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871.
We propose in this article a novel dimension reduction method for varying coefficient models. The proposed method explores the rank reducible structure of those varying coefficients, hence, can do dimension reduction and semiparametric estimation, simultaneously. As a result, the new method not only improves estimation accuracy but also facilitates practical interpretation. To determine the structure dimension, a consistent BIC criterion is developed. Numerical experiments are also presented. 相似文献
872.
The authors consider a partially linear autoregressive model and construct kernel‐based estimates for both the parametric and nonparametric components. They propose an estimation procedure for the model and illustrate it through simulated and real data. Their work shows that the proposed estimation procedure not only has good asymptotic properties but also works well numerically. It also suggests that a partially linear autoregression is more appropriate than a completely nonparametric autoregression for some sets of data. 相似文献
873.
When spatial data are correlated, currently available data‐driven smoothing parameter selection methods for nonparametric regression will often fail to provide useful results. The authors propose a method that adjusts the generalized cross‐validation criterion for the effect of spatial correlation in the case of bivariate local polynomial regression. Their approach uses a pilot fit to the data and the estimation of a parametric covariance model. The method is easy to implement and leads to improved smoothing parameter selection, even when the covariance model is misspecified. The methodology is illustrated using water chemistry data collected in a survey of lakes in the Northeastern United States. 相似文献
874.
Over forty years ago, Grenander derived the MLE of a monotone decreasing density f with known mode. Prakasa Rao obtained the asymptotic distribution of this estimator at a fixed point x where f' (x) < 0. Here, we obtain the asymptotic distribution of this estimator at a fixed point x when f is constant and nonzero in some open neighborhood of x. This limiting distribution is expressible as the convolution of a closed-form density and a rescaled standard normal density. Groeneboom (1983) derived the aforementioned closed-form density and we provide an alternative, more direct derivation. 相似文献
875.
Abstract. Functional measures of skewness and kurtosis, called asymmetry and gradient asymmetry functions, are described for continuous univariate unimodal distributions. They are defined and interpreted directly in terms of the density function and its derivative. Asymmetry is defined by comparing distances from points of equal density to the mode. Gradient asymmetry is defined, in novel fashion, as asymmetry of an appropriate function of the density derivative. Properties and illustrations of asymmetry and gradient asymmetry functions are presented. Estimation of them is considered and illustrated with an example. Scalar summary skewness and kurtosis measures associated with asymmetry and gradient asymmetry functions are discussed. 相似文献
876.
F. Abramovich T. Sapatinas & B. W. Silverman 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1998,60(4):725-749
We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed to capture the sparseness of wavelet expansion that is common to most applications. For the prior specified, the posterior median yields a thresholding procedure. Our prior model for the underlying function can be adjusted to give functions falling in any specific Besov space. We establish a relationship between the hyperparameters of the prior model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relationship gives insight into the meaning of the Besov space parameters. Moreover, the relationship established makes it possible in principle to incorporate prior knowledge about the function's regularity properties into the prior model for its wavelet coefficients. However, prior knowledge about a function's regularity properties might be difficult to elicit; with this in mind, we propose a standard choice of prior hyperparameters that works well in our examples. Several simulated examples are used to illustrate our method, and comparisons are made with other thresholding methods. We also present an application to a data set that was collected in an anaesthesiological study. 相似文献
877.
《Journal of Statistical Computation and Simulation》2012,82(3-4):167-180
The inverse of the Student's t-distribution is often needed in computer simulation and applied statistics, e.g, in generating random variates from t-distributions and in computing tables needed for statistical procedures which do not assume known variances. The t-distribution algorithm of Dudewicz and Dalal (1972) can be used to approximate the inverset t distribution function. The author notes an algorithm for evaluation of this inverse d.f. which can be implemented in a fast, accurate and short computer program. The error analysis is also reported. An application is considered for the problem of testing the hypothesis that a sequence of random variates follows Student's-t distribution. 相似文献
878.
Marianna Pensky 《Journal of statistical planning and inference》2000,90(2):275-292
Assume that in independent two-dimensional random vectors (X1,θ1),…,(Xn,θn), each θi is distributed according to some unknown prior density function g. Also, given θi=θ, Xi has the conditional density function q(x−θ), x,θ(−∞,∞) (a location parameter case), or θ−1q(x/θ), x,θ(0,∞) (a scale parameter case). In each pair the first component is observable, but the second is not. After the (n+1)th pair (Xn+1,θn+1) is obtained, the objective is to construct an empirical Bayes (EB) estimator of θ. In this paper we derive the EB estimators of θ based on a wavelet approximation with Meyer-type wavelets. We show that these estimators provide adaptation not only in the case when g belongs to the Sobolev space H with an unknown , but also when g is supersmooth. 相似文献
879.
蚁族现象的本质是大学毕业生选择在大城市还是中小城镇就业的问题。从理性人假设的角度来看,"蚁族"现象的原因在于"蚁族"们为了获得更多的就业机会、更高的就业质量等经济收益,和更多的教育收益、消费收益、心理收益和健康收益等非经济收益,从而主动选择在大城市就业的结果。减少"蚁族"现象的思路在于提高大学毕业生收入、促进教育公平和均衡发展、重视发展中小城镇、引导大学毕业生到中小城镇就业。 相似文献
880.
In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbour balls are used as a multidimensional analogue to univariate spacings. A class of information‐type measures is used to generalize the concept of maximum spacing estimators. Weak and strong consistency of these generalized maximum spacing estimators are proved both when the assigned model class is correct and when the true density is not a member of the model class. An example of the generalized maximum spacing method in model validation context is discussed. 相似文献