175 research outputs found
Robustifying principal component analysis with spatial sign vectors
No full textSara Taskinen, Inge Koch, Hannu Oj
Nonparametric location estimators in the randomized complete block design
No full textSeveral tests for the comparison of different groups in the randomized complete block design exist. However, there is a lack of robust estimators for the location difference between one group and all the others on the original scale. The relative marginal effects are commonly used in this situation, but they are more difficult to interpret and use by less experienced people because of the different scale. In this paper two nonparametric estimators for the comparison of one group against the others in the randomized complete block design will be presented. Theoretical results such as asymptotic normality, consistency, translation invariance, scale preservation, unbiasedness, and median unbiasedness are derived. The finite sample behavior of these estimators is derived by simulations of different scenarios. In addition, possible confidence intervals with these estimators are discussed and their behavior derived also by simulations
Rank scores tests of multivariate independence
No full textNew rank scores test statistics are proposed for testing whether two random vectors are independent. The tests are asymptotically distribution-free for elliptically symmetric marginal distributions. Recently, Gieser and Randles (1997), Taskinen, Kankainen and Oja (2003) and Taskinen, Oja and Randles (2005) introduced and discussed different multivariate extensions of the quadrant test, Kendall's tau and Spearman's rho statistics. In this paper, standardized multivariate spatial signs and the (univariate) ranks of the Mahalanobis-type distances of the observations from the origin are combined to construct ranks cores tests of independence. The limiting distributions of the test statistics are derived under the null hypothesis as well as under contiguous sequences of alternatives. Three different choices of the score functions, namely the sign scores, the Wilcoxon scores and the van der Waerden scores, are discussed in greater detail. The small sample and limiting efficiencies of the test procedures ara compared and the robustness properties are illustrated by an example. It is remarkable that, in the multinormal case, the limiting Pitman efficience of the van der Waerden scores test equals to that of the classical parametric Wilks’s test.peerReviewe
Monomial basis in Korenblum type spaces of analytic functions
No full text[EN] It is shown that the monomials A = (z(n))(n=0)(infinity) are a Schauder basis of the Frechet spaces A(+)(-gamma), gamma >= 0, that consists of all the analytic functions f on the unit disc such that (1 - vertical bar z vertical bar)(mu)vertical bar f(z)vertical bar is bounded for all mu > gamma. Lusky proved that A is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type H-infinity. A sequence space representation of the Frechet space A(+)(-gamma) is presented. The case of (LB)-spaces A(-)(-gamma), gamma > 0, that are defined as unions of weighted Banach spaces is also studied.Research of the third author was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2018). Monomial basis in Korenblum type spaces of analytic functions. Proceedings of the American Mathematical Society. 146(12):5269-5278. https://doi.org/10.1090/proc/14195S526952781461
Modelling multivariate spatio-temporal data with identifiable variational autoencoders
No full textModelling multivariate spatio-temporal data with complex dependency structures is a challenging task but can be simplified by assuming that the original variables are generated from independent latent components. If these components are found, they can be modelled univariately. Blind source separation aims to recover the latent components by estimating the unknown linear or nonlinear unmixing transformation based on the observed data only. In this paper, we extend recently introduced identifiable variational autoencoder to the nonlinear nonstationary spatio-temporal blind source separation setting and demonstrate its performance using comprehensive simulation studies. Additionally, we introduce two alternative methods for the latent dimension estimation, which is a crucial task in order to obtain the correct latent representation. Finally, we illustrate the proposed methods using a meteorological application, where we estimate the latent dimension and the latent components, interpret the components, and show how nonstationarity can be accounted and prediction accuracy can be improved by using the proposed nonlinear blind source separation method as a preprocessing method
On boundedness and compactness of Toeplitz operators in weighted H-infinity-spaces
No full text[EN] We characterize the boundedness and compactness of Toeplitz operators T-a with radial symbols a in weighted H-infinity-spaces H(v)(infinity)on the open unit disc of the complex plane. The weights v are also assumed radial and to satisfy the condition (B) introduced by the second named author. The main technique uses Taylor coefficient multipliers, and the results are first proved for them. We formulate a related sufficient condition for the boundedness and compactness of Toeplitz operators in reflexive weighted Bergman spaces on the disc. We also construct a bounded harmonic symbol f such that T-f is not bounded in H-v(infinity) for any v satisfying mild assumptions. As a corollary, the Bergman projection is never bounded with respect to the corresponding weighted sup-norms. However, we also show that, for normal weights v, all Toeplitz operators with a trigonometric polynomial as the symbol are bounded on H-v(infinity) . (C) 2020 Elsevier Inc. All rights reserved.The research of Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102 (Spain). The research of Taskinen was partially supported by a research grant from the Faculty of Science of the University of Helsinki.