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In this paper we establish a central limit theorem for weighted sums of $Y_n={\sum_{i=1}^{n}}a_n,_iX_i$, where $\{a_{n,i},\;n{\in}N,\;1{\leq}i{\leq}n\}$ is an array of nonnegative numbers such that ${\sup}_{n{\geq}1}{\sum_{i=1}^{n}}a_{n,i}^2$ < ${\infty}$, ${\max}_{1{\leq}i{\leq}n}a_{n,i}{\rightarrow}0$ and $\{X_i,\;i{\in}N\}$ is a sequence of linear negatively quadrant dependent random variables with $EX_i=0$ and $EX_i^2$ < ${\infty}$. Using this result we will obtain a central limit theorem for partial sums of linear processes.
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참고문헌 (12)
참고문헌 신청
P. Billingsley / 1968 / Convergence of Probability Measures / Wiley
T. Birkel / 1993 / A functional central limit theorem for positively dependent random variables / J. Multivariate Anal 11:314~320
J. T. Cox / 1984 / Central limit theorems for associated random variables and the percolation model / Ann. Probab 12:514~528
D. Ka°es / 1982 / Weak consistency of least squares estimators in linear models / J. Multivariate Anal 12:186~198
E. L. Lehmann / 1966 / Some concepts of dependence / Ann. Math. Stat 37:1137~1153
T. Birkel / 1993 / A functional central limit theorem for positively dependent random variables / J. Multivariate Anal 11:314~320
J. T. Cox / 1984 / Central limit theorems for associated random variables and the percolation model / Ann. Probab 12:514~528
D. Ka°es / 1982 / Weak consistency of least squares estimators in linear models / J. Multivariate Anal 12:186~198
E. L. Lehmann / 1966 / Some concepts of dependence / Ann. Math. Stat 37:1137~1153
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