Modified ridge analyses under nonstandard

A well-known procedure for the optimization of a second-degree response function over a spherical region of interest is that of ridge analysis. Khuri and Myers (1979) introduced a modification of this procedure by incorporating a certain constraint on the prediction variance. Both procedures, however, assume that the response variable has a constant variance throughtout the experimental region. In the present article, we consider two extensions to Khuri and Myers modifioed ridge analysis. The first extension relaxes the constant variance assumption. In the second extension. generalised linear models are used instead of the trasitional linear model. which are commenly used in responce variables that are not necessaily continusly distribution, including these have discreate distributions, Two examples are presented to illustrate the implementation of the proposed extensions.     

Some aspects of statistical inference on the lagrange (generalized) poisson distribution

A generalization of the Poisson distribution was defined by Consul and Jain (Ann. Math. Statist., 41, (1970)) and was obtained as a particular family of Lagrange distributions by Consul and Shenton (SIAM. J. Appl. Math., 23, (1972)). The distribution is subsequently named the generalized Poisson distribution (GPD). This GPD reduces to the Poisson distribution for ? = 0. When the data have a one-way layout structure, the asymptotically locally optimal Neyman's C(d) test is constructed and compared with the conditional test on the hypothesis H_o? = 0. Within the framework of the generalized linear models an appropriate link function is given, and the asymptotic distributions of the estimated parameters are derived.     

Report of the Ad Hoc Committee on Statistical Standards

Secretary's Note: At the meeting of the incoming Board and Council of December 29, 1952, the Committee on Committees submitted for consideration an outline regarding the tasks that should be undertaken by the Commission on Statistical Standards and Organization. The Board authorized President Cochran to appoint an ad hoc committee to explore the functions as outlined by the Committee on Committees. The ad hoc committee, under the chairmanship of Rensis Likert, Institute for Social Research, University of Michigan, has prepared an excellent report on this subject which should be the concern of all members of the Association.

The whole problem of standards in the statistical profession is a great and difficult one. The Board has authorized the publication of the ad hoc committee's report in The American Statistician in the hope that the members of the Association will submit their views regarding both the Report and the problem of standards. The entire ASA membership is invited to forward their thoughts and comments to the Office of the Secretary of the Association for possible publication in The American Statistician.     

New Developments in Statistical Computing: New Bias Evaluation Features of EXPLOR—A Program for Assessing Experimental Design Properties

Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis.     

Statistics Problems with Simple Numbers

This article concerns the construction of simple numerical illustrations of statistical techniques for use in introductory classes. Minimizing the amount of calculation facilitates checking, promotes reliability, is quicker, and reinforces the confidence of the student. Methods are described for generating (a) samples of size 3 upwards with integer-valued means and standard deviations, and (b) simple linear regressions with integer-valued intercepts and integer-valued or simple fractional slopes. Extensions to give exact pooled standard deviations in the two-sample problem and simple exact fractional correlation coefficients are also indicated. Further statistical procedures amenable to the same general approach are listed.     

A Recursive Formula for the Probability of Occurrence of at Least m out of N Events

A recursive same-sign relation is derived that reduces the probability of occurrence of at least m out of N independent events to the probability of occurrence of at least m out of N ? 1 of these N events.     

Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.     

Number of observations near the maximum in an F α-scheme

Let K _n (a) be the number of observations in the interval (M _n ,?a, M _n ), where M _n is the maximum value in a sequence of size n. We study the asymptotic properties of K _n (a) under the F ^α-scheme and discuss the influence of the associated sequence α _n on the limit behaviour of this random variable.     

ISO 45001 and controversial transnational private regulation for occupational health and safety

This article analyses the genesis of the ISO 45001 standard on occupational health and safety, a new initiative of transnational private regulation. The authors draw a picture of controversy from interviews with stakeholders involved in its design, approval and initial dissemination, and from a qualitative content analysis of the internal documentation of the committee responsible for its approval. Like its predecessors relating to environmental management – ISO 14001 – and corporate social responsibility – ISO 26000 – this new standard raises serious concerns among stakeholders given that it deals with substantive political, social and legal issues.