V. Fakoor  N. Nakhaei Rad 《统计学通讯:理论与方法》2013,42(12):2271-2279

In this article, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate O[(log n)^?λ] for some λ > 0. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.  相似文献   

    

《Journal of Statistical Computation and Simulation》2012,82(2):393-404

We propose a method that uses a sequential design instead of a space filling design for estimating tuning parameters of a complex computer model. The goal is to bring the computer model output closer to the real system output. The method fits separate Gaussian process (GP) models to the available data from the physical experiment and the computer experiment and minimizes the discrepancy between the predictions from the GP models to obtain estimates of the tuning parameters. A criterion based on the discrepancy between the predictions from the two GP models and the standard error of prediction for the computer experiment output is then used to obtain a design point for the next run of the computer experiment. The tuning parameters are re-estimated using the augmented data set. The steps are repeated until the budget for the computer experiment data is exhausted. Simulation studies show that the proposed method performs better in bringing a computer model closer to the real system than methods that use a space filling design.  相似文献   

    

Qiying Wang  Peter C. B. Phillips 《Econometrica : journal of the Econometric Society》2009,77(6):1901-1948

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill‐posed inverse problems. In functional cointegrating regressions where the regressor is an integrated or near‐integrated time series, it is shown here that inverse and ill‐posed inverse problems do not arise. Instead, simple nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving straightforward asymptotics that are useable in practical work. It is further shown that use of augmented regression, as is common in linear cointegration modeling to address endogeneity, does not lead to bias reduction in nonparametric regression, but there is an asymptotic gain in variance reduction. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series when there is a single integrated or near‐integrated regressor. The methods may be applied to a range of empirical models where functional estimation of cointegrating relations is required.  相似文献   

    

A. Asrat Atsedeweyn  K. Srinivasa Rao 《Journal of applied statistics》2014,41(2):364-381

Regression models play a dominant role in analyzing several data sets arising from areas like agricultural experiment, space experiment, biological experiment, financial modeling, etc. One of the major strings in developing the regression models is the assumption of the distribution of the error terms. It is customary to consider that the error terms follow the Gaussian distribution. However, there are some drawbacks of Gaussian errors such as the distribution being mesokurtic having kurtosis three. In many practical situations the variables under study may not be having mesokurtic but they are platykurtic. Hence, to analyze these sorts of platykurtic variables, a two-variable regression model with new symmetric distributed errors is developed and analyzed. The maximum likelihood (ML) estimators of the model parameters are derived. The properties of the ML estimators with respect to the new symmetrically distributed errors are also discussed. A simulation study is carried out to compare the proposed model with that of Gaussian errors and found that the proposed model performs better when the variables are platykurtic. Some applications of the developed model are also pointed out.  相似文献   

    

Fabienne Comte  Adeline Samson  Julien J Stirnemann 《Scandinavian Journal of Statistics》2014,41(2):325-345

In general, the precise date of onset of pregnancy is unknown and may only be estimated from ultrasound biometric measurements of the embryo. We want to estimate the density of the random variables corresponding to the interval between last menstrual period and true onset of pregnancy. The observations correspond to the variables of interest up to an additive noise. We suggest an estimation procedure based on deconvolution. It requires the knowledge of the density of the noise which is not available. But we have at our disposal another specific sample with replicate observations for twin pregnancies. This allows both to estimate the noise density and to improve the deconvolution step. Convergence rates of the final estimator are studied and compared with other settings. Our estimator involves a cut‐off parameter for which we propose a cross‐validation type procedure. Lastly, we estimate the target density in spontaneous pregnancies with an estimation of the noise obtained from replicate observations in twin pregnancies.  相似文献   

    

Jonathan Jaeger  Philippe Lambert 《Journal of applied statistics》2014,41(12):2709-2726

A full Bayesian approach based on ordinary differential equation (ODE)-penalized B-splines and penalized Gaussian mixture is proposed to jointly estimate ODE-parameters, state function and error distribution from the observation of some state functions involved in systems of affine differential equations. Simulations inspired by pharmacokinetic (PK) studies show that the proposed method provides comparable results to the method based on the standard ODE-penalized B-spline approach (i.e. with the Gaussian error distribution assumption) and outperforms the standard ODE-penalized B-splines when the distribution is not Gaussian. This methodology is illustrated on a PK data set.  相似文献   

  总被引：1，自引：0，他引：1  

Jesper Møller  Håkon Toftaker 《Scandinavian Journal of Statistics》2014,41(2):414-435

We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.  相似文献   

    

Martin Bilodeau 《Revue canadienne de statistique》2014,42(2):185-203

  相似文献   

    

Artur J. Lemonte 《统计学通讯:理论与方法》2014,43(15):3314-3328

In this article, we consider the class of censored exponential regression models which is very useful for modeling lifetime data. Under a sequence of Pitman alternatives, the asymptotic expansions up to order n^{? 1/2} of the non null distribution functions of the likelihood ratio, Wald, Rao score, and gradient statistics are derive in this class of models. The non null asymptotic distribution functions of these statistics are obtained for testing a composite null hypothesis in the presence of nuisance parameters. The power of all four tests, which are equivalent to first order, are compared based on these non null asymptotic expansions. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, we consider Monte Carlo simulations. We also present an empirical application for illustrative purposes.  相似文献   

    

Eric Ghysels  Fangfang Wang 《商业与经济统计学杂志》2014,32(1):88-111

Suppose one uses a parametric density function based on the first four (conditional) moments to model risk. There are quite a few densities to choose from and depending on which is selected, one implicitly assumes very different tail behavior and very different feasible skewness/kurtosis combinations. Surprisingly, there is no systematic analysis of the tradeoff one faces. It is the purpose of the article to address this. We focus on the tail behavior and the range of skewness and kurtosis as these are key for common applications such as risk management.  相似文献