The effects of model mis-specifications in linear measurement error models

In the literature, there are many results on the consequences of mis-specified models for linear models with error in the response only, see, e.g., Seber(1977). There are also discussions of estimation for the model writh errors both in the response and in the predictor variables (called measurement error models; see, e.g., Fuller(1987)). In this paper, we consider the problem of model mis-specification for measurement error models. Only a few special cases have been tackled in the past (Edland, 1996; Carroll and Ruppert, 1996 and Lakshminarayanan Amp; Gunst, 1984); we deal with the situation here in some generality. Results have been obtained as follows: (a) When a model is under-fitted, the estimate of the variance of the measurement error will be asymptotically biased, as will the regression coefficients, and the asymptotic biases in the estimates of the regression coefficients will always exist for under-fitted models. Even orthogonality of the variables in the model will not make the biases vanish. (b)For over-fitting, the estimates of the variances of measurement errors and of the regression coefficients are asymptotically unbiased. However, the variance of the estimated regression coefficients will increase. Over-fitting will cause larger changes in the variances of the estimated parameters in measurement error models than in no measurement error models.     

Ethnic population projections for the UK, 2001–2051

This paper reports on projections of the United Kingdom’s ethnic group populations for 2001–2051. For the years 2001–2007 we estimate fertility rates, survival probabilities, internal migration probabilities and international migration flows for 16 ethnic groups and 355 UK areas. We make assumptions about future component rates, probabilities and flows and feed these into our projection model. This model is a cohort-component model specified for single years of age to 100+. To handle this large state space, we employed a bi-regional model. We implement four projections: (1) a benchmark projection that uses the component inputs for 2001; (2) a trend projection where assumptions beyond 2007 are adjusted to those in the UK 2008-based National Population Projections (NPP); (3) a projection that modifies the NPP assumptions and (4) a projection that uses a different emigration assumption. The projected UK population ranges between a low of 63 millions in 2051 under the first projection to a high of 79 million in the third projection. Under all projections ethnic composition continues to change: the White British, White Irish and Black Caribbean groups experience the slowest growth and lose population share; the Other White and Mixed groups to experience relative increases in share; South Asian groups grow strongly as do the Chinese and Other Ethnic groups. The ethnic minority share of the population increases from 13% (2001) to 25% in the trend projection but to only 20% under our modified emigration projection. However, what is certain is that the UK can look forward to be becoming a more diverse nation by mid-century.     

State Educational Investments and Economic Growth in the United States: A Path Analysis*

Objective. This article investigates direct and indirect relationships between state investments in education and economic growth measured as change in per‐capita gross state product (GSP). As a basis for selecting control variables, it also applies a conceptual framework borrowed from the cross‐national growth research. Method. We gathered 18 years of panel data on the 48 continental states and ran GLS regressions with panel corrected standard errors after executing an AR1 correction for autocorrelation. Results. Per‐capita savings deposits, college attainment, and initial GSP are the most consistent predictors of GSP growth over the 18‐year period investigated. However, all the independent variables in the model, except high school attainment, predict per‐capita GSP growth from 1997 to 2005. Conclusion. The study supports the virtues of a path model and a cross‐national framework for explaining the relationship between educational expenditures and GSP growth, especially from 1997 to 2005.     

Fourth order rotatability

Fourth order rotatable designs are discussed. A general k, design moment inequality is given. The variance function for two-factor designs is derived, and plotted for a specific design. A minimum point set requirement for two-factor designs is established, thus enabling one to form an infinity of such designs. Some difficulties in obtaining deLigns for k>2 are described. Some questions are posed for future work.     

Assessing prior information for designed experiments

We examine, via a Bayesian analysis, in a general experimental situation, whether if is worthwhile to obtain additional prior information before performing an experiment. Examples illustrate the application of the techniques developed.     

Inspection errors in link sampling

Results of an investigation into the sensitivity to two types of inspection error of link sampling procedures described by Harischchandra and Srivenkataramana are reported. Relevant compound distributions are derived. Some comparisons with results obtained in a similar investigation for standard double sampling are also given.     

Dorfman-sterrett screening (group testing) schemes and the effects of faulty inspection

The Dorfman screening procedure is based on first testing a group of items as a whole, proceeding to individual testing only if the group-test indicates existence of at least one nonconforming item. A modification suggested by Sterrett allows for reintroduct-ion of group testing of all items, not yet tested individually, when an item is classified as nonconforming by an individual test. Effects of faulty test inspection on the properties of the modified procedures are studied.     

An investigation of first-order and second-order designs for extrapolation outside a hypersphere

Methods for selecting a first-order or second-order rotatable response surface design when both variance and bias error exist are applied to a situation in which it is desired to extrapolate the fitted model in all directions outside of a sphere within which all the experiments are to be made. The extrapolation region is a spherical shell.