Related papers: Functional sufficient dimension reduction through …
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…
As one of the most powerful tools for examining the association between functional covariates and a response, the functional regression model has been widely adopted in various interdisciplinary studies. Usually, a limited number of…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
Mahalanobis distance is a classical tool in multivariate analysis. We suggest here an extension of this concept to the case of functional data. More precisely, the proposed definition concerns those statistical problems where the sample…
Adjoint methods have gained popularity in recent years for driving adaptation procedures which aim to reduce error in solution functionals. While adjoint methods have been proven effective for functional-based adaptation, the practical…
Structural Health Monitoring (SHM) is increasingly applied in civil engineering. One of its primary purposes is detecting and assessing changes in structure conditions to increase safety and reduce potential maintenance downtime. Recent…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
In functional data analysis, functional linear regression has attracted significant attention recently. Herein, we consider the case where both the response and covariates are functions. There are two available approaches for addressing…
This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More…