Second Order Hadamard Differentiability in Statistical Applications
Copyright policy )Second Order Hadamard Differentiability in Statistical Applications
A formulation of the second-order Hadamard differentiability of (extended) statistical functionals and some related theoretical results are established. These results are applied to derive the limiting distributions of a class of generalized Cramér-von Mises type test statistics, which include some proposed new ones for the tests of goodness of fit in the 3-sample problems, the tests in linear regression models, and the tests of bivariate independence, as special cases.
- University of North Carolina at Greensboro United States
- Tulane University United States
- University of Nebraska-Lincoln United States
- University of North Carolina System United States
- University of North Carolina at Chapel Hill United States
Statistics and Probability, Cramér-von Mises statistic, Numerical Analysis, Cramér–von Mises statistic, Linear regression; mixed models, statistical functionals, Asymptotic distribution theory in statistics, Hadamard differentiability, \(M\)-estimator, M-estimator, Abstract differentiation theory, differentiation of set functions, uniform asymptotic linearity, goodness of fit test, weighted empirical processes, linear models, Statistics, Probability and Uncertainty, Nonparametric hypothesis testing, limiting distribution
Statistics and Probability, Cramér-von Mises statistic, Numerical Analysis, Cramér–von Mises statistic, Linear regression; mixed models, statistical functionals, Asymptotic distribution theory in statistics, Hadamard differentiability, \(M\)-estimator, M-estimator, Abstract differentiation theory, differentiation of set functions, uniform asymptotic linearity, goodness of fit test, weighted empirical processes, linear models, Statistics, Probability and Uncertainty, Nonparametric hypothesis testing, limiting distribution
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