A class of partially linear single‐index survival models

The authors define a class of “partially linear single‐index” survival models that are more flexible than the classical proportional hazards regression models in their treatment of covariates. The latter enter the proposed model either via a parametric linear form or a nonparametric single‐index form. It is then possible to model both linear and functional effects of covariates on the logarithm of the hazard function and if necessary, to reduce the dimensionality of multiple covariates via the single‐index component. The partially linear hazards model and the single‐index hazards model are special cases of the proposed model. The authors develop a likelihood‐based inference to estimate the model components via an iterative algorithm. They establish an asymptotic distribution theory for the proposed estimators, examine their finite‐sample behaviour through simulation, and use a set of real data to illustrate their approach.     

Empirical likelihood tests for two‐sample problems via nonparametric density estimation

The authors study the problem of testing whether two populations have the same law by comparing kernel estimators of the two density functions. The proposed test statistic is based on a local empirical likelihood approach. They obtain the asymptotic distribution of the test statistic and propose a bootstrap approximation to calibrate the test. A simulation study is carried out in which the proposed method is compared with two competitors, and a procedure to select the bandwidth parameter is studied. The proposed test can be extended to more than two samples and to multivariate distributions.     

The strong uniform convergence of multivariate variable kernel estimates

We show that sup, completely as, where f is a uniformly continuous density on are independent random vectors with common density f, and f_n is the variable kernel estimate Here H_ni is the distance between X_i and its kth nearest neighbour, K is a given density satisfying some regularity conditions, and k is a sequence of integers with the property that log asn     

机载SAR斜侧视成像的高效空变算法

针对机载合成孔径雷达ＳＡＲ斜侧视成像的二维处理特性，采用一种全聚焦的处理方法，它能方便地处理斜侧视ＳＡＲ参考函数的空间变化的特性，并提高计算效率。     

Nonparametric estimation of discrete hazard functions

A smoothing procedure for discrete time failure data is proposed which allows for the inclusion of covariates. This purely nonparametric method is based on discrete or continuous kernel smoothing techniques that gives a compromise between the data and smoothness. The method may be used as an exploratory tool to uncover the underlying structure or as an alternative to parametric methods when prediction is the primary objective. Confidence intervals are considered and alternative techniques of cross validation based choices of smoothing parameters are investigated.     

Random Weighted Bootstrap Method for Recurrent Events with Informative Censoring

Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption, the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable. Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for inpatient cares over time.     

The Recursive Kernel Distribution Function Estimator Based on Negatively and Positively Associated Sequences

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.     

Quantile Regression with Left-Truncated and Right-Censored Data in a Reproducing Kernel Hilbert Space

Li et al. (2007 Li, Y., Liu, Y., Zhu, J. (2007). Quantile regression in reproducing kernel Hilbert spaces. J. Amer. Statist. Assoc. 102:255–268.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) developed an estimation method for quantile functions in a reproducing kernel Hilbert space for complete data, and Park and Kim (2011 Park, J., Kim, J. (2011). Quantile regression with an epsilon-insensitive loss in a reproducing kernel Hilbert space. Statist. Probab. Lett. 81:62–70.[Crossref], [Web of Science ®] , [Google Scholar]) proposed an estimation method using the ε-insensitive loss. This article extends these estimation methods to left-truncated and right-censored data. As a measure of goodness of fit, the check loss and the ε-insensitive loss were used to estimate the quantile function. The ε-insensitive loss can shrink the estimated coefficients toward zero; hence, it can reduce the variability of the estimates. Simulation studies show that the estimated quantile functions based on the ε-insensitive loss perform slightly better when ε is adequately chosen.     

Mean intergrated squared error properties and optimal kernels when estimating a diatribution function

Let X₁,X₂,… X_n be a sample of independent identically distributed (i.i.d)random variables having an unknown absolutely continuous distribution function f with density f the twofold aim of his paper consists in, firstly deriving asymptotic expressions of the mean intergrated squared error (MISE) of a kernel estimator of F when f is either assumed to be continuous everywhere or problem of finding optimal kernels in these two cases is studied in detail.     

A plug-in technique in nonparametric regression with dependence

The problem addressed is that of smoothing parameter selection in kernel nonparametric regression in the fixed design regression model with dependent noise. An asymptotic expression of the optimum bandwidth parameter has been obtained in recent studies, where this takes the form h = C ₀ n ^?1/5. This paper proposes to use a plug-in methodology, in order to obtain an optimum estimation of the bandwidth parameter, through preliminary estimation of the unknown value of C ₀.