Related papers: High dimensional PCA: a new model selection criter…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…
In multivariate extreme value analysis, the estimation of the dependence structure in extremes is demanding, especially in the context of high-dimensional data. Therefore, a common approach is to reduce the model dimension by considering…
We propose two methods to evaluate the conditional Akaike information (cAI) for nonlinear mixed-effects models with no restriction on cluster size. Method 1 is designed for continuous data and includes formulae for the derivatives of fixed…
We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…
The semiparametric estimation approach, which includes inverse-probability-weighted and doubly robust estimation using propensity scores, is a standard tool in causal inference, and it is rapidly being extended in various directions. On the…
In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
In statistical modeling area, the Akaike information criterion AIC, is a widely known and extensively used tool for model choice. The {\phi}-divergence test statistic is a recently developed tool for statistical model selection. The…
Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed…
Based on some new robust estimators of the covariance matrix, we propose stable versions of Principal Component Analysis (PCA) and we qualify it independently of the dimension of the ambient space. We first provide a robust estimator of the…
Indirect comparisons of treatment-specific outcomes across separate studies often inform decision-making in the absence of head-to-head randomized comparisons. Differences in baseline characteristics between study populations may introduce…
Independent Component Analysis (ICA) is a fundamental unsupervised learning technique foruncovering latent structure in data by separating mixed signals into their independent sources. While substantial progress has been made in…
This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in…
Bayesian model averaging, model selection and its approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates og convergence than other methods such as AIC and leave-one-out cross-validation. On the…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is…
We propose a modified, high-dimensional version of a recent dimension estimation procedure that determines the dimension via the introduction of augmented noise variables into the data. Our asymptotic results show that the proposal is…
We emphasize that it is possible to improve the principle of unbiased risk estimation for model selection by addressing excess risk deviations in the design of penalization procedures. Indeed, we propose a modification of Akaike's…