Showing papers in "Australian & New Zealand Journal of Statistics in 1989"

On spline smoothing with autocorrelated errors

Abstract: summary The generalised cross-validation criterion for choosing the degree of smoothing in spline regression is extended to accommodate an autocorrelated error sequence. It is demonstrated via simulation that the minimum generalised cross-validation smoothing spline is an inconsistent estimator in the presence of autocorrelated errors and that ignoring even moderate autocorrelation structure can seriously affect the performance of the cross-validated smoothing spline. The method of penalised maximum likelihood is used to develop an efficient algorithm for the case in which the autocorrelation decays exponentially. An application of the method to a published data-set is described. The method does not require the data to be equally spaced in time.

SOCIOECONOMIC INFLUENCES ON EDUCATIONAL Attainment: EVIDENCE And IMPLICATIONS FOR THE TERTIARY EDUCATION FINANCE DEBATE

Abstract: Examination of educational continuation decisions from Year 10 to tertiary entrance indicates that the major decision point appears to be at the end of Year 10. This is true even for persons entering tertiary education. Policies aimed at altering the social composition of high school graduates or tertiary sector participants should therefore be aimed at the Year 10 threshold or at even earlier stages in the educational process. However, as differences in participation in education amongst various socioeconomic groups appear to reflect differences in attitudes rather than purely financial factors, it may be difficult for authorities to expand school retention in the short term.

Inverse gaussian control charts

Abstract: summary Control charts typically used to monitor process centrality and dispersion either assume normally distributed output or appeal to the viability of the central limit theorem. This appeal to the central limit theorem is frequently made on behalf of samples consisting of 10 or fewer items. Control charts for centrality and dispersion are presented for processes with inverse Gaussian distributed output.

Analysis of variations in an infection rate

Abstract: summary In a previous analysis of data from a smallpox epidemic in Abakaliki, Nigeria, it was found that the epidemic model based on uniform mixing was able to give an adequate description only when the infection rate was taken to be a function of time. Here we demonstrate that an alternative, and plausible, explanation is that the infection rate acting upon each given susceptible is constant over time, but that it varies between susceptibles. This variation in susceptibility of individuals can give the impression that the infection rate is declining over time, because highly susceptible individuals tend to be infected earlier so that the mean susceptibility of the remaining susceptibles is declining over time. The above example reveals that there is interest in exploring the nature of the dependence of the infection rate upon time. To this end we propose the nonparametric estimation of the infection rate and illustrate it with reference to the Abakaliki data.

Modelling of transitions between employment states for young australians

Abstract: Summary This paper reports results from modelling the employment state calendars merged from the Australian Longitudinal Survey's 1985 and 1986 Area Samples A semi-Markov model is proposed for the transitions between the three employment states: employed, unemployed and not-in-the-labour-force Sojourn times in each of the states are fitted by the non-parametric maximum likelihood methods proposed by Dinse & Larsen (1986), as are probabilities of transition between states These models contrast with existing work where, typically, only the unemployment state is modelled and where unemployment times are fitted by parametric means The richness of the ALS data enables us to take in sex, age and educational attainment factors at two levels each by use of cohorts rather than by parametric models We show that age and education both play a significant role in duration of employment and unemployment We also show that the initial state sampled (which will often be the first event post-schooling) may be different from the other events to a much greater degree than length-biasing would indicate We find that there is a significant “hard-core” of unemployed and employed, and that a Weibull model fits the data well after this effect is taken out

On selecting variables and assessing their performance in linear discriminant analysis

Abstract: Summary Linear discriminant analysis between two populations is considered in this paper. Error rate is reviewed as a criterion for selection of variables, and a stepwise procedure is outlined that selects variables on the basis of empirical estimates of error. Problems with assessment of the selected variables are highlighted. A leave-one-out method is proposed for estimating the true error rate of the selected variables, or alternatively of the selection procedure itself. Monte Carlo simulations, of multivariate binary as well as multivariate normal data, demonstrate the feasibility of the proposed method and indicate its much greater accuracy relative to that of other available methods.

