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【期刊论文】Complete convergence for weighted sums of negatively associated random variables
梁汉营, Han-Ying Liang
Statistics & Probability Letters 48(2000)317-325,-0001,():
-1年11月30日
We discuss complete convergence for weighted sums of negatively associated (NA) random variables. The result on i.i.d. case of Li et al. (J. Theoret. Probab. 8 (1995) 49-76) is generalized and extended. Also, Gut's (Probab. Theory Related Fields 97 (1993) 169-178) result on Cesaro summation of i.i.d. random variables is extended.
Complete convergence, Negatively associated random variable, Cesaro summation, Weighted sum
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【期刊论文】STRONG LAWS FOR WEIGHTED SUMS OF RANDOM ELEMENTS
梁汉营, Han-Ying Liang and Chun Su
Statistica Sinica 10 (2000), 1011-1019,-0001,():
-1年11月30日
Strong laws of large numbers for weighted sums of independent random variables are proved for Banach spaces of type p. Chen, Zhu and Fang's (1996) results on real-valued i.i.d. random variables are extended and generalized, and their unsolved problem is answered. Also, necessary conditions for these strong convergences are considered.
Banach space of type p,, random element,, strong law,, weighted sum.,
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【期刊论文】EQUIVALENCE OF COMPLETE CONVERGENCE AND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS**
梁汉营, LIANG HANYING*
Chin. Ann. Of Math. 21B: 1 (2000), 83-88.,-0001,():
-1年11月30日
Under some conditions on probability, this note discusses the equlvalence between the complete convergence and the law of large number for B-valued independent random elemerfts. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numberst and there exists an example to show that the conditions on probability are weaker.
Complete convergence,, B-valued random elementt Law of large number,, Equivalence
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梁汉营, HAN-YING LIANG, BING-YI JING
Journal of Applied Mathematics and Stochastic Analysis, 15: 3 (2002), 207-218.,-0001,():
-1年11月30日
In this paper we are concerned with the heteroscedastic regression model yi=xiβ+g(ti)+σiei 1≤i≤n) under correlated errors ei, where it is assumed that σ2i=f(yi), the design points (xi, ti, ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.
Partial Linear Model,, Negatively Associated Sample,, Weighted Least Square Estimator,, Strong Consistency.,
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【期刊论文】LAW OF THE ITERATED LOGARITHM FOR SELF-NORMALIZED SUMS AND THEIR INCREMENTS
梁汉营, HAN-YING LIANG, JONG-IL BAEK and JOSEF STEINEBACH
Studia Scientiarum Mathematicarum Hungarica 43 (1), 79-114 (2006),-0001,():
-1年11月30日
Let X1; X2, … be independent, but not necessarily identically distributed random variables in the domain of attraction of a stable law with index 0<α<2. This paper uses Mn=max1≤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 Horvath 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.
Self-normalized sum,, self-normalized increment,, law of the iterated logarithm,, weighted sum.,
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