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Testing Closeness of Discrete Distributions

Tuğkan Batu, Lance Fortnow, Ronitt Rubinfeld, Warren D. Smith, Patrick White
2013 Journal of the ACM  
Given samples from two distributions over an n-element set, we wish to test whether these distributions are statistically close.  ...  Our algorithm has applications to the problem of testing whether a given Markov process is rapidly mixing. We present sublinear algorithms for several variants of this problem as well.  ...  ACKNOWLEDGMENTS We are very grateful to Oded Goldreich and Dana Ron for sharing an early draft of their work with us and for several helpful discussions.  ... 
doi:10.1145/2432622.2432626 fatcat:nsgyaehwk5ds3icrfx7u4oajru

Testing Closeness of Discrete Distributions [article]

Tugkan Batu, Lance Fortnow, Ronitt Rubinfeld, Warren D. Smith, and Patrick White
2010 arXiv   pre-print
Given samples from two distributions over an n-element set, we wish to test whether these distributions are statistically close.  ...  Our algorithm has applications to the problem of testing whether a given Markov process is rapidly mixing. We present sublinear for several variants of this problem as well.  ...  Acknowledgments We are very grateful to Oded Goldreich and Dana Ron for sharing an early draft of their work with us and for several helpful discussions.  ... 
arXiv:1009.5397v2 fatcat:ics7453s4bbgrigjzdl6j5a6su

Local minimax rates for closeness testing of discrete distributions [article]

Joseph Lam-Weil, Alexandra Carpentier, Bharath K. Sriperumbudur
2021 arXiv   pre-print
We consider the closeness testing problem for discrete distributions.  ...  In view of the rate, closeness testing turns out to be substantially harder than the related one-sample testing problem over a wide range of cases.  ...  The work of A.  ... 
arXiv:1902.01219v3 fatcat:6i7fkhba25emhnluxlcygwiuoe

Differentially Private Testing of Identity and Closeness of Discrete Distributions [article]

Jayadev Acharya, Ziteng Sun, Huanyu Zhang
2017 arXiv   pre-print
We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over k elements, under differential privacy.  ...  Our closeness testing bounds are optimal in the sparse regime where the number of samples is at most k. Our upper bounds are obtained by privatizing non-private estimators for these problems.  ...  identity testing, and closeness testing of discrete distributions.  ... 
arXiv:1707.05128v3 fatcat:p5cpasezbfekdk2vvj5vzrfz2e

Near-Optimal Closeness Testing of Discrete Histogram Distributions

Ilias Diakonikolas, Daniel M. Kane, Vladimir Nikishkin, Marc Herbstritt
2017 International Colloquium on Automata, Languages and Programming  
We investigate the problem of testing the equivalence between two discrete histograms.  ...  Our algorithmic approach applies in a more general setting and yields improved sample upper bounds for testing closeness of other structured distributions as well.  ...  We do this as follows: By rounding p and q down to the nearest third of an integer, we obtain p ,q supported on set of size n.  ... 
doi:10.4230/lipics.icalp.2017.8 dblp:conf/icalp/DiakonikolasKN17 fatcat:i2ztwfon2zc3zcks6gxsqaf5he

Optimal Algorithms for Testing Closeness of Discrete Distributions [article]

Siu-On Chan and Ilias Diakonikolas and Gregory Valiant and Paul Valiant
2013 arXiv   pre-print
We study the question of closeness testing for two discrete distributions.  ...  Batu et al. gave the first sub-linear time algorithms for these problems, which matched the lower bounds of Valiant up to a logarithmic factor in n, and a polynomial factor of .  ...  Robust ℓ 2 testing In this section, we give an optimal algorithm for robust closeness testing of distributions with respect to ℓ 2 distance.  ... 
arXiv:1308.3946v1 fatcat:5ta5dzx3u5gsfgxbezgb7ncxbu

Near-Optimal Closeness Testing of Discrete Histogram Distributions [article]

Ilias Diakonikolas, Daniel M. Kane, Vladimir Nikishkin
2017 arXiv   pre-print
We investigate the problem of testing the equivalence between two discrete histograms.  ...  Our algorithmic approach applies in a more general setting and yields improved sample upper bounds for testing closeness of other structured distributions as well.  ...  Introduction In this work, we study the problem of testing equivalence (closeness) between two discrete structured distributions. Let D be a family of univariate distributions over [n] (or Z).  ... 
arXiv:1703.01913v1 fatcat:vapi4nljgrhvfnobyyq4vpovuu

Optimal Algorithms for Testing Closeness of Discrete Distributions [chapter]

Siu-On Chan, Ilias Diakonikolas, Paul Valiant, Gregory Valiant
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
We study the question of closeness testing for two discrete distributions.  ...  Batu et al [BFR + 00, BFR + 13] gave the first sub-linear time algorithms for these problems, which matched the lower bounds of [Val11] up to a logarithmic factor in n, and a polynomial factor of ε.  ...  Closeness testing in 1 norm We begin by describing our 1 closeness testing algorithm: Input: A constant C and m samples from distributions p, q, with X i , Y i denoting the number of occurrences of the  ... 
doi:10.1137/1.9781611973402.88 dblp:conf/soda/ChanDVV14 fatcat:n554ydlquretrfcq66cpetchda

