Statistical Inference Based on Divergence Measures

By Leandro Pardo. 2005

683 citations recorded by the source corpus.

DIVERGENCE MEASURES: DEFINITION AND PROPERTIES Introduction Phi-divergence. Measures between Two Probability Distributions: Definition and Properties Other Divergence Measures between Two Probability Distributions Divergence among k Populations Phi-disparities Exercises Answers to Exercises ENTROPY AS A MEASURE OF DIVERSITY: SAMPLING DISTRIBUTIONS Introduction Phi-entropies. Asymptotic Distribution Testing and Confidence Intervals for Phi-entropies Multinomial Populations: Asymptotic Distributions Maximum Entropy Principle and Statistical Inference on Condensed Ordered Data Exercises Answers to Exercises GOODNESS-OF-FIT: SIMPLE NULL HYPOTHESIS Introduction Phi-divergences and Goodness-of-fit with Fixed Number of Classes Phi-divergence Test Statistics under Sparseness Assumptions Nonstandard Problems: Tests Statistics based on Phi-divergences Exercises Answers to Exercises OPTIMALITY OF PHI-DIVERGENCE TEST STATISTICS IN GOODNESS-OF-FIT Introduction Asymptotic Effciency Exact and Asymptotic Moments: Comparison A Second Order Approximation to the Exact Distribution Exact Powers Based on Exact Critical Regions Small Sample Comparisons for the Phi-divergence Test Statistics Exercises Answers to Exercises MINIMUM PHI-DIVERGENCE ESTIMATORS Introduction Maximum Likelihood and Minimum Phi-divergence Estimators Properties of the Minimum Phi-divergence Estimator Normal Mixtures: Minimum Phi-divergence Estimator Minimum Phi-divergence Estimator with Constraints: Properties Exercises Answers to Exercises GOODNESS-OF-FIT: COMPOSITE NULL HYPOTHESIS Introduction Asymptotic Distribution with Fixed Number of Classes Nonstandard Problems: Test Statistics Based on Phi-divergences Exercises Answers to Exercises Testing Loglinear Models Using Phi-divergence Test Statistics Introduction Loglinear Models: Definition Asymptotic Results for Minimum Phi-divergence Estimators in Loglinear Models Testing in Loglinear Models Simulation Study Exercises Answers to Exercises PHI-DIVERGENCE MEASURES IN CONTINGENCY TABLES Introduction Independence Symmetry Marginal Homogeneity Quasi-symmetry Homogeneity Exercises Answers to Exercises TESTING IN GENERAL POPULATIONS Introduction Simple Null Hypotheses: Wald, Rao, Wilks and Phi-divergence Test Statistics Composite Null Hypothesis Multi-sample Problem Some Topics in Multivariate Analysis Exercises Answers to Exercises References Index

Subfields: Management Science and Operations Research, Statistical and Nonlinear Physics

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Citations in the corpus

Multi-stage distributionally robust optimization with risk aversion (2021, background): “The Kullback-Leibler divergence (KL-divergence) measure is the most famous special case of the φ-divergences measures family (see [35] and [3] for details).”
Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization (2016, background): “The divergence ball (13) can be written as Under twice continuous diﬀerentiability condition on φ , the theory of divergence-based inference (Pardo (2005)) stipulates that where χ 2 k 1 is the χ 2 -distribution with degree of freedom k − 1, and “ ” denotes convergence in distribution.”
A Bayesian view on the Hilbert transform and the Kramers-Kronig transform of electrochemical impedance data: Probabilistic estimates and quality scores (2020, background): “One particularly convenient one is called Hellinger distance (HD).[47] The square of the HD, (HD(f, g)) 2 , between two pdfs f(x) and g(x) can be defined as”
Generalized Wald-type tests based on minimum density power divergence estimators (2014, background): “More details about inference based on divergence measures can be found in [4, 5].”
Data-driven chance constrained stochastic program (2015, background): “1 in [26]) shows that 2N φ′′(1)Dφ(f ||f0) converges in distribution to a Chi-square distributed random variable with B̄ − 1 degrees of freedom as N goes to infinity, provided that φ′′(1) exists and is nonzero.”
Robust Solutions of Optimization Problems Affected by Uncertain Probabilities (2013, neutral): “Some examples, taken from [32], are given in Table 4.”
Divergences and Duality for Estimation and Test under Moment Condition Models (2010, background): “Cressie and Read (1984) (see also Liese and Vajda (1987) and Pardo (2006)).”
Practical and Consistent Estimation of f-Divergences (2019, background): “Chi square divergence between two d -variate Gaussian distributions both having covariance matrices proportional to identity can be computed as: The squared Hellinger divergence between two Gaussians is given in [33]: The KL -divergence between two d -variate Gaussians is:”
Distributionally Robust Optimization: A Review (2019, methodology): “Then, it is shown in Pardo [226] that under the true distribution, the statistics 2N φ′′(1)Dφ(P true, P0) converges in distribution to a χ 2 m−1-distribution, with m−1 degrees of freedom.”
Perspective Functions: Properties, Constructions, and Examples (2016, background): “In the case when N = 1 and G = R, it corresponds to a notion of φ-divergence which originates in [2, 26] and that has been used extensively in information theory, statistics, signal processing, and pattern recognition [4, 10, 44, 55]; see also [7, 35] for a discussion of discrete counterparts.”
Nonparametric Estimation of Renyi Divergence and Friends (2014, methodology): “In statistics, one can use these estimators to construct two-sample and independence tests between pairs of random variables [14].”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, background): “of (3) can be reformulated as a linear/ conic quadratic/ semidenite program. Moreover, the ˚-divergence ambiguity set is statistically meaningful and related to a statistical condence region (Pardo [34]). Hence it has been appealing to many researchers. Nevertheless, we point out that ˚-divergence m”