bluuebunny/crossref_metadata_2025 huggingface dataset:
ON RESOLVABLE INCOMPLETE BLOCK DESIGNS1
Authors: Sharma V. K. , Das M. N.
Published: February 2008

summary

A method of constructing resolvable incomplete block designs for v(=ks, 2 ≤ k ≤ s ‐ 1) treatments in blocks of size k using mutually orthogonal Latin squares is proposed. It has been seen in particular that when the number of replications is s — 1 (or s), which is feasible if s is a prime or a prime power, the method gives PBIB (3) (or semi‐regular GD) designs. The analysis of such designs has also been discussed.
ON ESTIMATION OF LONG‐MEMORY TIME SERIES MODELS
Authors: Yajima Yoshihiro
Published: February 2008

This paper discusses estimation associated with the long‐memory time series models proposed by Granger & Joyeux (1980) and Hosking (1981). We consider the maximum likelihood estimator and the least squares estimator. Certain regularity conditions introduced by several authors to develop the asymptotic theory of these estimators do not hold in this model. However we can show that these estimators are strongly consistent, and we derive the limiting distribution and the rate of convergence.
MULTISTAGE SAMPLING FOR RAW WOOL CHARACTERISTICS
Authors: Brown G. H.
Published: February 2008

The problem of evaluating the sampling variance of a mean when units are subsampled from a multistage sample is discussed. In particular, a specific problem arising in the sampling of wool where information on the identity of subsampled units is not available is dealt with by introducing a simple model to account for the variability in the unobserved numbers of observations within the multistage categories. Estimation aspects of the wool example are also dealt with.
THE CONVERGENCE RATE OF SEQUENTIAL FIXED‐WIDTH CONFIDENCE INTERVALS FOR REGULAR FUNCTIONALS
Authors: Aerts M. , Callaert H.
Published: February 2008

Let X1X2,.be i.i.d. random variables and let Un= (n r)‐1S̀(n,r) h (Xi1,., Xir,) be a U‐statistic with EUn= v, v unknown. Assume that g(X1) =E[h(X1,.,Xr) ‐ v |X1]has a strictly positive variance s̀2. Further, let a be such that φ(a) ‐ φ(‐a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S2n be the Jackknife estimator of n Var Un. Consider the stopping times N(d)= min {n: S2n: + n‐1≤2a‐2},d > 0, and a confidence interval for v of length 2d,of the form In,d= [Un,‐d, Un+ d].

We assume that Var Un is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let IN(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. limd → 0P(v ∈ IN(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ IN(d),d) converges to α is investigated. We obtain that |P(v ∈ IN(d),d) ‐ α| = 0 (d1/2‐(1+k)/2(1+m)), d → 0, where K = max {0,4 ‐ m}, under the condition that E|h(X1, Xr)|m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981).
MODELLING EXAMINATION MARKS
Authors: Daley D. J. , Seneta E.
Published: February 2008

The paper proposes a model to describe marks as awarded to students who select and sit for examinations in a subset of the courses offered.

For each subject a linear transformation of the raw marks is sought so as to place all marks on a common scale. In this guise, the set‐up reduces to a simple linear model with multiplicative interaction term, totally lacking in balance as would result from experimental design practice.

A variety of methods of estimating the linear transformation parameters is described.
ON ASYMPTOTIC OPTIMALITY OF SOME TESTS FOR EXPONENTIAL DISTRIBUTIONS
Authors: Samanta M.
Published: February 2008

The probability density function (pdf) of a two parameter exponential distribution is given by

f(x; p, s̀) =s̀‐1 exp {‐(x ‐ ρ)/s̀}

for x≥ρ and 0 elsewhere, where 0 < ρ < ∞ and 0 < s̀∞. Suppose we have k independent random samples where the ith sample is drawn from the ith population having the pdf f(x; ρi, s̀i), 0 < ρi < ∞, 0 < s̀i < s̀i < and f(x; ρ, s̀) is as given above. Let Xi1 < Xi2 <… < Xiri denote the first ri order statistics in a random sample of size ni, drawn from the ith population with pdf f(x; ρi, s̀i), i = 1, 2,…, k. In this paper we show that the well known tests of hypotheses about the parameters ρi, s̀i, i = 1, 2,…, k based on the above observations are asymptotically optimal in the sense of Bahadur efficiency. Our results are similar to those for normal distributions.
ON QUANTILES OF SUMS
Authors: Watson Ray , Gordon IAN
Published: February 2008

