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Journal articles on the topic 'Self-normalized sums'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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1

Mason, David M. "Cluster Sets of Self-Normalized Sums." Journal of Theoretical Probability 19, no. 4 (November 23, 2006): 911–30. http://dx.doi.org/10.1007/s10959-006-0042-1.

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2

Egorov, V. A. "Estimation of distribution tails for normalized and self-normalized sums." Journal of Mathematical Sciences 127, no. 1 (May 2005): 1717–22. http://dx.doi.org/10.1007/s10958-005-0132-0.

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3

Wang, Wensheng. "Self-normalized lag increments of partial sums." Statistics & Probability Letters 58, no. 1 (May 2002): 41–51. http://dx.doi.org/10.1016/s0167-7152(02)00101-3.

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4

Csörgő, Miklós, Barbara Szyszkowicz, and Qiying Wang. "Darling--Erdős theorem for self-normalized sums." Annals of Probability 31, no. 2 (2003): 676–92. http://dx.doi.org/10.1214/aop/1048516532.

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5

Novak, S. Y. "On Self-normalized Sums and Student's Statistic." Theory of Probability & Its Applications 49, no. 2 (January 2005): 336–44. http://dx.doi.org/10.1137/s0040585x97981081.

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6

Bertail, Patrice, Emmanuelle Gautherat, and Hugo Harari-Kermadec. "Exponential bounds for multivariate self-normalized sums." Electronic Communications in Probability 13 (2008): 628–40. http://dx.doi.org/10.1214/ecp.v13-1430.

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7

Csörgő, Miklós, and ZhiShui Hu. "A strong approximation of self-normalized sums." Science China Mathematics 56, no. 1 (June 22, 2012): 149–60. http://dx.doi.org/10.1007/s11425-012-4434-7.

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8

Griffin, Philip S., and David M. Mason. "On the asymptotic normality of self-normalized sums." Mathematical Proceedings of the Cambridge Philosophical Society 109, no. 3 (May 1991): 597–610. http://dx.doi.org/10.1017/s0305004100070018.

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AbstractLet X1, …, Xn be a sequence of non-degenerate, symmetric, independent identically distributed random variables, and let Sn(rn) denote their sum when the rn largest in modulus have been removed. We obtain necessary and sufficient conditions for asymptotic normality of the studentized version of Sn(rn), and compare this to the condition for asymptotic normality of the scalar normalized version. In particular, when rn = r these conditions are the same, but when rn → ∞the former holds more generally.

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9

ZHANG, Li-xin. "A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS." Journal of Zhejiang University SCIENCE 2, no. 1 (2001): 79. http://dx.doi.org/10.1631/jzus.2001.0079.

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10

Jonsson, Fredrik. "On the quadratic moment of self-normalized sums." Statistics & Probability Letters 80, no. 17-18 (September 2010): 1289–96. http://dx.doi.org/10.1016/j.spl.2010.04.008.

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11

Wang, Qiying. "Kolmogrov and Erdös test for self-normalized sums." Statistics & Probability Letters 42, no. 3 (April 1999): 323–26. http://dx.doi.org/10.1016/s0167-7152(98)00228-4.

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12

Wu, Qiying, Barbara Szyszkowicz, and Mikl�s Cs�rg? "Donsker's theorem for self-normalized partial sums processes." Annals of Probability 31, no. 3 (July 2003): 1228–40. http://dx.doi.org/10.1214/aop/1055425777.

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13

Pang, Tian Xiao, and Zheng Yan Lin. "A SELF-NORMALIZED LIL FOR CONDITIONALLY TRIMMED SUMS AND CONDITIONALLY CENSORED SUMS." Journal of the Korean Mathematical Society 43, no. 4 (July 1, 2006): 859–69. http://dx.doi.org/10.4134/jkms.2006.43.4.859.

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14

Liang, Han-Ying, Jong-Il Baek, and Josef Steinebach. "Law of the iterated logarithm for self-normalized sums and their increments." Studia Scientiarum Mathematicarum Hungarica 43, no. 1 (February 1, 2006): 79–114. http://dx.doi.org/10.1556/sscmath.43.2006.1.6.

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Let X1, X2,… be independent, but not necessarily identically distributed random variables in the domain of attraction of a stable law with index 0<a<2. This paper uses Mn=max 1?i?n|Xi| to establish a self-normalized law of the iterated logarithm (LIL) for partial sums. Similarly self-normalized increments of partial sums are studied as well. In particular, the results of self-normalized sums of Horváth and Shao[9]under independent and identically distributed random variables are extended and complemented. As applications, some corresponding results for self-normalized weighted sums of iid random variables are also concluded.

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15

Račkauskas, Alfredas, and Charles Suquet. "Invariance principles for adaptive self-normalized partial sums processes." Stochastic Processes and their Applications 95, no. 1 (September 2001): 63–81. http://dx.doi.org/10.1016/s0304-4149(01)00096-5.

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16

Hahn, Marjorie G., and Daniel C. Weiner. "Asymptotic Behavior of Self-Normalized Trimmed Sums: Nonnormal Limits." Annals of Probability 20, no. 1 (January 1992): 455–82. http://dx.doi.org/10.1214/aop/1176989937.

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17

Zhang, Yong. "Further research on limit theorems for self-normalized sums." Communications in Statistics - Theory and Methods 49, no. 2 (December 28, 2018): 385–402. http://dx.doi.org/10.1080/03610926.2018.1543767.

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18

Hahn, Marjorie G., Jim Kuelbs, and Daniel C. Weiner. "The Asymptotic Joint Distribution of Self-Normalized Censored Sums and Sums of Squares." Annals of Probability 18, no. 3 (July 1990): 1284–341. http://dx.doi.org/10.1214/aop/1176990747.

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19

Cai, Guang-Hui. "On the other law of the iterated logarithm for self-normalized sums." Anais da Academia Brasileira de Ciências 80, no. 3 (September 2008): 411–18. http://dx.doi.org/10.1590/s0001-37652008000300002.

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Inthisnote, we obtain a Chung's integral test for self-normalized sums of i.i.d. random variables. Furthermore, we obtain a convergence rate of Chung law of the iterated logarithm for self-normalized sums.

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20

Wu, Qunying. "Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/329391.

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LetX,X1,X2,…be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self-normalized products of sums of partial sums is established.

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21

Wu, Qunying, and Yuanying Jiang. "Almost sure convergence for self-normalized products of sums of partial sums of ρ¯-mixing sequences." Filomat 33, no. 8 (2019): 2471–88. http://dx.doi.org/10.2298/fil1908471w.

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Let X,X1,X2,... be a stationary sequence of ??-mixing positive random variables. A universal result in the area of almost sure central limit theorems for the self-normalized products of sums of partial sums (?kj =1(Tj/(j(j+1)?/2)))?=(?Vk) is established, where: Tj = ?ji=1 Si,Si = ?i k=1 Xk,Vk = ??ki=1 X2i,? = EX, ? > 0. Our results generalize and improve those on almost sure central limit theorems obtained by previous authors from the independent case to ??-mixing sequences and from partial sums case to self-normalized products of sums of partial sums.

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22

Qian, Bin, and Jun Yan. "The moderate deviation principle for self-normalized sums of sums of i.i.d. random variables." Applied Mathematics Letters 22, no. 5 (May 2009): 715–18. http://dx.doi.org/10.1016/j.aml.2008.08.008.

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23

Zang, Qing-pei. "A Limit Theorem for the Moment of Self-Normalized Sums." Journal of Inequalities and Applications 2009, no. 1 (2009): 957056. http://dx.doi.org/10.1155/2009/957056.

