多总体二阶随机占优对无约束的检验问题

Abstract

Abstract:

In this paper, we will study test problem of multi-sample second order stochastic dominance against no restriction by using isotonic regression estimates and bootstrap method. The specific steps are as follows:Firstly, a test statistic is constructed with the isotonic regression estimators and empirical distribution functions. Then, the critical value and p value of the test are given by bootstrap method. Finally, simulation results are presented to illustrate the proposed test method.

Key words: Second order stochastic dominance, Isotonic regression estimation, Bootstrap method, Multi-sample test

CLC Number:

O212

Jianling Zhang. Multi-Samples Testing for Second Stochastic Dominance Against Unrestricted Alternative[J].Acta mathematica scientia,Series A, 2020, 40(1): 212-220.

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Distributions			$n_1 = n_2 = n_3 = 50$	$n_1 = n_2 = n_3 = 100$	$n_1 = n_2 = n_3 = 200$
$F_1$	$F_2$	$F_3$	$\hat{p}$	$\hat{p}$	$\hat{p}$
U(0, 1)	U(0, 1)	U(0, 1)	0.048	0.051	0.057
E(1)	E(1)	E(1)	0.059	0.043	0.055
N(0, 1)	N(0, 1)	N(0, 1)	0.045	0.041	0.043
$\Gamma(2)$	$\Gamma(2)$	$\Gamma(2)$	0.039	0.051	0.049
$\chi^{2}(2)$	$\chi^{2}(2)$	$\chi^{2}(2)$	0.061	0.057	0.050
U(0, 1)	U(0, 1)	U(0, 0.9)	0.016	0.015	0.014
E(0.9)	E(1)	E(1)	0.020	0.014	0.009
N(0, 1.1)	N(0, 1)	N(0, 1)	0.056	0.057	0.058
U(0, 0.9)	U(0, 1)	U(0, 1)	0.207	0.343	0.576
E(1)	E(1)	E(0.9)	0.122	0.151	0.253
N(0, 1)	N(0, 1)	N(0, 1.1)	0.063	0.068	0.075

Multi-Samples Testing for Second Stochastic Dominance Against Unrestricted Alternative

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