@article{kachouie_lin_schwartzman_2017, title={FDR control of detected regions by multiscale matched filtering}, volume={46}, ISSN={["1532-4141"]}, DOI={10.1080/03610918.2014.957842}, abstractNote={ABSTRACT Feature extraction from observed noisy samples is a common important problem in statistics and engineering. This paper presents a novel general statistical approach to the region detection problem in long data sequences. The proposed technique is a multiscale kernel regression in conjunction with statistical multiple testing for region detection while controlling the false discovery rate (FDR) and maximizing the signal-to-noise ratio via matched filtering. This is achieved by considering a one-dimensional region detection problem as its equivalent zero-dimensional peak detection problem. The detection method does not require a priori knowledge of the shape of the nonzero regions. However, if the shape of the nonzero regions is known a priori, e.g., rectangular pulse, the signal regions can also be reconstructed from the detected peaks, seen as their topological point representatives. Simulations show that the method can effectively perform signal detection and reconstruction in the simulated data under high noise conditions, while controlling the FDR of detected regions and their reconstructed length.}, number={1}, journal={COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION}, author={Kachouie, Nezamoddin N. and Lin, Xihong and Schwartzman, Armin}, year={2017}, pages={127–144} }
 @article{ellingson_groisser_osborne_patrangenaru_schwartzman_2017, title={Nonparametric bootstrap of sample means of positive-definite matrices with an application to diffusion-tensor-imaging data analysis}, volume={46}, ISSN={["1532-4141"]}, DOI={10.1080/03610918.2015.1136413}, abstractNote={ABSTRACT This paper presents nonparametric two-sample bootstrap tests for means of random symmetric positive-definite (SPD) matrices according to two different metrics: the Frobenius (or Euclidean) metric, inherited from the embedding of the set of SPD metrics in the Euclidean set of symmetric matrices, and the canonical metric, which is defined without an embedding and suggests an intrinsic analysis. A fast algorithm is used to compute the bootstrap intrinsic means in the case of the latter. The methods are illustrated in a simulation study and applied to a two-group comparison of means of diffusion tensors (DTs) obtained from a single voxel of registered DT images of children in a dyslexia study.}, number={6}, journal={COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION}, author={Ellingson, Leif and Groisser, David and Osborne, Daniel and Patrangenaru, Vic and Schwartzman, Armin}, year={2017}, pages={4851–4879} }
 @article{scherrer_schwartzman_taquet_sahin_prabhu_warfield_2016, title={Characterizing brain tissue by assessment of the distribution of anisotropic microstructural environments in diffusion-compartment imaging (DIAMOND)}, volume={76}, number={3}, journal={Magnetic Resonance in Medicine}, author={Scherrer, B. and Schwartzman, A. and Taquet, M. and Sahin, M. and Prabhu, S. P. and Warfield, S. K.}, year={2016}, pages={963–977} }
 @article{schwartzman_2016, title={Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices}, volume={84}, ISSN={["1751-5823"]}, DOI={10.1111/insr.12113}, abstractNote={Summary}, number={3}, journal={INTERNATIONAL STATISTICAL REVIEW}, author={Schwartzman, Armin}, year={2016}, month={Dec}, pages={456–486} }
 @article{cheng_schwartzman_2015, title={Distribution of the height of local maxima of Gaussian random fields}, volume={18}, ISSN={["1572-915X"]}, DOI={10.1007/s10687-014-0211-z}, abstractNote={Let {f(t) : t ∈ T} be a smooth Gaussian random field over a parameter space T, where T may be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum [Formula: see text] is a local maximum of f(t)} when f is non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribution of a local maximum [Formula: see text] is a local maximum of f(t) and f(t0) > v} as v → ∞. Assuming further that f is isotropic, we apply techniques from random matrix theory related to the Gaussian orthogonal ensemble to compute such conditional probabilities explicitly when T is Euclidean or a sphere of arbitrary dimension. Such calculations are motivated by the statistical problem of detecting peaks in the presence of smooth Gaussian noise.}, number={2}, journal={EXTREMES}, author={Cheng, Dan and Schwartzman, Armin}, year={2015}, month={Jun}, pages={213–240} }
 @article{sun_reich_cai_guindani_schwartzman_2015, title={False discovery control in large-scale spatial multiple testing}, volume={77}, ISSN={["1467-9868"]}, DOI={10.1111/rssb.12064}, abstractNote={Summary}, number={1}, journal={JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY}, author={Sun, Wenguang and Reich, Brian J. and Cai, T. Tony and Guindani, Michele and Schwartzman, Armin}, year={2015}, month={Jan}, pages={59–83} }
