Merging information for semiparametric density estimation

Summary.  The density ratio model specifies that the likelihood ratio of m −1 probability density functions with respect to the m th is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt variants of well-established techniques to choose the smoothing parameter for the density estimators proposed.     

Modified cross-validation in density estimation

We propose a new modified (biased) cross-validation method for adaptively determining the bandwidth in a nonparametric density estimation setup. It is shown that the method provides consistent minimizers. Some simulation results are reported on which compare the small sample behavior of the new and the classical cross-validation selectors.     

几种岭参数选择方法的比较

比较了不同的几种岭参数选择方法的应用效果，结果表明，几种方法中没有一种方法被认为是优于其它的方法。但在均方误差准则下．几种岭参数选择方法所获得的估计都改进了设计阵呈病态时的最小二乘估计。     

Difference-based matrix perturbation method for semi-parametric regression with multicollinearity

This paper addresses the collinearity problems in semi-parametric linear models. Under the difference-based settings, we introduce a new diagnostic, the difference-based variance inflation factor (DVIF), for detecting the presence of multicollinearity in semi-parametric models. The DVIF is then used to device a difference-based matrix perturbation method for solving the problem. The electricities distribution data set is analyzed, and numerical evidences validate the effectiveness of the proposed method.     

Shrinkage estimation of proportion via logit penalty

By releasing the unbiasedness condition, we often obtain more accurate estimators due to the bias–variance trade-off. In this paper, we propose a class of shrinkage proportion estimators which show improved performance over the sample proportion. We provide the “optimal” amount of shrinkage. The advantage of the proposed estimators is given theoretically as well as explored empirically by simulation studies and real data analyses.     

Biased Bootstrap Methods for Reducing the Effects of Contamination

Contamination of a sampled distribution, for example by a heavy-tailed distribution, can degrade the performance of a statistical estimator. We suggest a general approach to alleviating this problem, using a version of the weighted bootstrap. The idea is to 'tilt' away from the contaminated distribution by a given (but arbitrary) amount, in a direction that minimizes a measure of the new distribution's dispersion. This theoretical proposal has a simple empirical version, which results in each data value being assigned a weight according to an assessment of its influence on dispersion. Importantly, distance can be measured directly in terms of the likely level of contamination, without reference to an empirical measure of scale. This makes the procedure particularly attractive for use in multivariate problems. It has several forms, depending on the definitions taken for dispersion and for distance between distributions. Examples of dispersion measures include variance and generalizations based on high order moments. Practicable measures of the distance between distributions may be based on power divergence, which includes Hellinger and Kullback–Leibler distances. The resulting location estimator has a smooth, redescending influence curve and appears to avoid computational difficulties that are typically associated with redescending estimators. Its breakdown point can be located at any desired value ε∈ (0, ½) simply by 'trimming' to a known distance (depending only on ε and the choice of distance measure) from the empirical distribution. The estimator has an affine equivariant multivariate form. Further, the general method is applicable to a range of statistical problems, including regression.     

A characteristic function approach to the biased sampling model,with application to robust logistic regression

Many sampling problems from multiple populations can be considered under the semiparametric framework of the biased, or weighted, sampling model. Included under this framework is logistic regression under case–control sampling. For any model, atypical observations can greatly influence the maximum likelihood estimate of the parameters. Several robust alternatives have been proposed for the special case of logistic regression. However, some current techniques can exhibit poor behavior in many common situations. In this paper a new family of procedures are constructed to estimate the parameters in the semiparametric biased sampling model. The procedures incorporate a minimum distance approach, but are instead based on characteristic functions. The estimators can also be represented as the minimizers of quadratic forms in simple residuals, thus yielding straightforward computation. For the case of logistic regression, the resulting estimators are shown to be competitive with the existing robust approaches in terms of both robustness and efficiency, while maintaining affine equivariance. The approach is developed under the case–control sampling scheme, yet is shown to be applicable under prospective sampling logistic regression as well.     

A new 'biased coin design' for the sequential allocation of two treatments

Summary.  Efron's biased coin design is a well-known randomization technique that helps to neutralize selection bias in sequential clinical trials for comparing treatments, while keeping the experiment fairly balanced. Extensions of the biased coin design have been proposed by several researchers who have focused mainly on the large sample properties of their designs. We modify Efron's procedure by introducing an adjustable biased coin design, which is more flexible than his. We compare it with other existing coin designs; in terms of balance and lack of predictability, its performance for small samples appears in many cases to be an improvement with respect to the other sequential randomized allocation procedures.     

A theoretical analysis of the power of biased coin designs

Outlining some recently obtained results of Hu and Rosenberger [2003. Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc. 98, 671–678] and Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835] on the relationship between sequential randomized designs and the power of the usual statistical procedures for testing the equivalence of two competing treatments, the aim of this paper is to provide theoretical proofs of the numerical results of Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835]. Furthermore, we prove that the Adjustable Biased Coin Design [Baldi Antognini A., Giovagnoli, A., 2004. A new “biased coin design” for the sequential allocation of two treatments. J. Roy. Statist. Soc. Ser. C 53, 651–664] is uniformly more powerful than the other “coin” designs proposed in the literature for any sample size.