多总体二阶随机占优对无约束的检验问题

数学物理学报 ›› 2020, Vol. 40 ›› Issue (1): 212-220.

多总体二阶随机占优对无约束的检验问题

张建玲()

^{潍坊学院数学与信息科学学院山东潍坊 261061}

收稿日期:2019-04-17 出版日期:2020-02-26 发布日期:2020-04-08
作者简介:张建玲, E-mail:zhangjianling@wfu.edu.cn
基金资助:
国家自然科学基金(31872847);山东省自然科学基金(ZR2019MA022);潍坊学院博士基金(2016BS11)

Multi-Samples Testing for Second Stochastic Dominance Against Unrestricted Alternative

Jianling Zhang()

^{School of Mathematics and Information Sciences, Weifang University, Shandong Weifang 261061}

Received:2019-04-17 Online:2020-02-26 Published:2020-04-08
Supported by:
国家自然科学基金(31872847);山东省自然科学基金(ZR2019MA022);潍坊学院博士基金(2016BS11)

摘要/Abstract

摘要：

该文将利用保序回归估计和Bootstrap方法对多总体二阶随机占优对无约束的检验问题进行研究，具体步骤如下：首先，利用保序回归估计和经验分布函数构造检验统计量；然后，利用Bootstrap方法给出检验问题的临界值和p值；最后，通过Monte Carlo模拟来说明该文所提出方法的可行性.

关键词: 二阶随机占优, 保序回归估计, Bootstrap方法, 多总体检验

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

中图分类号:

O212

张建玲. 多总体二阶随机占优对无约束的检验问题[J]. 数学物理学报, 2020, 40(1): 212-220.

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

图/表 1

参考文献 16

1	Anderson G . Nonparametric test of stochastic dominance in income distribution. Econometrica, 1996, 64, 1183- 1193 doi: 10.2307/2171961
2	Baringhaus L , Grübel R . Nonparametric two-sample tests for increasing convex order. Bernoulli, 2009, 15 (1): 99- 123 doi: 10.3150/08-BEJ151
3	Berrendero J R , Carcamo J . Test for the second order stochastic dominance based on L-statistics. Journal of Business and Economic Statistics, 2011, 29 (2): 260- 270 doi: 10.1198/jbes.2010.07224
4	Crawford I. A Nonparametric Test of Stochastic Dominance in Multivariate Distributions//Crawford I. School of Economics Discussion Papers. Surrey:University of Surrey, 2005:1205
5	Davidson R , Duclos J Y . Statistical inference for stochastic dominance and for the measurement of poverty and inequality. Econometrica, 2000, 68, 1435- 1464 doi: 10.1111/1468-0262.00167
6	El Barmi H , Marchev D . New and improved estimators of distribution functions under second-order stochastic dominance. Journal of Nonparametric Statistics, 2009, 21 (2): 143- 153 doi: 10.1080/10485250802322390
7	El Barmi H , Mukerjee H . Inferences under a stochastic ordering constraint:the k-sample case. Journal of the American Statistical Association, 2005, 469 (100): 252- 261
8	Fong W M . Speculative trading and stock returns:a stochastic dominance analysis of the Chinese A-share market. Journal of International Financial Markets, Institutions and Money, 2009, 19, 712- 727 doi: 10.1016/j.intfin.2008.12.003
9	Hogg R V . Iterated tests of the equality of several distributions. Journal of the American Statistical Association, 1962, 57 (299): 579- 585 doi: 10.1080/01621459.1962.10500546
10	Leung P , Wong W K . On testing the equality of the multiple sharpe ratios with application on the evaluation of ishares. Risk, 2008, 10 (3): 1- 16
11	Linton O , Song K , Whang Y J . An improved bootstrap test of stochastic dominance. Journal of Econometrics, 2010, 154 (2): 186- 202
12	Rojo J . On the weak convergence of certain estimators of stochastically ordered survival function. Nonparametric Statistics, 1995, 4, 349- 363 doi: 10.1080/10485259508832626
13	Schmid F , Trede M . A kolmogorov-type test for second order stochastic dominance. Statistics and Probability Letters, 1998, 37 (2): 183- 193
14	Tony NG H K , Tripathi R C , Balakrishnan N . A two-stage Wilcoxon-type nonparametric test for stochastic ordering in two samples. Journal of Nonparametric Statistics, 2013, 25 (1): 73- 89 doi: 10.1080/10485252.2012.735232
15	Zhang J L , Zhang Z Z . Multi-sample test based on bootstrap methods for second order stochastic dominance. Hacettepe Journal of Mathematics and Statistics, 2015, 44 (2): 503- 512
16	Zhang J L , Zhang Z Z , Wang W Z . Testing against second-order stochastic dominance of multiple distributions. International Journal of Biomathematics, 2015, 8 (3): 1550040- 1 doi: 10.1142/S1793524515500400

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