Abstract
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For d covariates, there are 2d basis coefficients to estimate, which renders conventional approaches computationally prohibitive when d is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error for moderate sample sizes, and (2) the computational complexity is lower for sparser densities. Our method also allows for flexible control of the trade-off between mean-squared error and computational complexity.
Original language | English (US) |
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Pages (from-to) | 820-858 |
Number of pages | 39 |
Journal | Electronic Journal of Statistics |
Volume | 7 |
Issue number | 1 |
DOIs | |
State | Published - 2013 |
Keywords
- Adaptive estimation
- Binary hypercube
- Density estimation
- Minimax estimation
- Sparsity
- Walsh basis
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty