Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates

By N. H. Anderson, Peter Hall, D. M. Titterington. 1994

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Anderson et al. (1994) constructs the two-sample test statistic using the L2 distance between the kernel density estimates, i.e., ‖f̂p − f̂q‖2 where f̂p(x) and f̂q(x) are the kernel density 108 109 estimates of densities p and q, respectively.”
A Kernel Test of Goodness of Fit (2016, background): “…test, based on differences in analytic functions of the sample and following the recent work of (Chwialkowski et al., 2015), is provided in (Chwialkowski et al., 2016, Appendix 5.1) bandwidth for consistent Parzen window estimates may not be a good choice for testing (Anderson et al., 1994).”
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, methodology): “…for any ﬁxed γ is in stark contrast to using Gaussian kernels for density estimation, where we must let the bandwidth go to zero with increasing n , and hence the gMMD statistic does not behave in the same way as the L2-distance between kernel density estimates, as done in Anderson et al. [1994].”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “L1 or L2) between Parzen window estimates of the densities as a test statistic [1, 3], based on the asymp totic distribution of this distance given p = q.”
Testing for Homogeneity with Kernel Fisher Discriminant Analysis (2007, methodology): “The lo w-power of the traditional density based statistics can be improved on using test statistics ba sed on kernel density estimators [2] and [1] and wavelet estimators [6].”
Two-sample tests in functional data analysis starting from discrete data (2007, background): “See, for example, the discussion by Ingster (1993), Fan (1994), Anderson et al. (1994), Fan (1998), Fan and Ullah (1999) and Li (1999).”
Inference for empirical Wasserstein distances on finite spaces (2016, methodology): “Bickel and Freedman (1981); Shorack and Wellner (1986); Johnson and Samworth (2005); Dümbgen et al. (2011); Dorea and Ferreira (2012)) as it metrizes weak convergence together with convergence of moments.”
Integrating structured biological data by Kernel Maximum Mean Discrepancy (2006, methodology): “L1 or L2) between estimates of the densities as a test statistic (Anderson et al., 1994; Biau and Gyorfi, 2005), based on the asymptotic distribution of this distance given p = q.”
On Estimating L 22 Divergence (2014, background): “We also show that this estimator is minimax optimal.”
Estimation of Information Theoretic Measures for Continuous Random Variables (2008, background): “For instance, the divergence is the error exponent in large deviation theory [5] and the divergence can be directly applied to solving the two-sample problem [1].”
Minimax optimality of permutation tests (2020, methodology): “statistic considered in Anderson et al. (1994). The Gaussian MMD statistic has a nice property that its expectation becomes zero if and only if PY = PZ . Given the U -statistic with the Gaussian kernel, we want to find a sufficient condition under which the resulting permutation test has nontrivial ”
Nonparametric Tests for Serial Independence Based on Quadratic Forms (2005, unknown): “Analytical support for a fixed optimal bandwidth was reported by Anderson, Hall, and Titterington (1994) in a two-sample test based on a statistic of the type T = R Rm (b f1(x) b f2(x))2dx.”
Kullback-Leibler divergence estimation of continuous distributions (2008, background): “Also the two-sample problem can be naturally approach using this divergence, as its goal is to detect whether two set of samples have been drawn from the same distribution [1].”
A Kernel Two-Sample Test (2012, methodology): “The prior work closest to the current approach is the Parzen window-based statistic of Anderson et al. (1994).”
Least-squares two-sample test (2011, background): “When multiple sets of data samples are available for learning, e.g., biological experimental results obtained from different laboratories (Borgwardt et al., 2006), the homogeneity test allows one to make a decision whether all the datasets are analyzed jointly as a single dataset or they should be…”
Empirical likelihood tests for two-sample problems via nonparametric density estimation (2006, background): “two densities are dieren t. Anderson, Hall and Titterington (1994) have studied the”