Related papers: Covariance and precision matrix estimation for hig…
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…
We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through…
We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column)…
High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in…
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…
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 $p$,…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an…
Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…
Temporal dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test…
Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…
In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically…
Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…