In this paper we investigate the relationship between the quantiles of a sum of independent continuous random variables and those of its components. Results concerning this relationship are given for the special cases of symmetric distributions, gamma distributions, and for the difference of identically distributed random variables.
OPTIMUM SINGULAR SPRING BALANCE WEIGHING DESIGNS WITH NON‐HOMOGENEITY OF THE VARIANCES OF ERRORS FOR ESTIMATING THE TOTAL WEIGHT
Authors: Ceranka B. , Katulska K.
Published: February 2008

The problem of estimation of the total weight of objects using a singular spring balance weighing design with non‐homogeneity of the variances of errors has been dealt with in this paper. Based on a theorem by Katulska (1984) giving a lower bound for the variance of the estimated total weight, a necessary and sufficient condition for this lower bound to be attained is obtained. It is shown that weighing designs for which the the lower bound is attainable, can be constructed from the incidence matrices of (α1,.,αt)‐resolvable block designs, α‐resolvable block designs, singular group divisible designs, and semi‐regular group divisible designs.
EXPRESSIONS FOR INVERSE MOMENTS OF POSITIVE QUADRATIC FORMS IN NORMAL VARIABLES
Authors: Jones M. C.
Published: February 2008

A unified approach to the provision of exact expressions for inverse moments of positive quadratic forms in normal variables is described, using the method of (essentially) integrating the moment‐generating‐function (Cressie, Davis, Folks & Policello (1981). A number of special cases, many familiar from the literature, are reviewed; some allow closed form representations, others are expressed in terms of well‐known mathematical functions. In the general case, our approach affords representations suitable for numerical computations.
The Evaluation of Long Term Trend I
Authors: Nicholls D. F. , Heathcote C. R. , Cunningham R. B.
Published: February 2008

summary

A procedure is presented for the determination of the long term trend in series of data. Robust data smoothing procedures are used to decompose the data into trend, seasonal and irregular components. Confirmatory data analysis is then used to model the deseasonalized data and hence determine the long term trend. A series of riverflow data is analysed using these methods.
Asymptotic Representations of the Multivariate Empirical Distribution Function and Applications
Authors: Ralescu Stefan
Published: February 2008

Often, many complicated statistics used as estimators or test statistics take the form of the (multivariate) empirical distribution function evaluated at a random vector (Vn). Denote such statistics by Sn. This paper describes methods for the study of various asymptotic properties of Sn. First, under minimal assumptions, a weak asymptotic representation for Sn is derived. This result may be used to show the asymptotic normality of Sn. Second, under slightly more stringent regularity conditions, an almost sure representation of Sn, with suitable order (as.) of the remainder term is studied and then a law of the iterated logarithm for Sn, is derived. In this context, strong convergence results from a sequential point of view are also studied. Finally, weak convergence to a Brownian motion process is established. As an application, we show the limiting normality of Sn, for a random number of summands.
Small Sample Theory of the Langevin Distribution
Authors: Chou Rouh‐jane
Published: February 2008

Summary

The one‐sample and multi‐sample problems for the Langevin distribution are studied. The asymptotic expansions of the distributions of several test statistics proposed by Watson (1983a) are obtained under both the null and the alternative hypotheses.
A Note on the Predictors of Differenced Sequences
Authors: Peiris M. Shelton
Published: February 2008

In this note we consider the problems of optimal linear prediction (o.l.p.) and the minimum mean squared error prediction (m.m.s.e.p.) of a sequence Xt, which fits to a stationary and invertible ARMA model through the filter (1 ‐ Bs)d Xt= Yt. It is shown that these two predictors are not identical in general from the theoretical point of view. Permitting the degree of differencing d to take any real value, a set of conditions for these commonly applied prediction formulas to be identical is given.
A new Method of Estimating the Asymptotic Standard Error of the Hodges‐Lehmann Estimator Based on Generalized Least Squares
Authors: Sheather Simon J.
Published: February 2008

