Srivastava and Jhajj [ 1 6] proposed a class of estimators for estimating population variance using multi auxiliary variables in simple random sampling and they utilized the means and variances of auxiliary variables....Srivastava and Jhajj [ 1 6] proposed a class of estimators for estimating population variance using multi auxiliary variables in simple random sampling and they utilized the means and variances of auxiliary variables. In this paper, we adapted this class and motivated by Searle [13], and we suggested more generalized class of estimators for estimating the population variance in simple random sampling. The expressions for the mean square error of proposed class have been derived in general form. Besides obtaining the minimized MSE of the proposed and adapted class, it is shown that the adapted classis the special case of the proposed class. Moreover, these theoretical findings are supported by an empirical study of original data.展开更多
Let an, n≥ 1 be a sequence of independent standard normal random variables. Consider the randomtrigonometric polynomial Tn（θ）=∑^n_i=1 aj cos（j θ）, 0≤θ≤π and let Nn be the number of real roots of Tn（θ）in...Let an, n≥ 1 be a sequence of independent standard normal random variables. Consider the randomtrigonometric polynomial Tn（θ）=∑^n_i=1 aj cos（j θ）, 0≤θ≤π and let Nn be the number of real roots of Tn（θ）in （0, 2π）. In this paper it is proved that limn→∞ Var（Nn）/n=co,where 0 〈 co〈 ∞.展开更多
We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some re...We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved展开更多
文摘Srivastava and Jhajj [ 1 6] proposed a class of estimators for estimating population variance using multi auxiliary variables in simple random sampling and they utilized the means and variances of auxiliary variables. In this paper, we adapted this class and motivated by Searle [13], and we suggested more generalized class of estimators for estimating the population variance in simple random sampling. The expressions for the mean square error of proposed class have been derived in general form. Besides obtaining the minimized MSE of the proposed and adapted class, it is shown that the adapted classis the special case of the proposed class. Moreover, these theoretical findings are supported by an empirical study of original data.
基金supported by National Natural Science Foundation of China (GrantNos. 10671176 and 11071213)Zhejiang Provincial Natural Science Foundation of China (Grant No. R6090034)+1 种基金Doctoral Programs Foundation of Ministry of Education of China (Grant No. J20110031)Competitive Earmarked Research Grant of Research Grants Council (Grant No. 602608)
文摘Let an, n≥ 1 be a sequence of independent standard normal random variables. Consider the randomtrigonometric polynomial Tn（θ）=∑^n_i=1 aj cos（j θ）, 0≤θ≤π and let Nn be the number of real roots of Tn（θ）in （0, 2π）. In this paper it is proved that limn→∞ Var（Nn）/n=co,where 0 〈 co〈 ∞.
基金supported by National Natural Science Foundation of China(Grant Nos. 11171303 and 60974006)the Specialized Research Fund for the Doctor Program of Higher Education(Grant No.20090101110020)the Natural Science Foundation of Zhejiang Province(Grant No.Y6100176)
文摘We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved
