The sparse Poisson means model
Copyright policy )The sparse Poisson means model
We consider the problem of detecting a sparse Poisson mixture. Our results parallel those for the detection of a sparse normal mixture, pioneered by Ingster (1997) and Donoho and Jin (2004), when the Poisson means are larger than logarithmic in the sample size. In particular, a form of higher criticism achieves the detection boundary in the whole sparse regime. When the Poisson means are smaller than logarithmic in the sample size, a different regime arises in which simple multiple testing with Bonferroni correction is enough in the sparse regime. We present some numerical experiments that confirm our theoretical findings.
- University of California United States
- University of California, San Diego United States
- University of California, San Francisco United States
- University of California United States
goodness-of-fit tests, Bonferroni's method, sparse Poisson means model, multiple testing, Mathematics - Statistics Theory, Statistics Theory (math.ST), Sparse Poisson means model, Pearson’s chi-squared test, sparse normal means model, Paired and multiple comparisons; multiple testing, Pearson's chi-squared test, Bonferroni’s method, Tukey's higher criticism, Asymptotic properties of nonparametric inference, FOS: Mathematics, Fisher’s method, Fisher's method, Tukey’s higher criticism, Point processes (e.g., Poisson, Cox, Hawkes processes), Nonparametric hypothesis testing
goodness-of-fit tests, Bonferroni's method, sparse Poisson means model, multiple testing, Mathematics - Statistics Theory, Statistics Theory (math.ST), Sparse Poisson means model, Pearson’s chi-squared test, sparse normal means model, Paired and multiple comparisons; multiple testing, Pearson's chi-squared test, Bonferroni’s method, Tukey's higher criticism, Asymptotic properties of nonparametric inference, FOS: Mathematics, Fisher’s method, Fisher's method, Tukey’s higher criticism, Point processes (e.g., Poisson, Cox, Hawkes processes), Nonparametric hypothesis testing
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