A method of estimating the asymptotic standard error of the Hodges‐Lehmann estimator based on generalized least squares is described. The results of a Monte Carlo study comparing the new method with existing ones are given.
Optimal Allocation of Observations for Inference on k Ordered Normal Population Means
Authors: Hirotsu C. , Herzberg Agnes M.
Published: February 2008

The optimal allocation of observations when there is a natural ordering in the k normal population means is discussed. It is shown that the design which minimizes the total mean square error of the maximum likelihood estimators in the null case allocates half the observations to each of the two extreme populations. The design is obviously optimal for testing the homogeneity of means against the simple ordered alternative. It is, however, hardly acceptable for the estimation in the nonnull case. It is, therefore, shown that the observations could be allocated to the non‐extreme populations according to weights which are proportional to the absolute values of the Abelson and Tukey scores at the same time keeping the minimum local power for testing the simple ordered alternative to be maximal. The design gives also the maximum minimum power, not local, for the alternative in the class of linear tests. It, of course, suffers from a small loss of efficiency for the estimation under the null case but is much better under the nonnull case than the extreme design which allocates half the observations to each of the two extreme populations. Some numerical comparisons of the mean square errors are given.
On Tests of Uniformity for Randomly Distributed Arcs on a Circle
Authors: Kokic P. N.
Published: February 2008

Let n points be independently distributed on a circle. Moving in a counter‐clockwise direction, place arcs of length a on the circle with the ith are starting at the ith point.

We describe three simple tests of the hypothesis of uniformity based on vacancy, on number of spacings and on the length of the maximal spacing. The tests do not require knowledge of the random points. The asymptotic power of these tests is investigated, and it is shown that vacancy‐based tests perform best of the three.
A Classification Rule Whose Probability of Misclassification is Independent of the Variance
Authors: Adegboye O. S.
Published: February 2008

An observation ×o is to be classified into one of two normal populations φ1 and φ2. A classification rule, the Two‐stage sample Rule, R(TS), whose probability of misclassification, P[MC], is independent of the common but unknown variance is proposed. Some optimal properties of R(TS) are also discussed and some values of P[MC | R(TS)], the probability of misclassification given the rule R(TS), are tabulated.
A One‐Sided Rank Test for Multivariate Censored Data
Authors: Wei L. J. , Knuiman M. W.
Published: February 2008

An asymptotically distribution‐free test is proposed for testing the equality of two multivariate failure distributions against a particular one‐sided alternative based on censored observations. This test may be interpreted as a multivariate one‐sided Gehan test. The consistency of the test is established. An illustrative example is given.
Diagnostic Displays for Assessing Leverage and Influence in Generalized Linear Models
Authors: Lee Andy H.
Published: February 2008

summary

A general technique for assessing leverage and influential observations in Generalized Linear Models is described. The procedure takes the form of Half‐Normal plots with envelopes derived from simulation to enhance overall assessment of the model. This procedure of assessment is more informative and provides additional insight compared with procedures based on the largest sample leverage and influence statistics. Application of the method is illustrated with an example in logistic regression.
Regression Type Estimators Using Multiple Auxiliary Information
Authors: Mukerjee Rahul , Rao T. J. , Vijayan K.
Published: February 2008

In this paper we consider a practical situation where information on two auxiliary variables related to the study variable is available at different levels. Following Kiregyera (1980, 1984) who has obtained a chain ratio‐to‐regression estimator and regression to regression estimator, we shall study several estimators that arise naturally in this context and compare them under the mean square error criterion. We extend these results to the case when multiple auxiliary information is available.
Response Inducing Techniques for Mail Surveys
Authors: Jackway Paul T. , Boyce Rosalie A.
Published: February 2008

A mail survey has been conducted to discover why certain hospital based health professionals did not reply to a previous mail survey. The results will assist in the design of future mail surveys for this group and may have a more general interest and applicability. Two return‐inducing techniques have been tested. Other such techniques, reported in the literature but untested in this study, are listed. The observed responses times are reported and some suggestions regarding timing are made.
The Construction of Optimal Imcomplete Block Designs When Observations Within a Block are Correlated
Authors: Russell K. G. , Eccleston J. A.
Published: February 2008