Differentially Private Identity and Closeness Testing of Discrete Distributions [article]

Maryam Aliakbarpour, Ilias Diakonikolas, Ronitt Rubinfeld
2017 arXiv   pre-print
We investigate the problems of identity and closeness testing over a discrete population from random samples.  ...  Our experiments illustrate that our private testers achieve small type I and type II errors with sample size sublinear in the domain size of the underlying distributions.  ...  We leverage recent progress in distribution property testing to obtain sample-efficient private algorithms for the problems of testing the identity and closeness of discrete distributions.  ... 
arXiv:1707.05497v1 fatcat:dgxmlkzhwzd7pgtvdwwln6ckim

Near-Optimal Closeness Testing of Discrete Histogram Distributions * †

Ilias Diakonikolas, Daniel Kane, Vladimir Nikishkin
unpublished
We investigate the problem of testing the equivalence between two discrete histograms.  ...  Our algorithmic approach applies in a more general setting and yields improved sample upper bounds for testing closeness of other structured distributions as well.  ...  We do this as follows: By rounding p and q down to the nearest third of an integer, we obtain p ,q supported on set of size n.  ... 
fatcat:ydmvxovb6ne6fhj7xz6d6vorb4

Simulated Power of Some Discrete Goodness-of-Fit Test Statistics For Testing the Null Hypothesis of a Zig-Zag Distribution [article]

Clement Ampadu, Daniel Wang, Michael Steele
2010 arXiv   pre-print
In this paper, we compare the powers of several discrete goodness-of-fit test statistics considered by Steele and Chaseling [10] under the null hypothesis of a 'zig-zag' distribution.  ...  In comparison to the uniform null of Steele and Chaseling [10], our investigation shows that the Discrete KS test statistic is most sensitive to the decreasing trend alternative; the Pearson Chi-Square  ...  In [10] the authors compared the powers of six discrete goodness-of-fit test statistics for a uniform null distribution against a variety of fully specified alternative distributions.  ... 
arXiv:1007.5109v2 fatcat:nlubgkr2eza6labgglhq2ttfte

Significance Tests in Discrete Distributions

H. O. Lancaster
1961 Journal of the American Statistical Association  
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Number 294 JUNE, 1961 Volume 56 SIGNIFICANCE TESTS IN DISCRETE DISTRIBUTIONS H. O.  ...  LANcastTER* University of Sydney In discrete distributions, it has often been recommended that an aux- iliary random experiment should be carried out so as to make the size of the test equal to the significance  ... 
doi:10.2307/2282247 fatcat:2tzkvxeanfa2tit4pavtz6ebs4

An Empirical Study on Arrival Rates of Limit Orders and Order Cancellation Rates in Borsa Istanbul [article]

Can Yilmaz Altinigne, Harun Ozkan, Veli Can Kupeli, Zehra Cataltepe
2019 arXiv   pre-print
In order to model the daily, weekly, and monthly arrival of limit order quantities, three different discrete probability distributions are tested: Geometric, Beta-Binomial and Discrete Weibull.  ...  Additionally, two theoretical models, namely, Exponential and Power law are also tested. We aim to model the arrival rates in the first fifteen bid and ask price levels.  ...  The ratios were close most of the time. Thus we perform uniformity tests on the ratios. We use Chi-Square Test to test if the ratios are distributed uniformly.  ... 
arXiv:1909.08308v1 fatcat:mzioftaiwjg5nc37ok7hzlbn7q

A Test of the Extreme Value Type I Assumption in the Bus Engine Replacement Model

Bradley Larsen, Florian Oswald, Gregor Reich, Dan Wunderli
2011 Social Science Research Network  
This note tests the assumption of dynamic discrete choice models that underlying utility shocks are distributed extreme value type I.  ...  We find that extreme value type I shocks cannot be rejected in most specifications of the Rust (1987) bus engine replacement model.  ...  In spite of its prevalence, the extreme value assumption of discrete choice models has rarely been tested.  ... 
doi:10.2139/ssrn.1989027 fatcat:pbcf7lyk2bhvbkwp5pdcwi3ldm

A test of the extreme value type I assumption in the bus engine replacement model

Bradley J. Larsen, Florian Oswald, Gregor Reich, Dan Wunderli
2012 Economics Letters  
This note tests the assumption of dynamic discrete choice models that underlying utility shocks are distributed extreme value type I.  ...  We find that extreme value type I shocks cannot be rejected in most specifications of the Rust (1987) bus engine replacement model.  ...  In spite of its prevalence, the extreme value assumption of discrete choice models has rarely been tested.  ... 
doi:10.1016/j.econlet.2012.02.031 fatcat:ocb5c5mlpneuxpdscho2b5muoq
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