Related papers: Detecting relevant changes in the spatiotemporal m…
This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…
Motivated by the need to statistically quantify the difference between two spatio-temporal datasets that arise in climate downscaling studies, we propose new tests to detect the differences of the covariance operators and their associated…
Consider an observation of a multivariate temporal point process $N$ with law $\mathcal P$ on the time interval $[0,T]$. To test the null hypothesis that $\mathcal P$ belongs to a given parametric family, we construct a convergent…
We present an efficient score statistic, called the $\textsf{S}^3 \textsf{T}$ statistic, to detect the emergence of a spatially and temporally correlated signal from either fixed-sample or sequential data. The signal may cause a men shift…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…
This article proposes a novel test for the martingale difference hypothesis based on the martingale difference divergence function, a recently developed dependence measure suitable for measuring the degree of conditional mean dependence of…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…
Non-terminal events can represent a meaningful change in a patient's life. Thus, better understanding and predicting their occurrence can bring valuable information to individuals. In a context where longitudinal markers could inform these…
The fundamental functional summary statistics used for studying spatial point patterns are developed for marked homogeneous and inhomogeneous point processes on the surface of a sphere. These are extended to point processes on the surface…
Sampling of a spatiotemporal field for environmental sensing is of interest. Traditionally, a few fixed stations or sampling locations aid in the reconstruction of the spatial field. Recently, there has been an interest in mobile sensing…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
We consider the problem of detecting a change point in a sequence of mean functions from a functional time series. We propose an $L^1$ norm based methodology and establish its theoretical validity both for classical and for relevant…
Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on…
Spatio-temporal point process (STPP) is a stochastic collection of events accompanied with time and space. Due to computational complexities, existing solutions for STPPs compromise with conditional independence between time and space,…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
We consider the change point testing problem for high-dimensional time series. Unlike conventional approaches, where one tests whether the difference $\delta$ of the mean vectors before and after the change point is equal to zero, we argue…