An algorithmic method is described for the construction of optimal incomplete block designs when a known correlation structure is assumed for observations from plots in the same block. The method is applicable to a wide class of designs and correlation structures. Some examples are given to illustrate the procedure.
Step Down Procedures for Comparison With a Control
Authors: Bofinger Eve
Published: February 2008

summary

“Step down” or “sequentially rejective” procedures for comparisons with a control are considered for both one sided and two sided comparisons. Confidence bounds (in terms of the control) are derived for those (location) parameters not in a selected set. Special results are derived for the normal distribution with unknown variance where the sample numbers are (possibly) unequal.
DISTRIBUTIONS OF QUADRATIC FORMS
Authors: Bock Mary Ellen , Solomon Herbert
Published: February 2008

summary

Exact expressions for the distribution function of a random variable of the form c1χ2m+c2χ2n are given where χ2m and χ2nχ2n are independent chi‐square random variables with m and n degrees of freedom respectively. (The positive ci are distinct). In particular, the exact asymptotic distribution function for the average Kendall tau statistic is written as a function of tables of Solomon (1960) and some found in Abramowitz and Stegun's Handbook of Mathematical Functions.
AN APPROXIMATION TO THE DISTRIBUTION OF QUADRATIC FORMS IN NORMAL RANDOM VARIABLES
Authors: Buckley M.J. , Eagleson G.K.
Published: February 2008

summary

A new approximation to the distribution of quadratic forms in normal random variables is derived. It is based on the Edgeworth expansion and a bound on the error involved in the approximation is given. The new approximation is compared with others for a particular quadratic form which arises in the estimation of variance in a non‐parametric regression.
A SIMPLE IMPROVED‐ACCURACY NORMAL APPROXIMATION FOR x2
Authors: Lewis Toby
Published: February 2008

summary

The following approximation for χ2 with v degrees of freedom is presented: 1/[1 ‐ 1/6 In(χ2/v)] is distributed approximately normally with mean 1 ‐ (9v)‐1 and standard deviation (18v)‐1/2+(18v)‐3/2. For use without resort to computer capability it is shown to compare favourably with various existing approximations, on grounds either of simplicity or accuracy or both. There is little to be gained from modifying this simple formula in order to secure higher‐order agreement with the Cornish‐Fisher expansion. The formula is readily adapted to give a simple normal approximation for noncentral χ2.
THE PROBLEM OF MISCLASSIFICATION OF MORTALITY STATISTICS
Authors: Heathcote C.R.
Published: February 2008

summary

The problem of misclassification of cause of death in mortality tables is discussed through the introduction of a classification matrix. This is a stochastic matrix whose off‐diagonal entries are the probabilities of a misclassification. An example is given in Section 2 which shows how a classification matrix can be estimated. An unbiased linear estimate of the unknown true numbers of deaths in different categories is obtained in Section 3 and its asymptotic normality is established. It is shown that the usual classical estimate is biased. Section 4 deals with the special case of a classification matrix whose rows define independent multinomial distributions.
WHITE NOISE ANALYSIS AND STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Authors: Hida Takewki
Published: February 2008

summary

White noise analysis has developed a calculus on the Hilbert space of generalized Brownian functionals by the use of the differential operators ∂t, ∈R1, and their adjoint operators∂*,t∈ R1, as well as their combinations. In the present note we deal with stochastic differential equations which involve the operators ∂t,∂*t and 1/dt, as an application of white noise analysis. Those equations are able to characterize some interesting generalized Brownian functionals, and further applications naturally follow.
DIFFERENTIAL OPERATORS ARISING FROM TRANSLATION OF POISSON FUNCTIONALS
Authors: Ito Yoshifusa
Published: February 2008

summary

A translation operator Tη on Poisson functionals is defined by Tηφ(x)=φ(x=y)dvη(y), where vη is a measure which defines a Poisson process with intensity η and independent of the basic Poisson process. By means of the translation operator the differential operators with respect to a Poisson white noise are redefined. This makes it possible to understand why the differential operators are actually difference operators when applied to suitable Poisson functionals, and provides a basis for applications of the differential operators.
ASSOCIATION AND MULTIVARIATE EXTREME VALUE DISTRIBUTIONS
Authors: Resnick Sidney I.
Published: February 2008

