共查询到20条相似文献,搜索用时 15 毫秒
1.
An example is given to reveal the abnormal behavior of the least squares estimate of multiple regression. It is shown that
the least squares estimate of the multiple linear regression may be “improved” in the sense of weak consistency when nuisance
parameters are introduced into the model. A discussion on the implications of this finding is given. 相似文献
2.
In this paper we determine all the bipartite graphs with the maximum sum of squares of degrees among the ones with a given number of vertices and edges. 相似文献
3.
4.
The convergence rates of empirical Bayes estimation in a multiple linear regression model 总被引:6,自引:0,他引:6
Empirical Bayes (EB) estimation of the parameter vector =(,2) in a multiple linear regression modelY=X+ is considered, where is the vector of regression coefficient, N(0,2
I) and 2 is unknown. In this paper, we have constructed the EB estimators of by using the kernel estimation of multivariate density function and its partial derivatives. Under suitable conditions it is shown that the convergence rates of the EB estimators areO(n
-(k-1)(k-2)/k(2k+p+1)), where the natural numberk3, 1/3<<1, andp is the dimension of vector .The project is supported by the National Natural Science Foundation of China. 相似文献
5.
6.
We construct a precise Berry-Esseen bound for the least squares error variance estimators of regression parameters. Our bound
depends explicitly on the sequence of design variables and is of the order O(N
−1/2) if this sequence is “regular” enough.
Supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published
in Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 1–8, January–March, 1999. 相似文献
7.
生产函数中参数估计方法的改进 总被引:2,自引:0,他引:2
在原有生产函数参数估计方法的基础上,提出一种新的估计方法。计算实例表明:该估计方法具有最小的残差平方和,是一种比较理想的估计方法 相似文献
8.
本文通过例子介绍多元线性回归中自变量共线性的诊断以及使用 SAS/SATA( 6.12 )软件中的 REG等过程的增强功能处理回归变量共线性的一些方法。包括筛选变量法 ,岭回归分析法 ,主成分回归法和偏最小二乘回归法 相似文献
9.
In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set. 相似文献
10.
In this article, we exhibit under suitable conditions a neat relationship between the least squares g-inverse for a sum of two matrices and the least squares g-inverses of the individual terms. We give a necessary and sufficient condition for the set equations (A?+?B){1,?3}?=?A{1,?3}?+?B{1,?3} and (A?+?B){1,?4}?=?A{1,?4}?+?B{1,?4}. 相似文献
11.
The unknown parameters in multiple linear regression models may be estimated using any one of a number of criteria such as the minimization of the sum of squared errors MSSE, the minimization of the sum of absolute errors MSAE, and the minimization of the maximum absolute error MMAE. At present, the MSSE or the least squares criterion continues to be the most popular. However, at times the choice of a criterion is not clear from statistical, practical or other considerations. Under such circumstances, it may be more appropriate to use multiple criteria rather than a single criterion to estimate the unknown parameters in a multiple linear regression model. We motivate the use of multiple criteria estimation in linear regression models with an example, propose a few models, and outline a solution procedure. 相似文献
12.
Empirical Bayes estimation in a multiple linear regression model 总被引:6,自引:0,他引:6
R. S. Singh 《Annals of the Institute of Statistical Mathematics》1985,37(1):71-86
Summary Estimation of the vector β of the regression coefficients in a multiple linear regressionY=Xβ+ε is considered when β has a completely unknown and unspecified distribution and the error-vector ε has a multivariate standard
normal distribution. The optimal estimator for β, which minimizes the overall mean squared error, cannot be constructed for
use in practice. UsingX, Y and the information contained in the observation-vectors obtained fromn independent past experiences of the problem, (empirical Bayes) estimators for β are exhibited. These estimators are compared
with the optimal estimator and are shown to be asymptotically optimal. Estimators asymptotically optimal with rates nearO(n
−1) are constructed.
Supported in part by a Natural Sciences and Engineering Research Council of Canada grant. 相似文献
13.
Evald Übi 《Central European Journal of Mathematics》2007,5(2):373-385
The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using
orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step
all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like
in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for
unstable and degenerate problems primarily.
相似文献
14.
For positive integers with a
r
= 2, the multiple zeta value or r-fold Euler sum is defined as [2]
. There is a celebrated sum formula [6, 10] among multiple zeta values as
,
where range over all positive integers with in the summation.
In this paper, we shall prove the so called restricted sum formula [4]. Namely, for all positive integers m and q with m ≥ q and a nonnegative integer p, that
. We prove the assertion by new expressions of multiple zeta values in terms of Drinfeld integrals.
This work was supported by the Department of Mathematics, National Chung Cheng University and by the National Science Council
of Taiwan, Republic of China. 相似文献
15.
In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation (MSE) and mean absolute estimation (MAE) criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations. 相似文献
16.
B.L.S.Prakasa Rao 《Statistics & probability letters》1985,3(1):15-18
The asymptotic properties of the least squares estimator are derived for a nonregular nonlinear model via the study of weak convergence of the least squares process. This approach was adapted earlier by the author in the smooth case. The model discussed here is not amenable to analysis via the normal equations and Taylor expansions used by earlier authors. 相似文献
17.
Shuai Zhai 《Journal of Number Theory》2013,133(11):3862-3876
Let denote the nth normalized Fourier coefficient of the classical holomorphic cusp form of even integral weight for the full modular group . In this paper, we investigate the average behavior of the power sum for , and . 相似文献
18.
Online signal extraction by robust linear regression 总被引:1,自引:0,他引:1
Summary In intensive care, time series of vital parameters have to be analysed online, i.e. without any time delay, since there may
be serious consequences for the patient otherwise. Such time series show trends, slope changes and sudden level shifts, and
they are overlaid by strong noise and many measurement artefacts. The development of update algorithms and the resulting increase
in computational speed allows to apply robust regression techniques to moving time windows for online signal extraction. By
simulations and applications we compare the performance of least median of squares, least trimmed squares, repeated median and deepest regression for online signal extraction. 相似文献
19.
In this paper,the estimation of joint dlstribution F(y,z)of(Y,Z)and the estimation in thelinear regression model Y=b'Z+εfor complete data are extended to that of the right censored data.Theregression parameter estimates of b and the variance of ε are weighted least square estimates with randomweights. The central limit theorems of the estimators are obtained under very weak conditions and the derivedasymptotic variance has a very simple form. 相似文献