Some hypothesis tests based on random projection

Fraiman, Ricardo; Moreno, Leonardo; Vallejo, Sebastián

doi:10.1007/s00180-017-0732-4

Cited by 7 publications

(4 citation statements)

References 31 publications

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“…(2,∞) n statistics. We will consider three competitors: the well known distance covariance test proposed in [24] and adapted to perform better in high dimensions in [23], the Hilbert-Schmidt Information Criterion proposed in [9], and that proposed more recently in [6] based on random projections. Basically, this test is based on the idea of choosing K pairs of random directions, and observing that if X and Y are independent, then the projections of X and Y in each one of K pairs of directions are independent.…”

Section: Comparison With Other Tests In High Dimensionmentioning

confidence: 99%

“…If at least one of these tests rejects the hypotheses of independence, then H 0 is rejected. To work at the 5%level, in [6] it is proposed to use a Bonferroni correction, that is, to compute the proportion of p-values smaller than 0.05/K to perform each one of the K uni-dimensional tests. We will call the RPK test.…”

Section: Comparison With Other Tests In High Dimensionmentioning

confidence: 99%

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An Independence Test Based on Recurrence Rates. An empirical study and applications to real data

Kalemkerian¹,

Fernández²

2020

Preprint

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In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that in high dimension, our test clearly outperforms, in almost all cases, the other widely used competitors. The test was performed on two data sets including small and large sample sizes and we show that in both cases the application of the test allows us to obtain interesting conclusions.

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Section: Comparison With Other Tests In High Dimensionmentioning

confidence: 99%

Section: Comparison With Other Tests In High Dimensionmentioning

confidence: 99%

An Independence Test Based on Recurrence Rates. An empirical study and applications to real data

Kalemkerian¹,

Fernández²

2020

Preprint

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“…In this Subsection we deal with construction of ranks by means of the scalar products of observations with a vector which is a function of these observations. Thus in difference from Fraiman, Moreno, and Vallejo (2017), where the multiplying vectors are chosen randomly and yield randomized tests with which various statisticians may come to various conclusions with the same data, the tests presented in this Subsection are not randomized.…”

Section: Ranks Constructed By Means Of a Random Vectormentioning

confidence: 99%

Nonparametric Tests Applicable to High Dimensional Data

Rublík

2019

AJS

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Constructions of data driven ordering of set of multivariate observations are presented. The methods employ also dissimilarity measures. The ranks are used in the construction of test statistics for location problem and in the construction of the corresponding multiple comparisons rule. An important aspect of the resulting procedures is that they can be used also in the multisample setting and in situations where the sample size is smaller than the dimension of the observations. The performance of the proposed procedures is illustrated by simulations.

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“…As a popular and useful dimension reduction technique in high dimensional learning in statistics, random projections have been of considerable independent interest, and their applications have appeared in machine learning [1], data mining [2], information retrieval [3], classification [4], clustering [5], hypothesis testing [6], regression [7], and similarity search [8], etc. Many papers have been devoted to the discussion of various aspects of random projections, to name a few, [9]- [17].…”

Section: Introductionmentioning

confidence: 99%

Improving Random Projections With Extra Vectors to Approximate Inner Products

Kuang

et al. 2020

IEEE Access

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This research concerns itself with increasing the accuracy of random projections used to quickly approximate the inner products of data vectors from a given dataset by adding additional information, namely, adding and storing more extra known vectors to the given dataset and associated information. We show how the variance of estimated inner products is reduced as more vectors are added, how variance reduction is related to the geometry of the dataset and moreover, the asymptotic behaviour of the variance as the number of extra vectors added goes to infinity. We provide the formulae governing the estimate of inner products for adding arbitrarily many extra vectors. Lastly, we demonstrate how to efficiently implement the computations of the estimates by showing we can use pre-computed and stored values for most of the computations. Numerical simulations are conducted to support the analytical results.

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Some hypothesis tests based on random projection

Cited by 7 publications

References 31 publications

An Independence Test Based on Recurrence Rates. An empirical study and applications to real data

An Independence Test Based on Recurrence Rates. An empirical study and applications to real data

Nonparametric Tests Applicable to High Dimensional Data

Improving Random Projections With Extra Vectors to Approximate Inner Products

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