 @article{kachouie_gerke_huybers_schwartzman_2015, title={Nonparametric Regression for Estimation of Spatiotemporal Mountain Glacier Retreat From Satellite Images}, volume={53}, ISSN={["1558-0644"]}, DOI={10.1109/tgrs.2014.2334643}, abstractNote={Historical variations in the extent of mountain glaciers give insight into natural and forced changes of these bellwethers of the climate. Because of the limited number of ground observations relative to the number of glaciers, it is useful to develop techniques that permit for the monitoring of glacier systems using satellite imagery. Here, we propose a new approach for identifying the glacier terminus over time from Landsat images. The proposed method permits for detecting inflection points in multispectral satellite imagery taken along a glacier's flow path in order to identify candidate terminus locations. A gated tracking algorithm is then applied to identify the best candidate for the glacier terminus location through time. Finally, the long-term trend of the terminus position is estimated with uncertainty bounds. This is achieved by applying nonparametric regression to the temporal sequence of estimated terminus locations. The method is shown to give results consistent with ground-based observations for the Franz Josef and Gorner glaciers and is further applied to estimate the retreat of Viedma, a glacier with no available ground measurements.}, number={3}, journal={IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING}, author={Kachouie, Nezamoddin N. and Gerke, Travis and Huybers, Peter and Schwartzman, Armin}, year={2015}, month={Mar}, pages={1135–1149} }
 @article{jung_schwartzman_groisser_2015, title={SCALING-ROTATION DISTANCE AND INTERPOLATION OF SYMMETRIC POSITIVE-DEFINITE MATRICES}, volume={36}, ISSN={["1095-7162"]}, DOI={10.1137/140967040}, abstractNote={We introduce a new geometric framework for the set of symmetric positive-definite (SPD) matrices, aimed at characterizing deformations of SPD matrices by individual scaling of eigenvalues and rotation of eigenvectors of the SPD matrices. To characterize the deformation, the eigenvalue-eigenvector decomposition is used to find alternative representations of SPD matrices and to form a Riemannian manifold so that scaling and rotations of SPD matrices are captured by geodesics on this manifold. The problems of nonunique eigen-decompositions and eigenvalue multiplicities are addressed by finding minimal-length geodesics, which gives rise to a distance and an interpolation method for SPD matrices. Computational procedures for evaluating the minimal scaling-rotation deformations and distances are provided for the most useful cases of $2 \times 2$ and $3 \times 3$ SPD matrices. In the new geometric framework, minimal scaling-rotation curves interpolate eigenvalues at constant logarithmic rate, and eigenvectors at...}, number={3}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, author={Jung, Sungkyu and Schwartzman, Armin and Groisser, David}, year={2015}, pages={1180–1201} }
 @article{azriel_schwartzman_2015, title={The Empirical Distribution of a Large Number of Correlated Normal Variables}, volume={110}, ISSN={["1537-274X"]}, DOI={10.1080/01621459.2014.958156}, abstractNote={Motivated by the advent of high-dimensional, highly correlated data, this work studies the limit behavior of the empirical cumulative distribution function (ecdf) of standard normal random variables under arbitrary correlation. First, we provide a necessary and sufficient condition for convergence of the ecdf to the standard normal distribution. Next, under general correlation, we show that the ecdf limit is a random, possible infinite, mixture of normal distribution functions that depends on a number of latent variables and can serve as an asymptotic approximation to the ecdf in high dimensions. We provide conditions under which the dimension of the ecdf limit, defined as the smallest number of effective latent variables, is finite. Estimates of the latent variables are provided and their consistency proved. We demonstrate these methods in a real high-dimensional data example from brain imaging where it is shown that, while the study exhibits apparently strongly significant results, they can be entirely explained by correlation, as captured by the asymptotic approximation developed here. Supplementary materials for this article are available online.}, number={511}, journal={JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION}, author={Azriel, David and Schwartzman, Armin}, year={2015}, month={Sep}, pages={1217–1228} }