Jiro Hodoshima 《统计学通讯:理论与方法》2013,42(5):661-674

This article considers the unconditional asymptotic covariance matrix of the least squares estimator in the linear regression model with stochastic explanatory variables. The asymptotic covariance matrix of the least squares estimator of regression parameters is evaluated relative to the standard asymptotic covariance matrix when the joint distribution of the dependent and explanatory variables is in the class of elliptically symmetric distributions. An empirical example using financial data is presented. Numerical examples and simulation experiments are given to illustrate the difference of the two asymptotic covariance matrices.  相似文献   

    

Rostyslav Maiboroda  Olena Sugakova 《统计学通讯:理论与方法》2013,42(1):96-116

A semiparametric two-component mixture model is considered, in which the distribution of one (primary) component is unknown and assumed symmetric. The distribution of the other component (admixture) is known. Generalized estimating equations are constructed for the estimation of the mixture proportion and the location parameter of the primary component. Asymptotic normality of the estimates is demonstrated and the lower bound for the asymptotic covariance matrix is obtained. An adaptive estimation technique is proposed to obtain the estimates with nearly optimal asymptotic variances.  相似文献   

    

Yongming Li  Chengdong Wei  Shanchao Yang 《统计学通讯:理论与方法》2013,42(20):3585-3595

Let {X _j , j ≥ 1} be a strictly stationary negatively or positively associated sequence of real valued random variables with unknown distribution function F(x). On the basis of the random variables {X _j , j ≥ 1}, we propose a smooth recursive kernel-type estimate of F(x), and study asymptotic bias, quadratic-mean consistency and asymptotic normality of the recursive kernel-type estimator under suitable conditions.  相似文献   

    

《Journal of Statistical Computation and Simulation》2012,82(2):335-343

A difference-based variance estimator is proposed for nonparametric regression in complex surveys. By using a combined inference framework, the estimator is shown to be asymptotically normal and to converge to the true variance at a parametric rate. Simulation studies show that the proposed variance estimator works well for complex survey data and also reveals some finite sample properties of the estimator.  相似文献   

    

Guosheng Yin  Hui Li 《Revue canadienne de statistique》2009,37(4):659-674

To enhance modeling flexibility, the authors propose a nonparametric hazard regression model, for which the ordinary and weighted least squares estimation and inference procedures are studied. The proposed model does not assume any parametric specifications on the covariate effects, which is suitable for exploring the nonlinear interactions between covariates, time and some exposure variable. The authors propose the local ordinary and weighted least squares estimators for the varying‐coefficient functions and establish the corresponding asymptotic normality properties. Simulation studies are conducted to empirically examine the finite‐sample performance of the new methods, and a real data example from a recent breast cancer study is used as an illustration. The Canadian Journal of Statistics 37: 659–674; 2009 © 2009 Statistical Society of Canada  相似文献   

    

Donald W. K. Andrews  Patrik Guggenberger 《Econometrica : journal of the Econometric Society》2003,71(2):675-712

In this paper, we propose a simple bias–reduced log–periodogram regression estimator, ^d_r, of the long–memory parameter, d, that eliminates the first– and higher–order biases of the Geweke and Porter–Hudak (1983) (GPH) estimator. The bias–reduced estimator is the same as the GPH estimator except that one includes frequencies to the power 2k for k=1,…,r, for some positive integer r, as additional regressors in the pseudo–regression model that yields the GPH estimator. The reduction in bias is obtained using assumptions on the spectrum only in a neighborhood of the zero frequency. Following the work of Robinson (1995b) and Hurvich, Deo, and Brodsky (1998), we establish the asymptotic bias, variance, and mean–squared error (MSE) of ^d_r, determine the asymptotic MSE optimal choice of the number of frequencies, m, to include in the regression, and establish the asymptotic normality of ^d_r. These results show that the bias of ^d_r goes to zero at a faster rate than that of the GPH estimator when the normalized spectrum at zero is sufficiently smooth, but that its variance only is increased by a multiplicative constant. We show that the bias–reduced estimator ^d_r attains the optimal rate of convergence for a class of spectral densities that includes those that are smooth of order s≥1 at zero when r≥(s−2)/2 and m is chosen appropriately. For s>2, the GPH estimator does not attain this rate. The proof uses results of Giraitis, Robinson, and Samarov (1997). We specify a data–dependent plug–in method for selecting the number of frequencies m to minimize asymptotic MSE for a given value of r. Some Monte Carlo simulation results for stationary Gaussian ARFIMA (1, d, 1) and (2, d, 0) models show that the bias–reduced estimators perform well relative to the standard log–periodogram regression estimator.  相似文献   

    

Mortaza Jamshidian  Ke‐Hai Yuan 《Wiley Interdisciplinary Reviews: Computational Statistics》2014,6(1):56-73

This paper reviews various methods of identifying missing data mechanisms. The three well‐known mechanisms of missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR) are considered. A number of tests deem rejection of homogeneity of means and/or covariances (HMC) among observed data patterns as a means to reject MCAR. Utility of these tests as well as their shortcomings are discussed. In particular, examples of MAR and MNAR data with homogeneous means and covariances between their observed data patterns are provided for which tests of HMC fail to reject MCAR. More generally, tests of homogeneity of parameter estimates between various subsets of data are reviewed and their utility as tests of MCAR and MAR (in special cases) is pointed out. Since many tests of MCAR assume multinormality, methods to assess this assumption in the context of incomplete data are reviewed. Tests of homogeneity of distributions among observed data patterns for MCAR are also considered. A new nonparametric test of this type is proposed on the basis of pairwise comparison of marginal distributions. Finally, methods of examining missing data mechanism based on sensitivity analysis including methods that model missing data mechanism based on logistic, probit, and latent variable regression models, as well as methods that do not require modeling of missing data mechanism are reviewed. The paper concludes with some practical comments about the validity and utility of tests of missing data mechanism. WIREs Comput Stat 2014, 6:56–73. doi: 10.1002/wics.1287 This article is categorized under:

• Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
• Applications of Computational Statistics > Psychometrics

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Karim Anaya&#x;Izquierdo  Frank Critchley  Paul Marriott 《Stat》2014,3(1):17-22

This paper looks at boundary effects on inference in an important class of models including, notably, logistic regression. Asymptotic results are not uniform across such models. Accordingly, whatever their order, methods asymptotic in sample size will ultimately “break down” as the boundary is approached, in the sense that effects such as infinite skewness, discreteness and collinearity will dominate. In this paper, a highly interpretable diagnostic tool is proposed, allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques. Copyright © 2014 John Wiley & Sons Ltd.  相似文献   

    

《Statistical Methodology》2014

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  总被引：1，自引：0，他引：1  

Antonio Martín Andrés  María Álvarez Hernández 《Journal of applied statistics》2014,41(7):1516-1529

This paper evaluates 29 methods for obtaining a two-sided confidence interval for a binomial proportion (16 of which are new proposals) and comes to the conclusion that: Wilson's classic method is only optimal for a confidence of 99%, although generally it can be applied when n≥50; for a confidence of 95% or 90%, the optimal method is the one based on the arcsine transformation (when this is applied to the data incremented by 0.5), which behaves in a very similar manner to Jeffreys’ Bayesian method. A simpler option, though not so good as those just mentioned, is the classic-adjusted Wald method of Agresti and Coull.  相似文献