49. Virta J. (2026) Spatial depth for data in metric spaces. Accepted for publication in Scandinavian Journal of Statistics.\u00a0<\/em>Preprint in arXiv<\/a>.<\/p>\n 48. Radoji\u010di\u0107 U., Nordhausen K., Virta J. (2026) Unsupervised linear discrimination using skewness. Journal of Multivariate Analysis, <\/em>211, 105524. Preprint in arXiv<\/a>.<\/p>\n 47. Heinonen L., Virta J. (2026) A method for sparse and robust independent component analysis. Journal of Multivariate Analysis,<\/em>\u00a0213, May 2026, 105587. <\/em>Preprint in arXiv<\/a>.<\/p>\n 46. Perkonoja K., Auranen K., Virta J. (2025) Methods for generating and evaluating synthetic longitudinal patient data: a systematic review. Journal of Healthcare Informatics Research, <\/em>10, 1-39. Preprint in arXiv<\/a>.<\/p>\n 45. Virta J., Nordhausen K., Nagy S. (2025) Projection-based estimators for matrix\/tensor-valued data. Accepted for publication in Scandinavian Journal of Statistics.<\/em><\/p>\n 44. Radoji\u010di\u0107 U., Virta J. (2025) Dimension estimation in a spiked covariance model using high-dimensional data augmentation. Biometrika,<\/em> 112(4). Preprint in arXiv<\/a>.<\/p>\n 43. Sotoudehnia-Falck P., Virta J., Lehto K., Tyystj\u00e4rvi E. (2025) Quince seed mucilage as an alternative for agar in plant tissue culture. Discover Plants, <\/em>2, 224.<\/p>\n 42. Radoji\u010di\u0107 U., Nordhausen K., Virta J. (2025) Kurtosis-based projection pursuit for matrix-valued data. Annals of Statistics,<\/em>\u00a053(6), 2563-2591. Preprint in arXiv<\/a>.<\/p>\n 41. Kartiosuo N., Virta J., Nevalainen J., Raitakari O., Auranen K. (2025) On the distribution of isometric log-ratio coordinates under extra-multinomial count data. Statistical Papers, <\/em>66.<\/p>\n 40. Virta J. (2025) Measure of shape for object data. Accepted for publication in Journal of Nonparametric Statistics<\/em>.<\/p>\n 39. Radoji\u010di\u0107 U., Lietz\u00e9n N., Nordhausen K., Virta J. (2025) Order determination for tensor-valued observations using data augmentation. Journal of Computational and Graphical Statistics, <\/em>35(1), 40-50.<\/p>\n 38. Heinonen L., Nyberg H., Virta J. (2025) Weighted embedding and outlier detection of metric space data. Advances in Data Analysis and Classification<\/em>, 1-37.<\/p>\n 37. Archimbaud A., Boulfani F., Gendre X., Nordhausen K., Ruiz-Gazen A., Virta J. (2022) ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control. Accepted for publication in Econometrics and Statistics<\/em>.<\/p>\n 36. Virta J., Artemiou A. (2024) Structure-preserving non-linear PCA for matrices. IEEE Transactions on Signal Processing, <\/em>72, 3658-3668. Preprint in arXiv<\/a>.<\/p>\n 35. Perkonoja K., Virta J. (2024) Asymptotic utility of spectral anonymization. In the proceedings of Privacy in Statistical Databases<\/em> (PSD2024), 51-66. Preprint in arXiv<\/a>.<\/p>\n 34. Bachoc F., M\u00fchlmann C., Nordhausen K., Virta J. (2024) Large-Sample Properties of Non-Stationary Source Separation for Gaussian Signals. Electronic Journal of Statistics<\/em>, Vol. 18, No. 1, 2241-2291.\u00a0Preprint in arXiv<\/a>.<\/p>\n 33. Virta J., Lietz\u00e9n N., Viitasaari L., Ilmonen P. (2024) Latent model extreme value index estimation. Journal of Multivariate Analysis<\/em>, Volume 202, July 2024, 105300.\u00a0Preprint in arXiv<\/a>.<\/p>\n 32. Virta J., Lietz\u00e9n N., and Nyberg H. (2023) Robust signal dimension estimation via SURE. Accepted for publication in Statistical Papers<\/em>. Preprint in arXiv<\/a>.