On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

Generalized partially linear varying-coefficient models

Generalized varying-coefficient models are useful extensions of generalized linear models. They arise naturally when investigating how regression coefficients change over different groups characterized by certain covariates such as age. In this paper, we extend these models to generalized partially linear varying-coefficient models, in which some coefficients are constants and the others are functions of certain covariates. Procedures for estimating the linear and non-parametric parts are developed and their associated statistical properties are studied. The methods proposed are illustrated using some simulations and real data analysis.     

Stochastic Modelling of Times to Temperature for Furnaces Supplying Titanium Blooms to a Rolling Mill at TIMET

In conjunction with TIMET at Waunarlwydd (Swansea, UK) a model has been developed that will optimise the scheduling of various blooms to their eight furnaces so as to minimise the time taken to roll these blooms into the finished mill products. This production scheduling model requires reliable data on times taken for the various furnaces that heat the slabs and blooms to reach the temperatures required for rolling. These times to temperature are stochastic in nature and this paper identifies the distributional form for these times using the generalised F distribution as a modelling framework. The times to temperature were found to be similarly distributed over all furnaces. The identified distributional forms were incorporated into the scheduling model to optimise a particular campaign that was run at TIMET Swansea. Amongst other conclusion it was found that, compared to the actual campaign, the model produced a schedule that reduced the makespan by some 35%.     

短杆菌(Brevibacterium sp WX-10)产酶条件研究

研究了碳源、氮源、无机盐、金属离子等培养基组成和初始pH、通风量、温度等发酵条件对短杆菌(Bre vibacteriumspWX 10)产酶的影响,通过正校试验优化得到的产酶培养基组成及发酵条件:蔗糖1%,NaCl2 5%,牛肉膏0 05%,NaNO30 05%,pH7 5,500mL三角瓶装培养基50mL,30℃于220r/min旋转式摇床上培养72h.在该培养条件下WX 10产酶量是原培养条件下的1 85倍.     

Estimating ordered parameters by linear programming

There are many models that require the estimation of a set of ordered parameters. For example, multivariate analysis of variance often is formulated as testing for the equality of the parameters versus an ordered alternative. This problem, referred to as isotonic inference, constrained inference, or isotonic regression, has led to the development of general solutions, not often easy to apply in special models. In this expository paper, we study the special case of a separable convex quadratic programming problem for which the optimality conditions lead to a readily solved linear complementarity problem in the Lagrange multipliers, and subsequently to an equivalent linear programming problem, whose solution can be used to recover the solution of the original isotonic problem. The method can be applied to estimating ordered correlations, ordered binomial probabilities, ordered Poisson parameters, ordered exponential scale parameters, or ordered risk differences.     

A graphical summary of disparities in health care and related summary measures

In order to assess the effectiveness of government programs designed to reduce disparities in the health care minority groups receive relative to the majority white population, a proper statistical measure should be used. This article proposes a measure of and its accompanying graph, which is readily interpretable and is not affected by the number of minority subgroups examined.     

Estimating the distribution function using k-tuple ranked set samples

The basic assumption underlying the concept of ranked set sampling is that actual measurement of units is expensive, whereas ranking is cheap. This may not be true in reality in certain cases where ranking may be moderately expensive. In such situations, based on total cost considerations, k-tuple ranked set sampling is known to be a viable alternative, where one selects k units (instead of one) from each ranked set. In this article, we consider estimation of the distribution function based on k-tuple ranked set samples when the cost of selecting and ranking units is not ignorable. We investigate estimation both in the balanced and unbalanced data case. Properties of the estimation procedure in the presence of ranking error are also investigated. Results of simulation studies as well as an application to a real data set are presented to illustrate some of the theoretical findings.     

Nonparametric estimation of the conditional distribution function in a semiparametric censorship model

In this paper we propose a new nonparametric estimator of the conditional distribution function under a semiparametric censorship model. We establish an asymptotic representation of the estimator as a sum of iid random variables, balanced by some kernel weights. This representation is used for obtaining large sample results such as the rate of uniform convergence of the estimator, or its limit distributional law. We prove that the new estimator outperforms the conditional Kaplan–Meier estimator for censored data, in the sense that it exhibits lower asymptotic variance. Illustration through real data analysis is provided.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

Two point priors and Γ-minimax estimating in families of uniform distributions

It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The Γ-minimax estimator is derived for sets Γ of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in Γ.