An optimal property of the “(r,k ) class estimators”

The purpose of this work is to display optimal conditions, in terms of the Mean Square Error criterion of the (r,k) class estimators. This will be done with respect to the ordinary ridge repression, principal components and ordinary least squares estimate.     

Many (22, 44, 14, 7, 4) — and (15, 42, 14, 5, 4)-balanced incomplete block designs

A Balanced Incomplete Block Design (BIBD) is a pair (V, B) where V is a v-set and B is a collection of b k-subsets of V, called blocks, such that every element of V occurs in exactly r of the k-subsets and every 2-subset of V occurs in exactly λ of the blocks. The number of non-isomorphic designs of a BIBD (22, 44, 14, 7, 4) whose automorphism group is divisible by 7 or 11 are investigated. From this work, results are obtained on the number of non-isomorphic BIBDs (15, 42, 14, 5, 4).     

Small -sample comparison of the exact and symptotic upper tail probabilitiesof chi-squared goodness -of-fit statistics: pearson's x 2,likelihood ratio,and power-divergence statistic(λ = 2/3)

The exact and asymptotic upper tail probabilities ( α= .l0, .05, .01, .001) of the three chi-squared goodness-of-fit statistics Pearson's X ², likelihood ratioG ², and power-divergence statisticD ² (λ ) , with λ = 2/3, are compared numerically for simple null hypotheses not involving parameter estimation. Three types of such hypotheses were investigated (equal cell probabilities, proportional cell probabilities, some fixed small expectations together with some increasing large expectations) for the number of cells being between 3 and 15, and for sample sizes from 10 to 40, increasing by steps of one. Rating the relative accuracy of the chi-squared approximation in terms of ±10% and ±20% intervals around α led to the following conclusions: 1. Using G ² is not recommended. 2 . At the more relevant significance levels α = .10 and α = .05X ² should be preferred over D ². Solely in case of unequal cell probabilitiesD ² is the better choice at α = .O1 and α = .001. 3 . Yarnold's (1970; Journal of the Amerin Statistical Association, 65, 864-886) rule for the minimum expectation when using X ² ("If the number of cells k is 3 or more, and if r denotes the number of expectations less than 5, then the minimum expectation may be as small as 5r/k.") generalizes to D ²; it gives a good lower limit for the expected cell frequencies, however, when the number of cells is greater than 3. For k = 3 , even sample sizes over 15 may be insufficient.     

Convergence Rates of Empirical Bayes Estimation for the Parameter of the Uniform Distribution U(0, θ) Under Random Censorship

ABSTRACT

This article considers the empirical Bayes estimation problem in the uniform distribution U(0, θ) with censored data. For the parameter θ, using the empirical Bayes (EB) approach, we propose an EB estimation of θ which possesses a rate of convergence can be arbitrarily close to O(n ^?1/2) when the historical samples are randomly censored from the right, where n is the number of historical sample. A sample and some simulation results are also presented.     

On the risk performance of extended sequence compound rules for classification between N(–1, 1) and N(1, 1) †

Since Robbins (1951) first introduced the compound decision problem, there has evolved a large literature on the subject for the most part dealing with the construction of compound rules whose excess risk over the simple envelope is no greater than zero in the limit as the number N of component problems goes to infinity. Such rules have compound risk which is asymptotically subminimax. Johns (1967) has introduced more stringent (extended) envelopes and has proposed extended compound rules whose risks achieve these envelopes in the limit. This paper reports some Monte Carlo results on the compound risk behavior of selected unextended and extended rules for moderate N values and certain parameter sequences for Robbins original example. The results show that the extended rules compare favorably with the minimax rule and the unextended rules for moderate N and parameter sequences exhibiting higher order empirical dependencies, for example, those generated by a Markov process.     

A note on the mean past and the mean residual life of a (n − k + 1)-out-of-n system under multi monitoring

In the study of the reliability of technical systems, k-out-of-n systems play an important role. In the present paper, we consider a (n − k + 1)-out-of-n system consisting of n identical components such that the lifetimes of components are independent and have a common distribution function F. It is assumed that the number of monitoring is l and the total number of failures of the components at time t _i is m _i , i = 1, . . . , l − 1. Also at time t _l (t ₁ < . . . < t _l ) the system have failed or the system is still working. Under these conditions, the mean past lifetime, the mean residual lifetime of system and their properties are investigated.     

A Note on Overdifferencing and the Equivalence of Seasonal Time Series Models With Monthly Means and Models With (0, 1, 1)12 Seasonal Parts When ⊖ = 1

Two general models for monthly seasonal time series are considered, one in which seasonality is modeled with monthly means and another in which seasonality is modeled with a (0, 1, 1)₁₂ ARIMA structure. The models are shown to be equivalent if the seasonal moving average parameter (?) is 1 and if the same assumptions about the 12 initial observations are made for both models. The role of the assumptions about the initial observations is analyzed, and it is argued that for practical purposes the two models can be regarded as equivalent when ? = 1. It is observed that the result extends easily to more general models involving overdifferencing.     

Modified tables for the selection of qss–1 quick switching system for a given (aql,lql)

This paper presents a set of new tables and procedures for the selection of the following three types of Quick Switching (QS) systems for a given Acceptable Quality Level (AQL), Limiting Quality Level (LQL), producer's risk and consumer's risk.

(1) A Single sampling QS system with equal sample sizes but with different acceptance numbers

(2) A Single sampling QS system with two different sample sizes but with same acceptance number and

(3) A QS systen with double sampling normal inspection and single sampling tightened inspection

The third type of QS systen is the one newly presented in this paper. The tables provide unique plans for a given set of conditions as well as providing a smaller sample size or a smaller sum of Average Sample Numbers(ASN) at the AQL and LQL     

A Note on the Lower Bounds on Maximum Number of Clear Two-Factor Interactions for (2 m−p III) and (2 m−p IV) Designs

ABSTRACT

In the reliability analysis of mechanical repairable equipment subjected to reliability deterioration with operating time, two forms of the non-homogeneous Poisson processes, namely the Power-Law (PL) and the Log-Linear (LL) model, have found general acceptance in the literature. Inferential procedures, conditioned on the assumption of the PL or LL model, underestimate the overall uncertainty about a quantity of interest because the PL and LL models can provide different estimates of the quantity of interest, even when both of them adequately fit the observed data. In this paper, a composite estimation procedure, which uses the PL and LL models as competing models, is proposed in the framework of Bayesian statistics, thus allowing the uncertainty involved in model selection to be considered. A model-free approach is then proposed for incorporating technical information on the failure mechanism into the inferential procedure. Such an approach, which is based on two model-free quantities defined irrespectively of the functional form of the failure model, prevents that the prior information on the failure mechanism can improperly introduce prior probabilities on the adequacy of each model to fit the observed data. Finally, numerical applications are provided to illustrate the proposed procedures.     

NISO Webinar: “The Case of the Disappearing Journal: Solving the Title Transfer and Online Display Mystery” (November 10, 2010)

Abstract

In December 2012, Eric Hanson interviewed Christopher Cronin, director of technical services at the University of Chicago, about their participation as an RDA test partner and issues surrounding RDA training and implementation.     

Comment on: On the role of data,statistics and decisions in a pandemic statistics for climate protection and health—dare (more) progress!

AStA Advances in Statistical Analysis - In the Corona pandemic, it became clear with burning clarity how much good quality statistics are needed, and at the same time how unsuccessful we are at...