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We develop a new approach for estimating the risk of an arbitrary estimator of the mean vector in the classical normal means problem. The key idea is to generate two auxiliary data vectors, by adding carefully constructed normal noise…
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…
In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to…
Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…
Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…
In longitudinal studies, time-varying covariates are often endogenous, meaning their values depend on both their own history and that of the outcome variable. This violates key assumptions of Generalized Linear Mixed Effects Models (GLMMs),…
Detecting abrupt changes in the mean of a time series, so-called changepoints, is important for many applications. However, many procedures rely on the estimation of nuisance parameters (like long-run variance). Under the alternative (a…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is…
In this paper, change-point problems for long memory stochastic volatility models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting…
We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…
The dissertation provides a comparative analysis of a number of variability tools currently in use. It serves as a catalogue for practitioners interested in the topic. We compare a range of modelling, configuring, and management tools for…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
We propose using a permutation test to detect discontinuities in an underlying economic model at a known cutoff point. Relative to the existing literature, we show that this test is well suited for event studies based on time-series data.…
We propose a new lack-of-fit test for quantile regression models that is suitable even with high-dimensional covariates. The test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the…
In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic…
We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing…
We introduce a rank-based bent linear regression with an unknown change point. Using a linear reparameterization technique, we propose a rank-based estimate that can make simultaneous inference on all model parameters, including the…
This article considers testing for mean-level shifts in functional data. The class of the famous Darling-Erd\H{o}s-type cumulative sums (CUSUM) procedures is extended to functional time series under short range dependence conditions which…
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…