LEADER 04900oam 2200481 450 001 9910812656403321 005 20190911112729.0 010 $a981-4531-75-8 035 $a(OCoLC)860388704 035 $a(MiFhGG)GVRL8REB 035 $a(EXLCZ)992550000001160086 100 $a20130716h20142014 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aStatistical tests of nonparametric hypotheses $easymptotic theory /$fOdile Pons, French National Institute for Agronomical Research, France 210 1$aNew Jersey :$cWorld Scientific,$d[2014] 210 4$d?2014 215 $a1 online resource (x, 293 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a981-4531-74-X 311 $a1-306-12040-3 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1. Introduction; 1.1 Definitions; 1.2 Rank tests and empirical distribution functions; 1.3 Hypotheses of the tests; 1.4 Weak convergence of the test statistics; 1.5 Tests for densities and curves; 1.6 Asymptotic levels of tests; 1.7 Permutation and bootstrap tests; 1.8 Relative efficiency of tests; 2. Asymptotic theory; 2.1 Parametric tests; 2.2 Parametric likelihood ratio tests; 2.3 Likelihood ratio tests against local alternatives; 2.4 Nonparametric likelihood ratio tests; 2.5 Nonparametric tests for empirical functionals; 2.6 Tests of homogeneity 327 $a2.7 Mixtures of exponential distributions2.8 Nonparametric bootstrap tests; 2.9 Exercises; 3. Nonparametric tests for one sample; 3.1 Introduction; 3.2 Kolmogorov-Smirnov tests for a distribution function; 3.3 Tests for symmetry of a density; 3.3.1 Kolmogorov-Smirnov tests for symmetry; 3.3.2 Semi-parametric tests, with an unknown center; 3.3.3 Rank test for symmetry; 3.4 Tests about the formof a density; 3.5 Goodness of fit test in biased length models; 3.6 Goodness of fit tests for a regression function; 3.7 Tests about the form of a regression function 327 $a3.8 Tests based on observations by intervals3.8.1 Goodness of fit tests for a density; 3.8.2 Goodness of fit tests for a regression function; 3.8.3 Tests of symmetry for a density; 3.8.4 Tests of a monotone density; 3.9 Exercises; 4. Two-sample tests; 4.1 Introduction; 4.2 Tests of independence; 4.2.1 Kolmogorov-Smirnov and Cramer-von Mises tests; 4.2.2 Tests based on the dependence function; 4.2.3 Tests based on the conditional distribution; 4.3 Test of homogeneity; 4.4 Goodness of fit tests in R2; 4.5 Tests of symmetry for a bivariate density; 4.6 Tests about the form of densities 327 $a4.7 Comparison of two regression curves4.8 Tests based on observations by intervals; 4.8.1 Test of independence; 4.8.2 Test of homogeneity; 4.8.3 Comparison of two regression curves; 4.9 Exercises; 5. Multi-dimensional tests; 5.1 Introduction; 5.2 Tests of independence; 5.3 Test of homogeneity of k sub-samples; 5.4 Test of homogeneity of k rescaled distributions; 5.5 Test of homogeneity of several variables of Rk; 5.6 Test of equality of marginal distributions; 5.7 Test of exchangeable components for a random variable; 5.8 Tests in single-indexmodels; 5.9 Comparison of k curves 327 $a5.10 Tests in proportional odds models5.11 Tests for observations by intervals; 5.11.1 Test of independence; 5.11.2 Test of homogeneity; 5.11.3 Comparison of k regression curves; 5.12 Competing risks; 5.13 Tests for Markov renewal processes; 5.14 Tests in Rkn as kn tends to infinity; 5.15 Exercises; 6. Nonparametric tests for processes; 6.1 Introduction; 6.2 Goodness of fit tests for an ergodic process; 6.3 Poisson process; 6.4 Poisson processes with scarce jumps; 6.5 Point processes in R+; 6.6 Marked point processes; 6.7 Spatial Poisson processes 327 $a6.8 Tests of stationarity for point processes 330 $aAn overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman-Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models defining the distributions of point processes and diffusions. With many new test statistics developed for smooth curves, the reliance on kernel estimators with bias corrections and the weak convergence of the 606 $aNonparametric statistics$xAsymptotic theory 615 0$aNonparametric statistics$xAsymptotic theory. 676 $a519.5/4 700 $aPons$b Odile$01090182 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910812656403321 996 $aStatistical tests of nonparametric hypotheses$94108211 997 $aUNINA