summary

Multivariate extreme value random vectors are associated, which is a result of Marshall and Olkin (1983). In fact this positive dependence result holds more generally for max‐infinitely divisible random vectors as well as for spectrally positive infinitely divisible distributions. The association is obtained from the association of the Poisson process and the fact that association is preserved under non‐decreasing transformations.
THE DAVIDSON‐KENDALL PROBLEM AND RELATED RESULTS ON THE STRUCTURE OF THE WISHART DISTRIBUTION
Authors: N.Shanbhag D.
Published: February 2008

summary

The random vectors (U, V, W) with U, W≥ 0 and V2=UW almost surely (as.) and the left extremity of U + W as zero for which the distribution of (U, V, W)Q for a 3 × 3 nonsingular real matrix Qis decomposable are identified and some further relevant results are given.
RATES OF CONVERGENCE FOR THE QUANTILE FUNCTION OF A LINEAR PROCESS
Authors: Hannan E.J. , Hesse C.H.
Published: February 2008

summary

This work explores limit theorems for the empirical quantile function of a stationary linear process of the form y(t)=s̀∞0ρ(j)∈(t ‐ j) and their applications. Under some regularity conditions and for parameters ρ(j) decreasing at a geometric rate, a strong consistency result is proved for the uniform convergence of the sample quantile function to the inverse of the distribution function of the y(t). These theorems are then applied to problems of autoregressive parameter estimation.
INTRODUCTION OF STATISTICAL DESIGN AND ANALYSIS BY THE QUEENSLAND BUREAU OF SUGAR EXPERIMENT STATIONS
Authors: Kerr John D.
Published: February 2008

summary

The pioneering role of the Queensland Bureau of Sugar Experiment Stations in the introduction of Fisher's methods for the design and analysis of experiments to Australia is described. The paper is based on the recollections of the former director of the Bureau and the person responsible for the adoption of statistical methodology, Dr H.W. (Bill) Kerr. Details of the early experiments and their analysis are given based on published reports.
AUSTRALIAN BIOMETRY AND MULTIPLE COMPARISONS1
Authors: Duncan D.B.
Published: February 2008

summary

My main recollections of Biometry in Australia prior lo 1951 are of the beginning of perhaps the first course in Biometry in the Sydney Faculty of Agriculture in 1935, of good consulting and computing services growing within the CSIR and the NSW Department of Agriculture, of aircrew‐selection work in the Empire Air Training Program, and of the beginnings in 1950 of the Statistical Society of NSW. My memories of work in multiple comparisons are of Mr Sawkins' ideas for a new rule, and my own in the early development of a decision‐theoretic approach which plays an integral role, together with subsequent Bayesian work, in solving the critical dilemma between using an experiment wise or comparison wise approach.
ASYMPTOTIC PROPERTIES OF LINEAR REGRESSION ESTIMATORS UNDER A FIXED CENSORSHIP MODEL
Authors: Smith Peter James
Published: February 2008

Modifications to the usual least squares normal equations have been proposed by Buckley and James (1979) when using distribution‐free linear regression modelling under fixed right‐censorship of the response. In this paper we consider large‐sample distributional properties of the modified normal equation for the slope parameter and of estimators which ‘satisfy’ this equation.
ADJUSTED ORTHOGONAL NESTED ROW‐COLUMN DESIGNS
Authors: Eccleston J.A. , John J.A.
Published: February 2008

Adjusted orthogonality in nested row‐column designs is defined and a sufficient condition established for its existence. It is shown that the properties of an adjusted orthogonal nested row‐column design are directly related to those of its separate row and column component designs. A method for constructing efficient adjusted orthogonal designs involving a single replicate of every treatment in each of two blocks is given.
NONNULL DISTRIBUTION OF LIKELIHOOD RATIO CRITERION FOR TESTING MULTISAMPLE SPHERICITY IN THE COMPLEX CASE
Authors: Gupta A.K. , Nagar D.K.
Published: February 2008