<\/p>\n 31. Autio R., Virta J., Nordhausen K., Fogelholm M., Erkkola M., and Nevalainen J. (2023) Tensorial principal component analysis in detecting temporal trajectories of purchase patterns in loyalty card data: Cohort study. Journal of Medical Internet Research,<\/em> 25, e44599.<\/p>\n 30. Virta J., Artemiou A. (2023) Poisson PCA for matrix count data. Pattern\u00a0<\/em>Recognition,\u00a0<\/i>138, 109401.<\/i>\u00a0Preprint in arXiv<\/a>.<\/p>\n 29. Nordhausen, K., Taskinen, S. and Virta, J. (2022) Signal Dimension Estimation in BSS Models with Serial Dependence. In the proceedings of the 2nd International Conference on Electrical, Computer, Communications and Mechatronics Engineering<\/em> (ICECCME), 360-366.<\/p>\n 28. Virta J., Lee K.-Y., Li L. (2022) Sliced inverse regression in metric spaces. Statistica Sinica<\/em>, 32, p. 2315-2337. Preprint in arXiv<\/a>.<\/p>\n 27. Leskinen T., Pasanen J., Suorsa K., Pulakka A., Virta J., Auranen K., Stenholm S. (2022) Effects of physical activity intervention on 24-hour movement behaviors: A compositional data analysis. Scientific Reports<\/i>, 12<\/i>(1), 8712.<\/p>\n 26. H\u00e4nninen J., M\u00e4kinen K., Nordhausen K., Laaksonlaita J., Loisa O., Virta, J. (2022) The \u201cSeili-index\u201d for the prediction of chlorophyll- \u03b1 levels in the archipelago sea of the northern Baltic Sea, Southwest Finland. Environmental Modeling & Assessment<\/i>, 27<\/i>(4), 571-584.<\/p>\n 25. Radoji\u010di\u0107 U., Nordhausen K., Virta J. (2021), Large-sample properties of blind estimation of the linear discriminant using projection pursuit. Electronic Journal of Statistics<\/em>, 15(2), p. 6677-6739.<\/em>\u00a0Preprint in arXiv<\/a>.<\/p>\n 24. Virta J. (2021), Testing for subsphericity when n and p are of different asymptotic order. Statistics & Probability Letters<\/em>, 179, 109209. Link.<\/a><\/p>\n 23. Radoji\u010di\u0107 U., Lietz\u00e9n N., Nordhausen K., Virta J. (2021), Dimension estimation in two-dimensional PCA. Accepted for publication in the proceedings of the 12th International Symposium on Image and Signal Processing and Analysis (ISPA)<\/em>.<\/p>\n 22. Paindaveine D., Virta J. (2021), On the behavior of extreme spatial quantiles under minimal assumptions. In A. Daouia and A. Ruiz-Gazen (editors) Advances in Contemporary Statistics and Econometrics: Festschrift in Honor of Christine Thomas-Agnan<\/em>, p. 243-260, Springer, Cham.<\/p>\n 21. Nordhausen K., Matilainen M., Miettinen J., Virta J., Taskinen S. (2021), Dimension reduction for timeseries in a BSS context using R. Journal of Statistical Software<\/em>, 98, p. 1-30.<\/p>\n 20. Virta J., Lietz\u00e9n N., Ilmonen P., Nordhausen K. (2021), Fast tensorial JADE. Scandinavian Journal of Statistics<\/em>, 48(1), p. 164-187. Preprint in arXiv<\/a>.<\/p>\n 19. Virta J., Nordhausen K. (2021), Determining the signal dimension in second order source separation. Statistica Sinica<\/em>, 31, p. 135-156. Preprint in arXiv<\/a>.<\/p>\n 18. Bachoc F., Genton M.G., Nordhausen K., Ruiz-Gazen A., Virta J. (2020), Spatial blind source separation. Biometrika<\/em>, 107, p. 627-646. Preprint in arXiv<\/a>.<\/p>\n 17. Lietz\u00e9n N., Virta J., Nordhausen K., Ilmonen P.(2020), Minimum distance index for BSS, Generalization, interpretation and asymptotics. Austrian Journal of Statistics<\/em>, 49, p. 57-68.<\/p>\n 16. Virta J., Li B., Oja H., Nordhausen K. (2020), Independent component analysis for multivariate functional data. Journal of Multivariate Analysis<\/em>, 176, 104568. Preprint in arXiv<\/a>.