This paper obtains asymptotic normality for double array sum of linear time series zeta(t), and gives its application in the regression model. This generalizes the main results in [1].
In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-li...In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n Xi（yi -μ（Xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nXiXi′, Xi are bounded p × q regressors, and yi are q × 1 responses.展开更多
Abstract In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given c...Abstract In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covariate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator. Applications include trimmed mean and quantile function estimators.These applications demonstrate the usefulness of the new matrix products.展开更多
Suppose that we have a partially linear model Yi = xiβ ＋ g（ti） ＋εi with independent zero mean errors εi, where （xi,ti, i = 1, ... ,n} are non-random and observed completely and （Yi, i = 1,...,n} are missing a...Suppose that we have a partially linear model Yi = xiβ ＋ g（ti） ＋εi with independent zero mean errors εi, where （xi,ti, i = 1, ... ,n} are non-random and observed completely and （Yi, i = 1,...,n} are missing at random（MAR）. Two types of estimators of β and g（t） for fixed t are investigated： estimators based on semiparametric regression and inverse probability weighted imputations. Asymptotic normality of the estimators is established, which is used to construct normal approximation based confidence intervals on β and g（t）. Results are reported of a simulation study on the finite sample performance of the estimators and confidence intervals proposed in this paper.展开更多
<span style="font-family:Verdana;">In the applications of Tobit regression models we always encounter the data sets which contain too many variables that only a few of them contribute to the model. The...<span style="font-family:Verdana;">In the applications of Tobit regression models we always encounter the data sets which contain too many variables that only a few of them contribute to the model. Therefore, it will waste much more samples to estimate the “non-effective” variables in the inference. In this paper, we use a sequential procedure for constructing the fixed size confidence set for the “effective” parameters to the model by using an adaptive shrinkage estimate such that the “effective” coefficients can be efficiently identified with the minimum sample size based on Tobit regression model. Fixed design is considered for numerical simulation.</span>展开更多
Some moment inequalities for the strong mixing random variable sequence are established, and applied to discuss the asymptotic normality of the general weight function estimate for the fixed design regression mo...Some moment inequalities for the strong mixing random variable sequence are established, and applied to discuss the asymptotic normality of the general weight function estimate for the fixed design regression model.展开更多
Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao ...Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao （1996）. To show the application of the inequalities, we apply them to discuss the asymptotic normality of the weight function estimate for the fixed design regression model.展开更多
基金the National Natural ScienceFoundation of China(19971001)
文摘This paper obtains asymptotic normality for double array sum of linear time series zeta(t), and gives its application in the regression model. This generalizes the main results in [1].
基金the National Natural Science Foundation of China under Grant Nos.10171094,10571001,and 30572285the Foundation of Nanjing Normal University under Grant No.2005101XGQ2B84+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No.07KJD110093the Foundation of Anhui University under Grant No.02203105
文摘In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n Xi（yi -μ（Xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nXiXi′, Xi are bounded p × q regressors, and yi are q × 1 responses.
基金Partially supported by the National Natural Science Foundation of China (No.10071092).
文摘Abstract In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covariate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator. Applications include trimmed mean and quantile function estimators.These applications demonstrate the usefulness of the new matrix products.
基金Supported by the National Natural Science Foundation of China(No.11271088,11361011,11201088)Guangxi"Bagui Scholar"Special Project Foundationthe Natural Science Foundation of Guangxi(No.2013GXNS-FAA019004,2013GXNSFAA019007,2013GXNSFBA019001)
文摘Suppose that we have a partially linear model Yi = xiβ ＋ g（ti） ＋εi with independent zero mean errors εi, where （xi,ti, i = 1, ... ,n} are non-random and observed completely and （Yi, i = 1,...,n} are missing at random（MAR）. Two types of estimators of β and g（t） for fixed t are investigated： estimators based on semiparametric regression and inverse probability weighted imputations. Asymptotic normality of the estimators is established, which is used to construct normal approximation based confidence intervals on β and g（t）. Results are reported of a simulation study on the finite sample performance of the estimators and confidence intervals proposed in this paper.
文摘<span style="font-family:Verdana;">In the applications of Tobit regression models we always encounter the data sets which contain too many variables that only a few of them contribute to the model. Therefore, it will waste much more samples to estimate the “non-effective” variables in the inference. In this paper, we use a sequential procedure for constructing the fixed size confidence set for the “effective” parameters to the model by using an adaptive shrinkage estimate such that the “effective” coefficients can be efficiently identified with the minimum sample size based on Tobit regression model. Fixed design is considered for numerical simulation.</span>
基金Supported by the Natural Science Foundation of Guangxi the College Science Foundation of Guangxi !(9711017)
文摘Some moment inequalities for the strong mixing random variable sequence are established, and applied to discuss the asymptotic normality of the general weight function estimate for the fixed design regression model.
基金the Natural Science Foundation of China(10161004)the Natural Science Foundation of Guangxi(04047033)
文摘Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao （1996）. To show the application of the inequalities, we apply them to discuss the asymptotic normality of the weight function estimate for the fixed design regression model.
