coincidence point results for self-mappings satisfying rational type contractions in generalized metric spaces in the sense of Branciari [7]. Presented coincidence point theorems weak and extend numerous…
In this article, we consider the estimation of the structural change point in the nonparametric model with dependent observations. We introduce a maximum-CUSUM-estimation procedure, where the CUSUM statistic is constructed based on the…
The aim of this paper is to show the interest in fitting features with an $\alpha$-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way…
Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over…
Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…
Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…