共查询到20条相似文献,搜索用时 506 毫秒
1.
Fikri Akdeniz Esra Akdeniz Duran Mahdi Roozbeh Mohammad Arashi 《Journal of Statistical Computation and Simulation》2015,85(1):147-165
In this paper, a generalized difference-based estimator is introduced for the vector parameter β in the semiparametric regression model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter β in the semiparametric regression model. Under the linear nonstochastic constraint Rβ=r, the generalized restricted difference-based Liu estimator is given. The risk function for the β?GRD(η) associated with weighted balanced loss function is presented. The performance of the proposed estimators is evaluated by a simulated data set. 相似文献
2.
In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized-difference-based almost unbiased two-parameter estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, we introduce a new generalized-difference-based weighted mixed almost unbiased two-parameter estimator. The performance of this new estimator over the generalized-difference-based estimator and generalized- difference-based almost unbiased two-parameter estimator in terms of the MSEM criterion is investigated. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset. 相似文献
3.
《Journal of Statistical Computation and Simulation》2012,82(6):679-691
In this article, the restricted r–k class estimator and restricted r–d class estimator are introduced, which are general estimators of the r–k class estimator by Baye and Parker [Combining ridge and principal component regression: A money demand illustration, Commun. Stat. Theory Methods 13(2) (1984), pp. 197–205] and the r–d class estimator by Kaç?ranlar and Sakall?o?lu [Combining the Liu estimator and the principal component regression estimator, Commun. Stat. Theory Methods 30(12) (2001), pp. 2699–2705], respectively. For the two cases when the restrictions are true and not true, the superiority of the restricted r–k class estimator and r–d class estimator over the restricted ridge regression estimator by Sarkar [A new estimator combining the ridge regression and the restricted least squares methods of estimation, Commun. Stat. Theory Methods 21 (1992), pp. 1987–2000] and the restricted Liu estimator by Kaç?ranlar et al. [A new biased estimator in linear regression and a detailed analysis of the widely analysed dataset on Portland cement, Sankhya - Indian J. Stat. 61B(3) (1999), pp. 443–459] are discussed with respect to the mean squared error matrix criterion. Furthermore, a Monte Carlo evaluation of the estimators is given to illustrate some of the theoretical results. 相似文献
4.
Hu Yang 《Statistics》2013,47(6):759-766
In this paper, we introduce a stochastic restricted k–d class estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. The stochastic restricted k–d class estimator is a generalization of the ordinary mixed estimator and the k–d class estimator. We show that our new biased estimator is superior in the mean squared error matrix sense to the k–d class estimator [S. Sakall?o?lu and S. Kaçiranlar, A new biased estimator based on ridge estimation, Statist. Papers 49 (2008), pp. 669–689] and the stochastic restricted Liu estimator [H. Yang and J.W. Xu, An alternative stochastic restricted Liu estimator in linear regression, Statist. Papers 50 (2009), pp. 639–647]. Finally, a numerical example is given to show the theoretical results. 相似文献
5.
《统计学通讯:理论与方法》2013,42(12):2699-2705
In this paper we introduce a class of estimators which includes the ordinary least squares (OLS), the principal components regression (PCR) and the Liu estimator [1]. In particular, we show that our new estimator is superior, in the scalar mean-squared error (mse) sense, to the Liu estimator, to the OLS estimator and to the PCR estimator. 相似文献
6.
A new biased estimator based on ridge estimation 总被引:3,自引:0,他引:3
In this paper we introduce a new biased estimator for the vector of parameters in a linear regression model and discuss its
properties. We show that our new biased estimator is superior, in the mean square error(mse) sense, to the ordinary least
squares (OLS) estimator, the ordinary ridge regression (ORR) estimator and the Liu estimator. We also compare the performance
of our new biased estimator with two other special Liu-type estimators proposed in Liu (2003). We illustrate our findings
with a numerical example based on the widely analysed dataset on Portland cement. 相似文献
7.
《Journal of Statistical Computation and Simulation》2012,82(5):653-688
The purpose of this paper is to combine several regression estimators (ordinary least squares (OLS), ridge, contraction, principal components regression (PCR), Liu, r?k and r?d class estimators) into a single estimator. The conditions for the superiority of this new estimator over the PCR, the r?k class, the r?d class, β?(k, d), OLS, ridge, Liu and contraction estimators are derived by the scalar mean square error criterion and the estimators of the biasing parameters for this new estimator are examined. Also, a numerical example based on Hald data and a simulation study are used to illustrate the results. 相似文献
8.
