The least concave majorant of the empirical distribution function

The author compares two estimators of a continuous, concave distribution function having support on the positive half line. In terms of samples from uniform distributions, he gives stochastic bounds for the pointwise and sup‐norm differences between the least concave majorant of the empirical distribution function and the underlying distribution function. He also offers evidence demonstrating the almost paradoxical result that the empirical distribution function is not as good an estimator as its least concave majorant in terms of sup‐norm error but a better pointwise estimator of the true distribution function in terms of mean squared error.     

Confidence regions for the common mean vector of several multivariate normal populations

Suppose that there are independent samples available from several multivariate normal populations with the same mean vector m? but possibly different covariance matrices. The problem of developing a confidence region for the common mean vector based on all the samples is considered. An exact confidence region centered at a generalized version of the well-known Graybill-Deal estimator of m? is developed, and a multiple comparison procedure based on this confidence region is outlined. Necessary percentile points for constructing the confidence region are given for the two-sample case. For more than two samples, a convenient method of approximating the percentile points is suggested. Also, a numerical example is presented to illustrate the methods. Further, for the bivariate case, the proposed confidence region and the ones based on individual samples are compared numerically with respect to their expected areas. The numerical results indicate that the new confidence region is preferable to the single-sample versions for practical use.     

Sieve Empirical Likelihood and Extensions of the Generalized Least Squares

The empirical likelihood cannot be used directly sometimes when an infinite dimensional parameter of interest is involved. To overcome this difficulty, the sieve empirical likelihoods are introduced in this paper. Based on the sieve empirical likelihoods, a unified procedure is developed for estimation of constrained parametric or non-parametric regression models with unspecified error distributions. It shows some interesting connections with certain extensions of the generalized least squares approach. A general asymptotic theory is provided. In the parametric regression setting it is shown that under certain regularity conditions the proposed estimators are asymptotically efficient even if the restriction functions are discontinuous. In the non-parametric regression setting the convergence rate of the maximum estimator based on the sieve empirical likelihood is given. In both settings, it is shown that the estimator is adaptive for the inhomogeneity of conditional error distributions with respect to predictor, especially for heteroscedasticity.     

Combining information from multiple surveys through the empirical likelihood method

It is often desirable to combine information collected in compatible multiple surveys in order to improve estimation and meet consistency requirements. Zieschang (1990) and Renssen & Nieuwenbroek (1997) suggested to this end the use of the generalized regression estimator with enlarged number of auxiliary variables. Unfortunately, adjusted weights associated with their approach can be negative. The author uses the notion of pseudo empirical likelihood to construct new estimators that are consistent, efficient and possess other attractive properties. The proposed approach is asymptotically equivalent to the earlier one, but it has clear maximum likelihood interpretations and its adjusted weights are always positive. The author also provides efficient algorithms for computing his estimators.     

Dealing with Ties in Failure Time Data

In dealing with ties in failure time data the mechanism by which the data are observed should be considered. If the data are discrete, the process is relatively simple and is determined by what is actually observed. With continuous data, ties are not supposed to occur, but they do because the data are grouped into intervals (even if only rounding intervals). In this case there is actually a non–identifiability problem which can only be resolved by modelling the process. Various reasonable modelling assumptions are investigated in this paper. They lead to better ways of dealing with ties between observed failure times and censoring times of different individuals. The current practice is to assume that the censoring times occur after all the failures with which they are tied.     

有调整因子的回归弱相关估计

针对回归分析中自变量数据间的共线性问题，本文基于降低解释变量间相关程度的弱相关思想，构造出一个新的回归估计式。并证明了估计式与最小二乘相比，具有均方差意义下 的优良性。还证明了相对于最小二乘估计，新估计式是一种模压缩。该估计式具有意义直观明了，便于分析，应用的特性。     

一种NLOS环境定位精度提高方法

用蜂窝网络对移动台进行定位估计时,为了降低电波的非视距传播对定位精度的不利影响,提出了一种先对电波到达时间差和到达时间测量值进行平滑和重构,再采用两次加权最小二乘算法对移动台进行定位估计的算法。仿真结果表明,该算法在电波的非视距环境中能显著提高对移动台的定位性能。     

On geometry of the set of admissible invariant quadratic estimators in balanced two variance components model

Two variance components model for which each invariant quadratic admissible estimator of a linear function of variance components (under quadratic loss function) is a linear combination of two quadratic forms,Z ₁,Z ₂, say, is considered. A setD={(d ₁,d ₂)′:d ₁ Z ₁+d ₂ Z ₂ is admissible} is described by giving formulae on the boundary ofD. Different forms of the setD are presented on figures.     

On the discretization of nonparametric isotropic covariogram estimators

In this article, we describe the discretization of nonparametric covariogram estimators for isotropic stationary stochastic processes. The use of nonparametric estimators is important to avoid the difficulties in selecting a parametric model. The key property the isotropic covariogram must satisfy is to be positive definite and thus have the form characterized by Yaglom's representation of Bochner's theorem. We present an optimal discretization of the latter in the sense that the resulting nonparametric covariogram estimators are guaranteed to be smooth and positive definite in the continuum. This provides an answer to an issue raised by Hall, Fisher and Hoffmann (1994). Furthermore, from a practical viewpoint, our result is important because a nonlinear constrained algorithm can sometimes be avoided and the solution can be found by least squares. Some numerical results are presented for illustration.