Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems

被引:0
作者
Beckedorf, Pascal [1 ]
Rohde, Angelika [1 ]
机构
[1] Univ Freiburg, Freiburg, Germany
关键词
Edgeworth expansion; Non-uniform bounds; Central limit theorem; Local limit theorem; Entropy; Total variation distance; Self-normalized sums; Student t-statistic; Rate of convergence; FOURIER-TRANSFORMS; CONVERGENCE; DEVIATIONS; BOOTSTRAP; ACCURACY; MODULI; RATES;
D O I
10.1007/s10959-024-01376-8
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while imposing only minimal moment conditions. Within this result, we address the case of non-integer moments leading to a reduced remainder. Furthermore, we provide non-uniform bounds for expansions in local limit theorems. The enhanced tail accuracy of our non-uniform bounds allows for deriving an Edgeworth-type expansion in the entropic central limit theorem as well as a central limit theorem in total variation distance for self-normalized sums.
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页数:94
相关论文
共 56 条
[1]  
Alt HW, 2016, UNIVERSITEXT, P1, DOI 10.1007/978-1-4471-7280-2
[2]   EDGEWORTH EXPANSION OF A FUNCTION OF SAMPLE MEANS [J].
BAI, ZD ;
RAO, CR .
ANNALS OF STATISTICS, 1991, 19 (03) :1295-1315
[3]  
Barbe P., 1995, The Weighted Bootstrap, DOI [10.1007/978-1-4612-2532-4, DOI 10.1007/978-1-4612-2532-4]
[4]   ENTROPY AND THE CENTRAL-LIMIT-THEOREM [J].
BARRON, AR .
ANNALS OF PROBABILITY, 1986, 14 (01) :336-342
[5]  
Bentkus V, 1997, ANN STAT, V25, P851
[6]  
Bentkus V, 1996, ANN PROBAB, V24, P491
[7]   ON MOMENT CONDITIONS FOR VALID FORMAL EDGEWORTH EXPANSIONS [J].
BHATTACHARYA, RN ;
GHOSH, JK .
JOURNAL OF MULTIVARIATE ANALYSIS, 1988, 27 (01) :68-79
[8]   VALIDITY OF FORMAL EDGEWORTH EXPANSION [J].
BHATTACHARYA, RN ;
GHOSH, JK .
ANNALS OF STATISTICS, 1978, 6 (02) :434-451
[9]  
BHATTACHARYA RN, 1976, NORMAL APPROXIMATION
[10]  
Bloznelis M, 2002, THEOR PROBAB APPL+, V47, P300