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24

Wang, Qiying, and Bing-Yi Jing. "An Exponential Nonuniform Berry-Esseen Bound for Self-Normalized Sums." Annals of Probability 27, no. 4 (October 1999): 2068–88. http://dx.doi.org/10.1214/aop/1022874829.

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25

Spătaru, Aurel. "Convergence and Precise Asymptotics for Series Involving Self-normalized Sums." Journal of Theoretical Probability 29, no. 1 (May 18, 2014): 267–76. http://dx.doi.org/10.1007/s10959-014-0560-1.

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26

Hahn, Marjorie G., and Daniel C. Weiner. "Asymptotic behavior of self-normalized trimmed sums: Nonnormal limits II." Journal of Theoretical Probability 5, no. 1 (January 1992): 169–96. http://dx.doi.org/10.1007/bf01046784.

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27

Zang, Qing-pei. "A kind of complete moment convergence for self-normalized sums." Computers & Mathematics with Applications 60, no. 6 (September 2010): 1803–9. http://dx.doi.org/10.1016/j.camwa.2010.07.012.

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28

Zhao, Yuexu, and Jingxuan Tao. "Precise asymptotics in complete moment convergence for self-normalized sums." Computers & Mathematics with Applications 56, no. 7 (October 2008): 1779–86. http://dx.doi.org/10.1016/j.camwa.2008.04.005.

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29

Liu, Weidong, Qi-Man Shao, and Qiying Wang. "Self-normalized Cramér type moderate deviations for the maximum of sums." Bernoulli 19, no. 3 (August 2013): 1006–27. http://dx.doi.org/10.3150/12-bej415.

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30

Deng, Dianliang. "Precise asymptotics in the deviation probability series of self-normalized sums." Journal of Mathematical Analysis and Applications 376, no. 1 (April 2011): 136–53. http://dx.doi.org/10.1016/j.jmaa.2010.10.005.

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31

Liu, Weidong, and Zheng-Yan Lin. "Asymptotics for Self-Normalized Random Products of Sums for Mixing Sequences." Stochastic Analysis and Applications 25, no. 2 (February 27, 2007): 293–315. http://dx.doi.org/10.1080/07362990601139487.

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32

Liu, Weidong, and Zheng-yan Lin. "Asymptotics for Self-Normalized Random Products of Sums for Mixing Sequences." Stochastic Analysis and Applications 25, no. 4 (June 26, 2007): 739–62. http://dx.doi.org/10.1080/07362990701419938.

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33

Zang, Qing-pei. "A General Law of Complete Moment Convergence for Self-Normalized Sums." Journal of Inequalities and Applications 2010, no. 1 (2010): 760735. http://dx.doi.org/10.1155/2010/760735.

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34

Hu, Zhishui, Qi-Man Shao, and Qiying Wang. "Cramér Type Moderate deviations for the Maximum of Self-normalized Sums." Electronic Journal of Probability 14 (2009): 1181–97. http://dx.doi.org/10.1214/ejp.v14-663.

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35

Csörgő, Miklós, Zhishui Hu, and Hongwei Mei. "Strassen-Type Law of the Iterated Logarithm for Self-normalized Sums." Journal of Theoretical Probability 26, no. 2 (March 22, 2011): 311–28. http://dx.doi.org/10.1007/s10959-011-0353-8.

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36

Norvaiša, Rimas, and Alfredas Račkauskas. "Uniform asymptotic normality of self-normalized weighted sums of random variables*." Lithuanian Mathematical Journal 59, no. 4 (October 2019): 575–94. http://dx.doi.org/10.1007/s10986-019-09461-w.

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37

Huang, Sai-Hua, and Tian-Xiao Pang. "An almost sure central limit theorem for self-normalized partial sums." Computers & Mathematics with Applications 60, no. 9 (November 2010): 2639–44. http://dx.doi.org/10.1016/j.camwa.2010.08.093.