<\/p>\n 15. Lietz\u00e9n N., Virta J., Nordhausen K., Ilmonen P. (2019), Minimum distance index for non-square complex valued mixing matrices. In Filzmoser P. and Kharin Y. (editors) Proceedings of the 12th International Conference on Computer Data Analysis and Modeling<\/em>, p. 79-86, Minsk Publishing Center BSU, Minsk.<\/p>\n 14. Virta J., Nordhausen K. (2019), Estimating the number of signals using principal component analysis. Stat<\/em>, 8, e231.<\/p>\n 13. Nordhausen K., Virta J. (2019), An overview of properties and extensions of FOBI. Knowledge-Based Systems<\/em>, 173, p. 113-116.<\/p>\n 12. Teschendorff A., Han J., Paul D., Virta J., Nordhausen K. (2018), Tensorial blind source separation for improved analysis of multi-omic data. Genome Biology<\/em>, 19, 76. Preprint in bioRxiv<\/a>.<\/p>\n 11. Nordhausen K., Virta J. (2018), Ladle estimator for time series signal dimension. In the proceedings of IEEE Statistical Signal Processing Workshop (SSP)<\/em>, p. 428-432.<\/p>\n 10. Matilainen M., Nordhausen K., Virta J. (2018), On the number of signals in multivariate time series. In Deville Y., Gannot S., Mason R., Plumbley M., Ward D. (editors) Latent Variable Analysis and Signal Separation (LVA\/ICA)<\/em>, Lecture Notes in Computer Science, 10891. Springer, Cham. Preprint in arXiv<\/a>.<\/p>\n 9. Virta J., Li B., Nordhausen K., Oja H. (2018), JADE for tensor-valued observations. Journal of Computational and Graphical Statistics<\/em>, 27(3), p. 628-637. Preprint in arXiv<\/a>..<\/p>\n 8. Virta J., Li B., Nordhausen K., Oja H. (2017), Independent component analysis for tensor-valued data. Journal of Multivariate Analysis<\/em>, 162, p. 172-192. Preprint in arXiv<\/a>.<\/p>\n 7. Virta J., Nordhausen K. (2017), Blind source separation for nonstationary tensor-valued time series. In the proceedings of IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP)<\/em>.<\/p>\n 6. Virta J., Nordhausen K. (2017), Blind source separation of tensor-valued time series. Signal Processing<\/em>,141, p. 204\u2013216. Preprint in arXiv<\/a>.<\/p>\n 5. Nordhausen K., Oja H., Tyler D.E., Virta J. (2017), Asymptotic and bootstrap tests for the dimension of the non-Gaussian subspace. IEEE Signal Processing Letters<\/em>, 24(6), p. 887\u2013891. Preprint in arXiv<\/a>.<\/p>\n 4. Virta J., Nordhausen K. (2017), On the optimal non-linearities for Gaussian mixtures in FastICA. In Tichavsk\u00fd P., Babaie-Zadeh M., Michel O., Thirion-Moreau N. (editors), Latent Variable Analysis and Signal Separation (LVA\/ICA)<\/em>. Lecture Notes in Computer Science, 10169. Springer, Cham.<\/p>\n 3. Miettinen J., Nordhausen K., Oja H., Taskinen S., Virta J. (2017), The squared symmetric FastICA estimator. Signal Processing<\/em>, 131, p. 402-411. Preprint in arXiv<\/a>.<\/p>\n 2. Virta J., Taskinen S., Nordhausen K. (2016), Applying fully tensorial ICA to fMRI data. In the proceedings of IEEE Signal Processing in Medicine and Biology Symposium 2016 (SPMB)<\/em>.<\/p>\n 1. Virta J. (2015), One-step M-estimates of scatter and the independence property. Statistics & Probability Letters<\/em>, 110, p. 133-136.<\/p>\n Virta J.: On characterizations of the covariance matrix. Preprint in arXiv<\/a>.<\/p>\n Virta J., Nordhausen K., Oja H.: Projection pursuit for non-Gaussian independent components. Preprint in arXiv<\/a>.<\/p>\nPreprints<\/h3>\n
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