Influence of family background on the educational and labour‐force outcomes of year 12 school‐leavers

Abstract: Summary Current Government education policy presents some stark contrasts. While subsidies to secondary students are being increased significantly by an expansion of secondary allowances, individual subsidies at the tertiary level are to be reduced via a system of fees or taxes. This policy development is substantially predicated upon the Government's belief that higher education students tend to come from privileged backgrounds. This study explores that hypothesis by analysing the influence of family background on the transition of Year 12 school-leavers to further education or the labour-force. Excellent data from the Australian Longitudinal Survey are used to focus on some previously under-researched aspects of this question. Six models axe reported, each offering different trade-offs between the competing needs for comprehensive coverage of explanatory variables and data coverage. The strongest result obtained is the consistent significance of the mother's educational qualifications in the child's decision to proceed to further education. Equally interesting is the insignificance of the father's educational level. The paternal variables which influence tertiary outcomes are income and/or occupation. Attendance at a private non-Catholic school is also influential. The paper reports provocative evidence on the outcomes of the children of non-English speaking migrants. While this group is often perceived as educationally disadvantaged by their parents' ethnic origins, the results of this study indicate that they are more likely to proceed to tertiary studies than are the children of English speakers. Part-time employment of school children is an increasingly common phenomenon. The preliminary evidence here indicates that the children involved subsequently have lower representation in tertiary institutions but higher employment probabilities in the labour-force. The results imply that mothers and fathers play different roles in influencing their children's outcomes. But there is often a high degree of correlation between maternal and paternal characteristics which makes it difficult to identify separately their respective influences. In summary, the results suggest that family background matters. But the implications for public policy which aims at redressing imbalances in society are complex. On the one hand the children of the well educated and from private schools are more likely to attend tertiary institutions. On the other hand, the migrant “success” story suggests that motivated individuals have it within their grasp to determine their educational and work outcomes. Together, the results point to the importance of attitudes in determining participation in tertiary education and suggest that attention to this factor could enhance the effects of educational subsidies provided to low income families.

A Discrete Time Parametric Model for the Analysis of Failure Time Data

Abstract: Summary This paper introduces a parametric discrete failure time model which allows a variety of smooth hazard function shapes, including shapes which are not readily available with continuous failure time models. The model is easy to fit, and statistical inference is simple. Further, it is readily extended to allow for differences between subjects while retaining the ease of fit and simplicity of statistical inference. The performance of the discrete time analysis is demonstrated by application to several data sets.

What drives australian teenage labour force participation

Abstract: Summary This paper examines the disaggregated components of Australian teenage labour force participation rates for males and females, for part-time and full-time participants and for those still at school. The paper also examines school participation rates for the same group of teenagers. Data are analysed for the period 1978 quarter 1 to 1987 quarter 2. In line with previous research, labour market demand factors are found to be major explanators of participation rates, but supply side effects due to the government's secondary school student allowance and also unemployment benefits are found to be important determinants of work and schooling decisions.

Decompositions for conditional symmetry model into palindromic symmetry and modified marginal homogeneity models

Abstract: Summary For square contingency tables with ordered categories, the conditional symmetry model is decomposed into the palindromic symmetry and the modified marginal homogeneity models, and moreover into the generalized palindromic symmetry model and two other models. The data on unaided vision first analysed by Stuart (1953, 1955) is analysed again by using the decompositions.

A SELECTED BIBLIOGRAPHY ON THE ANALYSIS OF REPEATED MEASUREMENTS and RELATED AREAS

Abstract: summary Different approaches to the analysis of repeated measurements are outlined. For each approach, a few key references are given as a possible basis for further reading. Related methodological areas are mentioned, again accompanied by key references in each case.