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2020). On boundedness and compactness of Toeplitz operators in weighted H-infinity-spaces. Journal of Functional Analysis. 278(10):1-26. https://doi.org/10.1016/j.jfa.2019.108456S12627810Bonet, J., Lusky, W., & Taskinen, J. (2018). Solid hulls and cores of weighted H ∞ -spaces. Revista Matemática Complutense, 31(3), 781-804. doi:10.1007/s13163-018-0265-6Bonet, J., Lusky, W., & Taskinen, J. (2019). Solid cores and solid hulls of weighted Bergman spaces. Banach Journal of Mathematical Analysis, 13(2), 468-485. doi:10.1215/17358787-2018-0049Constantin, O., & Peláez, J. Á. (2015). Boundedness of the Bergman projection on Lp-spaces with exponential weights. Bulletin des Sciences Mathématiques, 139(3), 245-268. doi:10.1016/j.bulsci.2014.08.012Dostanić, M. R. (2004). UNBOUNDEDNESS OF THE BERGMAN PROJECTIONS ON SPACES WITH EXPONENTIAL WEIGHTS. Proceedings of the Edinburgh Mathematical Society, 47(1), 111-117. doi:10.1017/s0013091501000190Engliš, M. (2008). Toeplitz operators and weighted Bergman kernels. Journal of Functional Analysis, 255(6), 1419-1457. doi:10.1016/j.jfa.2008.06.026Grudsky, S., & Vasilevski, N. (2001). Bergman-Toeplitz operators: Radial component influence. Integral Equations and Operator Theory, 40(1), 16-33. doi:10.1007/bf01202952Harutyunyan, A., & Lusky, W. (2010). On L1-subspaces of holomorphic functions. Studia Mathematica, 198(2), 157-175. doi:10.4064/sm198-2-4Luecking, D. H. (1987). Trace ideal criteria for Toeplitz operators. Journal of Functional Analysis, 73(2), 345-368. doi:10.1016/0022-1236(87)90072-3Luecking, D. H. (2007). Finite rank Toeplitz operators on the Bergman space. Proceedings of the American Mathematical Society, 136(05), 1717-1724. doi:10.1090/s0002-9939-07-09119-8Lusky, W. (1995). On Weighted Spaces of Harmonic and Holomorphic Functions. Journal of the London Mathematical Society, 51(2), 309-320. doi:10.1112/jlms/51.2.309Lusky, W. (2006). On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Mathematica, 175(1), 19-45. doi:10.4064/sm175-1-2Lusky, W., & Taskinen, J. (2008). Bounded holomorphic projections for exponentially decreasing weights. Journal of Function Spaces and Applications, 6(1), 59-70. doi:10.1155/2008/217160Lusky, W., & Taskinen, J. (2011). Toeplitz operators on Bergman spaces and Hardy multipliers. Studia Mathematica, 204(2), 137-154. doi:10.4064/sm204-2-3Mannersalo, P. (2016). Toeplitz operators with locally integrable symbols on Bergman spaces of bounded simply connected domains. Complex Variables and Elliptic Equations, 61(6), 854-874. doi:10.1080/17476933.2015.1120293STROETHOFF, K. (1998). Compact Toeplitz operators on Bergman spaces. Mathematical Proceedings of the Cambridge Philosophical Society, 124(1), 151-160. doi:10.1017/s0305004197002375Taskinen, J., & Virtanen, J. (2010). Toeplitz operators on Bergman spaces with locally integrable symbols. Revista Matemática Iberoamericana, 693-706. doi:10.4171/rmi/614Zorboska, N. (2003). Toeplitz operators with BMO symbols and the Berezin transform. International Journal of Mathematics and Mathematical Sciences, 2003(46), 2929-2945. doi:10.1155/s016117120321203
Multivariate nonparametric tests of independence
No full textNew test statistics are proposed for testing whether two random vectors are independent. Gieser and Randles, as well as Taskinen, Kankainen, and Oja have introduced and discussed multivariate extensions of the quadrant test of Blomqvist. This article serves as a sequel to this work and presents new multivariate extensions of Kendall's tau and Spearman's rho statistics. Two different approaches are discussed. First, interdirection proportions are used to estimate the cosines of angles between centered observation vectors and between differences of observation vectors. Second, covariances between affine-equivariant multivariate signs and ranks are used. The test statistics arising from these two approaches appear to be asymptotically equivalent if each vector is elliptically symmetric. The spatial sign versions are easy to compute for data in common dimensions, and they provide practical, robust alternatives to normal-theory methods. Asymptotic theory is developed to approximate the finite-sample null distributions as well, as to calculate limiting Pitman efficiencies. Small-sample null permutation distributions are also described. A simple simulation study is used to compare the proposed tests with the classical Wilks test. Finally, the theory is illustrated by an example.peerReviewe
Spectral gaps for the linear water-wave problem in a channel with thin structures
No full textPeer reviewe
fICA : FastICA Algorithms and Their Improved Variants
No full textAbstract In independent component analysis (ICA) one searches for mutually independent non gaussian latent variables when the components of the multivariate data are assumed to be linear combinations of them. Arguably, the most popular method to perform ICA is FastICA. There are two classical versions, the deflation-based FastICA where the components are found one by one, and the symmetric FastICA where the components are found simultaneously. These methods have been implemented previously in two R packages, fastICA and ica. We present the R package fICA and compare it to the other packages. Additional features in fICA include optimization of the extraction order in the deflation-based version, possibility to use any nonlinearity function, and improvement to convergence of the deflation-based algorithm. The usage of the package is demonstrated by applying it to the real ECG data of a pregnant woman.peerReviewe
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