In this paper, nonnull moments of the likelihood ratio statistic for testing multisample sphericity in the complex case have been derived in series involving zonal polynomials. The nonnull asymptotic distribution of the statistic is also derived for certain alternatives.
ON THE SIMPLE PROJECTION PREDICTOR IN FINITE POPULATIONS
Authors: Bolfarine Heleno , Rodrigues Josemar
Published: February 2008

In this paper, necessary and sufficient conditions for optimality of the simple projection predictor (SPP) are considered under a superpopula‐tion model with a not necessarily diagonal covariance matrix. Conditions under which the SPP remains optimal, under possible covariance matrix misspecifications, are also considered.
A NOTE ON THE EFFICIENCY OF PROPORTIONAL STRATIFICATION
Authors: Sadooghi‐Alvandi S.M.
Published: February 2008

In stratified random sampling, it is generally recognised that nonproportional allocation is worthwhile only if the gain in precision is substantial. This note presents a sharp lower bound for the relative precision of proportional to optimum (Neyman) allocation, in terms of the ratio of the largest to the smallest stratum standard deviations. This provides a quick measure of the efficiency of proportional allocation, and may be used as a formal basis for deriving useful practical rules. In particular, it is formally confirmed that for estimating a proportion nonproportional allocation is rarely worthwhile.
CONVERGENT SERIES EXPRESSIONS FOR INVERSE MOMENTS OF QUADRATIC FORMS IN NORMAL VARIABLES
Authors: Smith Murray D.
Published: February 2008

Using relatively recent results from multivariate distribution theory, a direct approach to evaluating the inverse moments of a quadratic form in normal variables is proposed. Convergent infinite series expressions involving the invariant polynomials of matrix argument are obtained. The solution also depends upon a positive scalar which is arbitrarily chosen. For the solution to converge an upper bound upon this scalar is derived.
METHOD OF ESTIMATION FOR SAMPLING FROM INCOMPLETE FRAMES
Authors: Singh Randhir
Published: February 2008

The planning of any sample survey or census requires the existence of a sampling frame comprising a list of all the sampling units. But unfortunately there is hardly a situation in practice where the frame is available in the form the sampler desires to use. Most commonly some units of the target population are not listed in the frame, and the frame may contain units which do not belong to the target population. In this investigation a suitable method of estimation is proposed when sampling is done from such imperfect frames and a geographical ordering of the units can be established.
ON THE ESTIMATION OF TOTAL WEIGHT IN SINGULAR SPRING BALANCE WEIGHING DESIGNS UNDER THE CO VARIANCE MATRIX OF ERRORS s2G
Authors: Katulska Krystyna
Published: February 2008

The problem of the estimation of the linear combination of weights, c′w, in a singular spring balance weighing design when the error structure takes the form E(ee′) =s̀2G has been studied. A lower bound for the variance of the estimated linear combination of weights is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The general results are applied to the case of the total of the weights. For a specified form for G, some optimum spring balance weighing designs for the estimated total weight are found.
SELECTING THE t BEST POPULATIONS — SCALE PARAMETER CASE
Authors: Mengersen Kerrie , Bofinger Eve
Published: February 2008

Selection from k independent populations of the t (< k) populations with the smallest scale parameters has been considered under the Indifference Zone approach by Bechhofer k Sobel (1954). The same problem has been considered under the Subset Selection approach by Gupta & Sobel (1962a) for the normal variances case and by Carroll, Gupta & Huang (1975) for the more general case of stochastically increasing distributions. This paper uses the Subset Selection approach to place confidence bounds on the probability of selecting all “good” populations, or only “good” populations, for the Case of scale parameters, where a “good” population is defined to have one of the t smallest scale parameters. This is an extension of the location parameter results obtained by Bofinger & Mengersen (1986). Special results are obtained for the case of selecting normal populations based on variances and the necessary tables are presented.
ON TRANSITION PROBABILITIES OF SKIP‐FREE MARKOV CHAINS
Authors: Kijima Masaaki
Published: February 2008

