ctmva - Continuous-Time Multivariate Analysis

Implements a basis function or functional data analysis framework for several techniques of multivariate analysis in continuous-time setting. Specifically, we introduced continuous-time analogues of several classical techniques of multivariate analysis, such as principal component analysis, canonical correlation analysis, Fisher linear discriminant analysis, K-means clustering, and so on. Details are in Biplab Paul, Philip T. Reiss and Erjia Cui (2023) "Continuous-time multivariate analysis" <doi:10.48550/arXiv.2307.09404>.

Last updated 10 months ago

1.00 score 192 downloads

bvpa - Bivariate Pareto Distribution

Implements the EM algorithm with one-step Gradient Descent method to estimate the parameters of the Block-Basu bivariate Pareto distribution with location and scale. We also found parametric bootstrap and asymptotic confidence intervals based on the observed Fisher information of scale and shape parameters, and exact confidence intervals for location parameters. Details are in Biplab Paul and Arabin Kumar Dey (2023) <doi:10.48550/arXiv.1608.02199> "An EM algorithm for absolutely continuous Marshall-Olkin bivariate Pareto distribution with location and scale"; E L Lehmann and George Casella (1998) <doi:10.1007/b98854> "Theory of Point Estimation"; Bradley Efron and R J Tibshirani (1994) <doi:10.1201/9780429246593> "An Introduction to the Bootstrap"; A P Dempster, N M Laird and D B Rubin (1977) <www.jstor.org/stable/2984875> "Maximum Likelihood from Incomplete Data via the EM Algorithm".

Last updated 1 years ago

1.00 score 219 downloads

HDLSSkST - Distribution-Free Exact High Dimensional Low Sample Size k-Sample Tests

Testing homogeneity of k multivariate distributions is a classical and challenging problem in statistics, and this becomes even more challenging when the dimension of the data exceeds the sample size. We construct some tests for this purpose which are exact level (size) alpha tests based on clustering. These tests are easy to implement and distribution-free in finite sample situations. Under appropriate regularity conditions, these tests have the consistency property in HDLSS asymptotic regime, where the dimension of data grows to infinity while the sample size remains fixed. We also consider a multiscale approach, where the results for different number of partitions are aggregated judiciously. Details are in Biplab Paul, Shyamal K De and Anil K Ghosh (2021) <doi:10.1016/j.jmva.2021.104897>; Soham Sarkar and Anil K Ghosh (2019) <doi:10.1109/TPAMI.2019.2912599>; William M Rand (1971) <doi:10.1080/01621459.1971.10482356>; Cyrus R Mehta and Nitin R Patel (1983) <doi:10.2307/2288652>; Joseph C Dunn (1973) <doi:10.1080/01969727308546046>; Sture Holm (1979) <doi:10.2307/4615733>; Yoav Benjamini and Yosef Hochberg (1995) <doi: 10.2307/2346101>.

Last updated 3 years ago

cpp

1.00 score 201 downloads