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Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
We present a robust test for change-points in time series which is based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on the two-sample U-quantile processes, in the case of short…
Residual-based goodness-of-fit tests for parametric time-series models are often complicated by parameter-estimation effects, which can alter the limiting behavior of diagnostic statistics. We propose a sample-splitting generalized spectral…
In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…
Change point testing for high-dimensional data has attracted a lot of attention in statistics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…
We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from $L_p$ norms whose behavior is similar under $H_0$ but potentially different…
Most studies in real time change-point detection either focus on the linear model or use the CUSUM method under classical assumptions on model errors. This paper considers the sequential change-point detection in a nonlinear quantile model.…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
Change point detection is a crucial aspect of analyzing time series data, as the presence of a change point indicates an abrupt and significant change in the process generating the data. While many algorithms for the problem of change point…
Time series data can be subject to changes in the underlying process that generates them and, because of these changes, models built on old samples can become obsolete or perform poorly. In this work, we present a way to incorporate…
Inferring causal directions on discrete and categorical data is an important yet challenging problem. Even though the additive noise models (ANMs) approach can be adapted to the discrete data, the functional structure assumptions make it…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…