03268nam 22006015 450 991048311890332120250609110559.0981-13-2616-910.1007/978-981-13-2616-5(CKB)4100000011321553(MiAaPQ)EBC6238665(DE-He213)978-981-13-2616-5(PPN)248593315(MiAaPQ)EBC6238690(EXLCZ)99410000001132155320200628d2020 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNon-Asymptotic Analysis of Approximations for Multivariate Statistics /by Yasunori Fujikoshi, Vladimir V. Ulyanov1st ed. 2020.Singapore :Springer Nature Singapore :Imprint: Springer,2020.1 online resource (133 pages)JSS Research Series in Statistics,2364-0065981-13-2615-0 Includes bibliographical references.1. Introduction -- 2. Correlation Coefficient -- 3. MANOVA Test Statistics -- 4. Linear and Quadratic Discriminant Functions -- 5. Bootstrap Confidence Sets -- 6. Gaussian Comparison -- 7. Cornish-Fisher Expansions -- 8 Approximations for Statistics Based on Random Sample Sizes -- 9. Power-divergence Statistics -- 10.General Approach to Construct Non-asymptotic Bounds -- 11 - Other Topics -- Index.This book presents recent non-asymptotic results for approximations in multivariate statistical analysis. The book is unique in its focus on results with the correct error structure for all the parameters involved. Firstly, it discusses the computable error bounds on correlation coefficients, MANOVA tests and discriminant functions studied in recent papers. It then introduces new areas of research in high-dimensional approximations for bootstrap procedures, Cornish–Fisher expansions, power-divergence statistics and approximations of statistics based on observations with random sample size. Lastly, it proposes a general approach for the construction of non-asymptotic bounds, providing relevant examples for several complicated statistics. It is a valuable resource for researchers with a basic understanding of multivariate statistics. .JSS Research Series in Statistics,2364-0065StatisticsMathematical statisticsData processingStatisticsStatistical Theory and MethodsStatistics and ComputingApplied StatisticsStatistics.Mathematical statisticsData processing.Statistics.Statistical Theory and Methods.Statistics and Computing.Applied Statistics.519.535Fujikoshi Yasunoriauthttp://id.loc.gov/vocabulary/relators/aut618912Ulyanov Vladimir Vauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910483118903321Non-Asymptotic Analysis of Approximations for Multivariate Statistics2351475UNINA