Jibo Wu 《统计学通讯:理论与方法》2013,42(17):5193-5203
ABSTRACTRegression models are usually used in forecasting (predicting) unknown values of the response variable y. This article considers the predictive performance of the almost unbiased Liu estimator compared to the ordinary least-squares estimator, principal component regression estimator, and Liu estimator. Finally, we present a numerical example to explain the theoretical results and we obtain a region where the almost unbiased Liu estimator is uniformly superior to the ordinary least-squares estimator, principal component regression estimator, and Liu estimator. 相似文献
9.
Gülesen Üstündaĝ Şiray 《统计学通讯:理论与方法》2013,42(22):4742-4756
Omission of some relevant explanatory variables and multicollinearity in regression models are very serious problems in applied works. There are some papers examining the multicollinearity and misspecification which is due to omission of some relevant explanatory variables, concurrently. To remedy the problem of multicollinearity, Kaç?ranlar and Sakall?o?lu (2001) proposed the r-d class estimator that includes the ordinary least squares, principal components regression, and Liu estimators as special cases. The aim of this paper is to examine the performance of the r-d class estimator in misspecificied linear models. 相似文献
10.
In the multiple linear regression analysis, the ridge regression estimator and the Liu estimator are often used to address multicollinearity. Besides multicollinearity, outliers are also a problem in the multiple linear regression analysis. We propose new biased estimators based on the least trimmed squares (LTS) ridge estimator and the LTS Liu estimator in the case of the presence of both outliers and multicollinearity. For this purpose, a simulation study is conducted in order to see the difference between the robust ridge estimator and the robust Liu estimator in terms of their effectiveness; the mean square error. In our simulations, the behavior of the new biased estimators is examined for types of outliers: X-space outlier, Y-space outlier, and X-and Y-space outlier. The results for a number of different illustrative cases are presented. This paper also provides the results for the robust ridge regression and robust Liu estimators based on a real-life data set combining the problem of multicollinearity and outliers. 相似文献
11.
Improvement of the Liu estimator in linear regression model 总被引:2,自引:0,他引:2
In the presence of stochastic prior information, in addition to the sample, Theil and Goldberger (1961) introduced a Mixed
Estimator
for the parameter vector β in the standard multiple linear regression model (T,Xβ,σ2
I). Recently, the Liu estimator which is an alternative biased estimator for β has been proposed by Liu (1993).
In this paper we introduce another new Liu type biased estimator called Stochastic restricted Liu estimator
for β, and discuss its efficiency. The necessary and sufficient conditions for mean squared error matrix of the Stochastic restricted Liu estimator
to exceed the mean squared error matrix of the mixed estimator
will be derived for the two cases in which the parametric restrictions are correct and are not correct. In particular we
show that this new biased estimator is superior in the mean squared error matrix sense to both the Mixed estimator
and to the biased estimator introduced by Liu (1993). 相似文献
12.
Kai F Yu 《统计学通讯:理论与方法》2013,42(9):3075-3087
Let (?,X) be a random vector such that E(X|?) = ? and Var(x|?) a + b? + c?2 for some known constants a, b and c. Assume X1,…,Xn are independent observations which have the same distribution as X. Let t(X) be the linear regression of ? on X. The linear empirical Bayes estimator is used to approximate the linear regression function. It is shown that under appropriate conditions, the linear empirical Bayes estimator approximates the linear regression well in the sense of mean squared error. 相似文献
13.
Yo Sheena † 《Statistics》2013,47(5):371-379
We consider the estimation of Σ of the p-dimensional normal distribution Np (0, Σ) when Σ?=?θ0 Ip ?+?θ1 aa′, where a is an unknown p-dimensional normalized vector and θ0?>?0, θ1?≥?0 are also unknown. First, we derive the restricted maximum likelihood (REML) estimator. Second, we propose a new estimator, which dominates the REML estimator with respect to Stein's loss function. Finally, we carry out Monte Carlo simulation to investigate the magnitude of the new estimator's superiority. 相似文献
14.