Consider an ergodic Markov chain X(t) in continuous time with an infinitesimal matrix Q = (qij) defined on a finite state space {0, 1,…, N}. In this note, we prove that if X(t) is skip‐free positive (negative, respectively), i.e., qij, = 0 for j > i+ 1 (i > j+ 1), then the transition probability pij(t) = Pr[X(t)=j | X(0) =i] can be represented as a linear combination of p0N(t) (p(m)(N0)(t)), 0 ≤ m ≤N, where f(m)(t) denotes the mth derivative of a function f(t) with f(0)(t) =f(t). If X(t) is a birth‐death process, then pij(t) is represented as a linear combination of p0N(m)(t), 0 ≤m≤N ‐ |i‐j|.
A BERRY‐ESSEEN BOUND FOR THE RATIO ESTIMATOR
Authors: Kokic P.N.
Published: February 2008

Suppose that R is the ratio estimator based on a simple random sample of size n drawn without replacement from a bivariate population of N elements. A Berry‐Esseen bound for von Mises statistics based on samples from a finite population is used to derive a Berry‐Esseen bound for R.
ESTIMATING DISTRIBUTION FUNCTIONS FROM SURVEY DATA WITH LIMITED BENCHMARK INFORMATION
Authors: Dunstan R. , Chambers R. L.
Published: February 2008

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.
ESTIMATING A NON‐GAUSSIAN REGRESSION MODEL WITH MULTICOLLINEARITY
Authors: And R. B. Cunningham , Heathcote C. R.
Published: February 2008

summary

The paper discusses practical issues that arose in estimating a Linear model subject to heteroscedasticity, skewness and multicollinearity. The context of the problem required that linearity of the model as originally formulated be preserved. A seemingly satisfactory fit was obtained using a Gamma model and principal components.
THE ESTIMATION OF PLUTONIUM CONCENTRATIONS IN SOIL
Authors: And Keith Wise , Kabaila Paul
Published: February 2008

summary

In this paper we examine the consequences, for statistical analysis and interpretation, of the particulate nature of radioactive contamination of a nuclear weapons test site. We propose a probabilistic model which incorporates the particulate nature of the contamination and which is simple enough to be statistically fitted to the data. Parameter estimation involves the reconciliation and combination of measurements of (a) 59.5 ke V gamma rays from americium‐241, a decay product of plutonium‐241, using a portable medium resolution NaI detector, on a regular survey grid at a test site and (b) 59.5 ke V radiation from soil samples obtained at grid points. The implications of the model for measurement of levels of contamination are considered.
MINIMUM DISTANCE and INDUCED STATISTICS FOR TESTING INEQUALITIES
Authors: Rogers Alan J.
Published: February 2008

summary

Minimum distance statistics for testing inequality restrictions on the mean vector of a multivariate normal population are considered and are shown to be equivalent to certain induced (or intersection) test statistics. Tests based on these statistics are shown to be admissible.
UNIFORM ASYMPTOTIC EXPANSIONS APPLIED TO SEQUENTIAL t ‐ and t2‐TESTS
Authors: Govindarajulu Z. , Howard H. C.
Published: February 2008

summary

Using some uniform asymptotic expansions for parabolic cylinder functions recently developed by Olver (1959), various integrals associated with the sequential t‐ and t2 ‐tests are evaluated asymptotically in terms of the sample size. Then the continuation region inequalities for these tests are inverted and expressed in terms of well known test criteria. It should be pointed out that the inversion of the continuation regions in terms of the well known statistics yields forms for the sequential tests that are more easily applicable by the practitioner than the forms yielded by the method of Rushton. Furthermore, using these inequalities and the asymptotic normality of the test criteria, finite sure termination of sequential t‐ and t2‐test procedures readily follow. Based on simulation studies, power comparisons of the two approximations are also made.
COMPUTER AIDED‐CONSTRUCTION OF D‐OPTIMAL 2m FRACTIONAL DESIGNS OF RESOLUTION V
Authors: Nguyen Nam‐Ky , Dey Aloke
Published: February 2008

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.
A REVIEW OF BOUNDS FOR THE EFFICIENCY FACTOR OF BLOCK DESIGNS
Authors: Jarrett Richard
Published: February 2008