A review of bounds for the efficiency factor of block designs

Abstract: summary This paper draws together bounds for the efficiency factor of block designs, starting with the papers of Conniffe & Stone (1974) and Williams & Patterson (1977). By extending the methods of Jarrett (1983), firstly to cover supercomplete block designs and then to cover resolvable designs, a set of bounds is obtained which provides the best current bounds for any block design with equal replication and equal block size, including resolvable designs and two-replicate resolvable designs as special cases. The bounds given for non-resolvable designs apply strictly only to designs which are either regular-graph (John & Mitchell, 1977) or whose duals are regular-graph. It is conjectured (John & Williams, 1982) that they are in fact global bounds. Similar qualifications apply to the bounds for resolvable designs.

A sequential method of constructing optimal block designs

Abstract: Summary An algorithm for the construction of a wide class of block designs including Balanced Incomplete Blocks (BIB) is described. The algorithm which allows the experimenter to give weights for a set of treatment contrasts uses an initial starting design to generate an optimal block design sequentially. The performance of the algorithm is illustrated by examples, and designs constructed by the algorithm compare favourably with designs generated by other methods.

Small sample variance estimators for u-statistics

Abstract: Summary New unbiased estimators are presented for the dominant and lower-order terms of the variance expansion for U-statistics. In small samples these provide important corrections to the usual estimate of asymptotic standard error which is based on the leading term in the expansion. The new estimators for the first term cannot be recommended. The ordinary jackknife estimator is found to be more effective than the direct estimates of the separate terms.

Covariance models for lattice data

Abstract: summary Given observations on an m × n lattice, approximate maximum likelihood estimates are derived for a family of models including direct covariance, spatial moving average, conditional autoregressive and simultaneous autoregressive models. The approach involves expressing the (approximate) covariance matrix of the observed variables in terms of a linear combination of neighbour relationship matrices, raised to a power. The structure is such that the eigenvectors of the covariance matrix are independent of the parameters of interest. This result leads to a simple Fisher scoring type algorithm for estimating the parameters. The ideas are illustrated by fitting models to some remotely sensed data.

Unbiased estimation of parametric functions in sampling from two one-truncation parameter families

Abstract: Summary We consider the problem of minimum variance unbiased estimation of a U-estimable function of two unknown truncation parameters based on independent random samples from two one-truncation parameter families. In particular, we obtain the UMVU estimator of the probability that Y > X.

A remark on testing significance of an observed correlation matrix

Abstract: summary A simple test for the diagonality of the covariance matrix of a multi-variate normal population is proposed The test, which is based upon the sum of squares of the z-transforms of the sample correlations, is seen to compare well with the current tests in terms of both the null distribution approximations and the powers

Lower bounds for the normal approximation of a sum of independent random variables

Abstract: Summary The rates of convergence to the normal distribution are investigated for a sum of independent random variables. Using Stein's method, we derive a lower bound of the uniform distance between two distributions of independent sum and normal.

Estimating distribution functions from survey data with limited benchmark information

Abstract: summary The model-based approach to estimation of finite population distribution functions introduced in Chambers & Dunstan (1986) is extended to the case where only summary information is available for the auxiliary size variable. Monte Carlo results indicate that this ‘limited information’ extension is almost as efficient as the ‘full information’ method proposed in the above reference. These results also indicate that the model-based confidence intervals generated by either of these methods have superior coverage properties to more conventional design-based confidence intervals.

An approach to the sampling theorem for continuous time processes

Abstract: Summary In this paper we extend the sampling theorem to the full spectrum of weakly stationary stochastic processes. The mean square approximation error bound is also given.

The sign test for stochastic processes

Abstract: summary It is shown that the sign test may be applied to the residuals from the use of model fitting procedures, such as conditional least squares, to make inferences on the predictable part of a stochastic process. Minimal assumptions on the distribution of the process, apart from those already required for the model fitting procedure, are needed. The results are illustrated with an application to first order autoregressive processes.