A restricted Liu estimator for binary regression models and its application to an applied demand system 总被引:1,自引:0,他引:1
In this article, we propose a restricted Liu regression estimator (RLRE) for estimating the parameter vector, β, in the presence of multicollinearity, when the dependent variable is binary and it is suspected that β may belong to a linear subspace defined by Rβ?=?r. First, we investigate the mean squared error (MSE) properties of the new estimator and compare them with those of the restricted maximum likelihood estimator (RMLE). Then we suggest some estimators of the shrinkage parameter, and a simulation study is conducted to compare the performance of the different estimators. Finally, we show the benefit of using RLRE instead of RMLE when estimating how changes in price affect consumer demand for a specific product. 相似文献
15.
In this paper, we consider, using technique based on Girsanov theorem, the problem of efficient estimation for the drift of subfractional Brownian motion SH ? (SHt)t ∈ [0, T]. We also construct a class of biased estimators of James-Stein type which dominate, under the usual quadratic risk, the natural maximum likelihood estimator. 相似文献
16.
In this article, we introduce a new two-parameter estimator by grafting the contraction estimator into the modified ridge estimator proposed by Swindel (1976). This new two-parameter estimator is a general estimator which includes the ordinary least squares, the ridge, the Liu, and the contraction estimators as special cases. Furthermore, by setting restrictions Rβ = r on the parameter values we introduce a new restricted two-parameter estimator which includes the well-known restricted least squares, the restricted ridge proposed by Groß (2003), the restricted contraction estimators, and a new restricted Liu estimator which we call the modified restricted Liu estimator different from the restricted Liu estimator proposed by Kaç?ranlar et al. (1999). We also obtain necessary and sufficient condition for the superiority of the new two-parameter estimator over the ordinary least squares estimator and the comparison of the new restricted two-parameter estimator to the new two-parameter estimator is done by the criterion of matrix mean square error. The estimators of the biasing parameters are given and a simulation study is done for the comparison as well as the determination of the biasing parameters. 相似文献
17.
Hu Yang 《统计学通讯:理论与方法》2013,42(1):70-80
Sakall?oglu et al. (2001) dealt with the comparisons among the ridge estimator, Liu estimator, and iteration estimator. Akdeniz and Erol (2003) have compared the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean squared error sense. In this article, we study the ridge estimator and Liu estimator with respect to linear equality restriction, and establish some sufficient conditions for the superiority of the restricted ridge estimator over the restricted Liu estimator and the superiority of the restricted Liu estimator over the restricted ridge estimator under mean squared error matrix, respectively. Furthermore, we give a numerical example. 相似文献
18.
We re-examine the criteria of “hyper-admissibility” and “necessary bestness”, for the choice of estimator, from the point of view of their relevance to the design of actual surveys. Both these criteria give rise to a unique choice of estimator (viz. the Horvitz-Thompson estimator ?HT) whatever be the character under investigation or sample design. However, we show here that the “principal hyper-surfaces” (or “domains”) of dimension one (which are practically uninteresting)play the key role in arriving at the unique choice. A variance estimator v1(?HT) (due to Horvitz-Thompson), which takes negative values “often”, is shown to be uniquely “hyperadmissible” in a wide class of unbiased estimators of the variance of ?HT. Extensive empirical evidence on the superiority of the Sen-Yates-Grundy variance estimator v2(?HT) over v1(?HT) is presented. 相似文献
19.
Jibo Wu 《统计学通讯:理论与方法》2018,47(18):4433-4442
In this paper, a generalized difference-based mixed Liu estimator in partially linear model is presented, when it is supposed that the regression parameter may be restricted to a subspace and compare the proposed estimators in the sense of matrix mean squared error criteria. Finally a simulation study is presented to show the performance of the estimators. 相似文献
20.
We consider two consistent estimators for the parameters of the linear predictor in the Poisson regression model, where the
covariate is measured with errors. The measurement errors are assumed to be normally distributed with known error variance
σ
u
2
. The SQS estimator, based on a conditional mean-variance model, takes the distribution of the latent covariate into account,
and this is here assumed to be a normal distribution. The CS estimator, based on a corrected score function, does not use
the distribution of the latent covariate. Nevertheless, for small σ
u
2
, both estimators have identical asymptotic covariance matrices up to the order of σ
u
2
. We also compare the consistent estimators to the naive estimator, which is based on replacing the latent covariate with
its (erroneously) measured counterpart. The naive estimator is biased, but has a smaller covariance matrix than the consistent
estimators (at least up to the order of σ
u
2
). 相似文献