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In this paper, we address the question of comparison between populations of trees. We study an statistical test based on the distance between empirical mean trees, as an analog of the two sample z statistic for comparing two means. Despite its simplicity, we can report that the test is quite powerful to separate distributions with different means but it does not distinguish between different populations with the same mean, a more complicated test should be applied in that setting. The performance of the test is studied via simulations on Galton-Watson branching processes. We also show an application to a real data problem in genomics.
Two-sample tests have been one of the most classical topics in statistics with wide application even in cutting edge applications. There are at least two modes of inference used to justify the two-sample tests. One is usual superpopulation inference
This paper proposes a new statistic to test independence between two high dimensional random vectors ${mathbf{X}}:p_1times1$ and ${mathbf{Y}}:p_2times1$. The proposed statistic is based on the sum of regularized sample canonical correlation coefficie
For dendrite graphs from biological experiments on mouses retinal ganglion cells, a paper by Nakatsukasa, Saito and Woei reveals a mysterious phase transition phenomenon in the spectra of the corresponding graph Laplacian matrices. While the bulk of
We study the problem of estimating the mean of a multivariatedistribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the