ON COMPONENTS OF VARIANCE and MODELLING EXCEEDANCES OVER A THRESHOLD

Abstract: summary Variance component estimates from a simple hierarchical model are used to model the distribution of large data values exceeding a threshold. The advantages of interrelating the components of variance and the exceedances are stressed. The theory is outlined and an analysis of some data on blood pressure is discussed.

Quantiles of sums and expected values of ordered sums

Abstract: Summary Watson & Gordon (1986) investigated the relationship between the quantiles of a sum of independent continuous random variables and the sum of the individual quantiles. In this note some further results are obtained. Also corresponding relationships are developed for the expected values of the order statistics of a sum, and for the sum of the expected values of the individual order statistics.

Optimal designs for fitting a proportional hazards regression model to data subject to censoring

Abstract: Summary Suppose the probability model for failure time data, subject to censoring, is specified by the hazard function λ(t)exp(βT x), where x is a vector of covariates. Analytical difficulties involved in finding the optimal design are avoided by assuming that λ is completely specified and by using D-optimality based on the information matrix for β Optimal designs are found to depend on β, but some results of practical consequence are obtained. It is found that censoring does not affect the choice of design appreciably when βT x ≥ 0 for all points of the feasible region, but may have an appreciable effect when βixi 0, for all i and all points in the feasible experimental region. The nature of the effect is discussed in detail for the cases of one and two parameters. It is argued that in practical biomedical situations the optimal design is almost always the same as for uncensored data.

The efficiency of the cochrane‐orcutt procedure

Abstract: Summary It is well known that the ordinary least squares (OLS) estimator, though unbiased, is inefficient in the presence of autocorrelated disturbances. Further, it is also widely accepted that the Cochrane-Orcutt (C-O) estimator is more efficient than the OLS estimator. However, Kadiyala (1968) and Maeshiro (1976, 1978) have argued that OLS is more efficient than C-O when the independent variable is trended and the autocorrelation coefficient is positive. We re-examine this issue and show that C-O is more efficient than OLS for the model without an intercept term.

The transition from full‐time study to work

Abstract: Summary The transition from full-time study to first full-time job is modelled using data from the first phase of the Australian Longitudinal Survey (ALS). The transition process is modelled using an ordinal probit model since the time from leaving school to first job is only observed categorically in the ALS. Variables found to be significant in explaining transition time are sex, parental education level, years of schooling, perceived ability and reasons for leaving school.

The sojourn time distribution of an alternating renewal process

Abstract: summary Ordinary, modified, and equilibrium alternating renewal processes are defined in such a way that the distribution of the sojourn time in one state of a two-state system may be considered conditional on the starting state. The double Laplace transform of a non-negative stochastic process is also defined, and used to express a result of Takacs (1957) on sojourn time distributions.

COMPUTER AIDED‐CONSTRUCTION OF D‐OPTIMAL 2m FRACTIONAL DESIGNS OF RESOLUTION V

Abstract: summary A new exchange algorithm for construction of 2mD-optimal fractional factorial design (FFD) is devised. This exchange algorithm is a modification of the one due to Fedorov (1969, 1972) and is an improvement over similar algorithm due to Mitchell (1974) and Galil & Kiefer (1980). This exchange algorithm is then used to construct 54 D-optimal 2m-FFD's of resolution V for m = 4,5,6.

On testing against restricted alternatives for the variances of gaussian models

Abstract: Summary Let π1,…,πp be p independent normal populations with means μ1…, μp and variances σ21,…, σ2p respectively. Let X(ni) be a simple random sample of size ni from πi, i = 1,…,p. Given the simple random samples X(n1),…, X(np) from π1,…,πp respectively, a test has been proposed for testing the homogeneity of variances H0: σ21=…σ2p, against the restricted alternative, H1: σ21≥…≥σ2p, with at least one strict inequality. Some properties of the test are discussed and critical values are tabulated.