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38

Zhang, Yong, and Xiao-yun Yang. "An almost sure central limit theorem for self-normalized weighted sums." Acta Mathematicae Applicatae Sinica, English Series 29, no. 1 (January 2013): 79–92. http://dx.doi.org/10.1007/s10255-010-8247-6.

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39

Juodis, Mindaugas, and Alfredas Račkauskas. "A central limit theorem for self-normalized sums of a linear process." Statistics & Probability Letters 77, no. 15 (September 2007): 1535–41. http://dx.doi.org/10.1016/j.spl.2007.03.034.

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40

Hwang, Kyo-Shin, and Tian-Xiao Pang. "A nonclassical law of the iterated logarithm for self-normalized partial sums." Acta Mathematica Hungarica 141, no. 3 (April 30, 2013): 238–53. http://dx.doi.org/10.1007/s10474-013-0323-y.

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41

Wu, Qunying, and Yuanying Jiang. "Almost sure central limit theorem for self-normalized partial sums and maxima." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 110, no. 2 (December 9, 2015): 699–710. http://dx.doi.org/10.1007/s13398-015-0259-x.

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42

Peligrad, Magda, and Qi-Man Shao. "Self-normalized central limit theorem for sums of weakly dependent random variables." Journal of Theoretical Probability 7, no. 2 (April 1994): 309–38. http://dx.doi.org/10.1007/bf02214272.

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43

Račkauskas, Alfredas, and Charles Suquet. "Functional central limit theorems for self-normalized partial sums of linear processes." Lithuanian Mathematical Journal 51, no. 2 (April 2011): 251–59. http://dx.doi.org/10.1007/s10986-011-9123-7.

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44

Pang, Tian-Xiao, Zheng-Yan Lin, and Kyo-Shin Hwang. "Asymptotics for self-normalized random products of sums of i.i.d. random variables." Journal of Mathematical Analysis and Applications 334, no. 2 (October 2007): 1246–59. http://dx.doi.org/10.1016/j.jmaa.2006.12.085.

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45

Xu, Feng, and Qunying Wu. "Almost sure central limit theorem for self-normalized partial sums ofρ−-mixing sequences." Statistics & Probability Letters 129 (October 2017): 17–27. http://dx.doi.org/10.1016/j.spl.2017.04.023.

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46

Csörgő, Miklós, Zhishui Hu, and Hongwei Mei. "Strassen-type law of the iterated logarithm for self-normalized increments of sums." Journal of Mathematical Analysis and Applications 393, no. 1 (September 2012): 45–55. http://dx.doi.org/10.1016/j.jmaa.2012.03.047.

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47

Vrbik, Jan. "A Note on “Limit Distributions of Self-Normalized Sums” Using Cauchy-Generated Samples." Applied Mathematics 10, no. 11 (2019): 863–75. http://dx.doi.org/10.4236/am.2019.1011062.

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48

Hörmann, Siegfried, and Yvik Swan. "A note on the normal approximation error for randomly weighted self-normalized sums." Periodica Mathematica Hungarica 67, no. 2 (March 26, 2013): 143–54. http://dx.doi.org/10.1007/s10998-013-4789-8.

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49

Fu, Ke-ang, and Wei Huang. "A weak invariance principle for self-normalized products of sums of mixing sequences." Applied Mathematics-A Journal of Chinese Universities 23, no. 2 (June 2008): 183–89. http://dx.doi.org/10.1007/s11766-008-0207-z.

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50

Wu, Qunying, and Yuanying Jiang. "Almost sure central limit theorem for self-normalized partial sums of negatively associated random variables." Filomat 31, no. 5 (2017): 1413–22. http://dx.doi.org/10.2298/fil1705413w.

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Let X,X1,X2,... be a stationary sequence of negatively associated random variables. A universal result in almost sure central limit theorem for the self-normalized partial sums Sn/Vn is established, where: Sn = ?ni=1 Xi,V2n = ?ni=1 X2i .

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