Pmc-optimal nonparametric quantile estimator

According to Pitman's Measure of Closeness, if T₁and T₂are two estimators of a real parameter $[d], then T₁is better than T₂if Po[d]{\T₁-o[d] < \T₂-0[d]\} > 1/2 for all 0[d]. It may however happen that while T₁is better than T₂and T₂is better than T₃, T₃is better than T₁. Given q ? (0,1) and a sample X₁, X₂, ..., X_nfrom an unknown F ? F, an estimator T* = T*(X₁,X₂...X_n)of the q-th quantile of the distribution F is constructed such that P_F{\F(T*)-q\ <[d] \F(T)-q\} >[d] 1/2 for all F?F and for all T€T, where F is a nonparametric family of distributions and T is a class of estimators. It is shown that T* =X_j:n'for a suitably chosen jth order statistic.     

Ridge regression estimators in the linear regression models with non-spherical errors

The present paper considers a family of ordinary ridge regression estimators in the linear regression model when the disturbances covariance matrix depends upon a few unknown parameters. An asymptotic expansion for the distribution of the ridge regression estimator is developed and under the quadratic loss function its asymptotic risk is compared with that of the feasible GLS estimator.     

On the recovery of intra- and interblock information in n-ary designs

This note presents an extension of Q-method of analysis for binary designs given by Rao (1956) to n-ary balanced and partially balanced block designs. Here a linked n-ary block (LNB) design is defined as the dual of balanced n-ary (BN) design. Having a note on Yates’ (1939, 1940) method of P-analysis, we further extend the expressions for binary linked block (LB) designs given by Rao (1956) to linked n-ary block (LNB) designs which admit easy estimation of parameters for these type of all n-ary designs.     

Forecasting lead times with economic data

Procurement lead time estimates are critical factors in production planning; however, they are generally based on a buyer&amp;apos;s experience. The Westinghouse Corporation developed a linear model which successfully predicted procurement lead times for hot and cold rolled steel. This paper discusses nine models which use utilization and inventory data to predict lead time planning factors for aluminum, magnesium, steel and titanium products. The Lockheed-Georgia Company, which produces aerospace products, provided data for this research. The functional form of the models is significant and suggests that a nonlinear transformation of utilization based upon simple queueing models is a significant predictor of lead time duration.     

“教”的读音演变及其与“叫”的历时更替

在表"使令"义上,唐代以前,主要以"使"、"令"为主;宋金时期,"教(交)"取代"使"和"令"成为当时口语中表"使令"义的主导词;而大约在明末清初,"教"在与"叫"的竞争中失去优势,被淘汰出局,"叫"成为至今表"使令"义的主导词。"教"本读去声,表"使令"义的"教"读作平声是为与原义区别而产生的一种破读,之所以后来又重新读为去声,是受"叫"读音影响的结果。     

A strong law of large number for negatively dependent and non identical distributed random variables in the framework of sublinear expectation

Abstract

In this article, in the framework of sublinear expectation initiated by Peng, we derive a strong law of large numbers (SLLN) for negatively dependent and non identical distributed random variables. This result includes and extends some existing results. Furthermore, we give two examples of our result for applications.     

Time-based goal chasing method for mixed-model assembly line problem with multiple work stations

In sequencing problems for mixed-model assembly line in JIT production system, the Goal Chasing method (GC) is widely used for parts used leveling goal. The difference in assembly time of each product is not taken into consideration in the Goal Chasing method. Assembly time usually varies with product types. In recent years, the Time-Based Goal Chasing method (TBGC) has been proposed. The advantage of TBGC is to consider the influence of different assembly time of each product and idle time in production period. TBGC, however, has been only applied to single work station problems. In this paper, TBGC is applied to an assembly line problem with multiple work stations. Furthermore, the sequencing method and use of Simulated Annealing (SA) or Local Search (LS) for this problem are proposed.     

On Necessary and Sufficient Conditions for Ordinary Least Squares Estimators to Be Best Linear Unbiased Estimators

Two often-quoted necessary and sufficient conditions for ordinary least squares estimators to be best linear unbiased estimators are described. Another necessary and sufficient condition is described, providing an additional tool for checking to see whether the covariance matrix of a given linear model is such that the ordinary least squares estimator is also the best linear unbiased estimator. The new condition is used to show that one of the two published conditions is only a sufficient condition.     

Hierarchical Variable Selection in Polynomial Regression Models

Significance tests on coefficients of lower-order terms in polynomial regression models are affected by linear transformations. For this reason, a polynomial regression model that excludes hierarchically inferior predictors (i.e., lower-order terms) is considered to be not well formulated. Existing variable-selection algorithms do not take into account the hierarchy of predictors and often select as “best” a model that is not hierarchically well formulated. This article proposes a theory of the hierarchical ordering of the predictors of an arbitrary polynomial regression model in m variables, where m is any arbitrary positive integer. Ways of modifying existing algorithms to restrict their search to well-formulated models are suggested. An algorithm that generates all possible well-formulated models is presented.     

Child custody issues and co‐occurrence of intimate partner violence and child maltreatment: controversies and points of agreement amongst practitioners

The situation of families undergoing separation in a context of co‐occurrence of intimate partner violence (IPV) and child maltreatment raises certain issues related to child custody. The results presented in this paper were collected and analysed within the framework of a qualitative study aiming to identify the principal points of agreement and the main controversies amongst practitioners in several different types of organizations. Focus groups were held with a total of 43 practitioners from six different settings concerned with child custody in cases of co‐occurrence of IPV and child maltreatment. Although they agreed on the importance of ensuring the safety of victims of violence, their views diverged on three points: (1) the importance of preserving the father–child relationship; (2) collaboration between voluntary organizations and semi‐voluntary or legal agencies; and (3) consideration of cultural differences.