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.
CONDITIONAL INFERENCE ABOUT AN EQUICORRELATION COEFFICIENT
Authors: Williams Evan J. , Yip Paul
Published: February 2008

summary

SenGupta (1987) proposed a locally most powerful test which is globally (one sided) unbiased, and an estimator of p, the equicorrelation coefficient of a standard symmetric multivariate normal (SSMN) distribution. Here we use the idea in Williams (1984) to illustrate the construction and use of ancillary statistics to make inference about p. The test and confidence intervals based on this construction are conditionally optimal.
FAMILIES AND EARLY LABOUR MARKET EXPERIENCE: AN ANALYSIS OF SIBLINGS
Authors: Bradbury Bruce , McRae Ian , Woyzbun Lyn
Published: February 2008

How much does family background matter in determining the labour market success of young people? What role does education play in the transmission of advantage from one generation to another? Studies which have examined observable family characteristics have generally concluded that family background has only a moderate influence upon labour market outcomes, and that this influence is generally mediated through educational attainment.

However the relevant family characteristics are typically difficult to identify, let alone measure. This paper examines a sample of siblings from the Australian Longitudinal Survey in order to capture the effects of unobservable family characteristics. Siblings, by definition, have their families and associated environments in common. Thus the extent to which siblings have similar outcomes in the labour market is an indicator of the effect of family background (defined broadly) on labour market success.

A number of different outcome measures are examined, including earnings, incomes and experience of unemployment. The effect of transitory variations on these outcomes is discussed. Sibling outcomes are found to be quite strongly correlated, though differences are observed between brother, sister and mixed sibling pairs.

Because unmeasured family characteristics are associated with both education and labour market outcomes, their addition to conventional human capital models leads to a downward revision of the effects of education. However such conclusions must be considered in the light of the reliability and validity of the measures of educational attainment.
INFLUENCE OF FAMILY BACKGROUND ON THE EDUCATIONAL AND LABOUR‐FORCE OUTCOMES OF YEAR 12 SCHOOL‐LEAVERS
Authors: Prior Heather , Beggs John J.
Published: February 2008

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.
THE TRANSITION FROM FULL‐TIME STUDY TO WORK
Authors: Eyland E. Ann , Johnson Lester W.
Published: February 2008

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 EFFICIENCY OF THE COCHRANE‐ORCUTT PROCEDURE
Authors: Hoque Asraul
Published: February 2008

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.
BAYESIAN TESTS FOR SOME PRECISE HYPOTHESES ON MULTI‐NORMAL MEANS
Authors: Groenewald P.C.N. , de Waal D.J.
Published: February 2008

Bayesian counterparts of some standard tests concerning the means of multi‐normal distribution are discussed. In particular the hypothesis that the multi‐normal mean is equal to a specified value, and the hypothesis that the means are equal. Lower bounds on the Bayes factor in favour of the null hypothesis are obtained over the class of conjugate priors. The P‐value, or observed significance level of the standard sampling‐theoretic test procedure are compared with the posterior probability. The results correspond closely with those of Good (1967), Berger & Sellke (1987), Pepple (1988) and others and illustrate the conflict between posterior probabilities and P‐values as measures of evidence.
ON SELECTING VARIABLES AND ASSESSING THEIR PERFORMANCE IN LINEAR DISCRIMINANT ANALYSIS
Authors: Ganeshanandam S. , Krzanowski W.J.
Published: February 2008

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 DIAGNOSTICS FOR THE NORMAL LINEAR MODEL WITH CENSORED DATA
Authors: Weissfeld L.A. , Schneider H.
Published: February 2008

Methods of detecting influential observations for the normal model for censored data are proposed. These methods include one‐step deletion methods, deletion of observations and the empirical influence function. Emphasis is placed on assessing the impact that a single observation has on the estimation of coefficients of the model. Functions of the coefficients such as the median lifetime are also considered. Results are compared when applied to two sets of data.
THE POWER OF STUDENT'S t TEST: CAN A NON‐SIMILAR TEST DO BETTER?
Authors: King Maxwell L.
Published: February 2008

Lehmann & Stein (1948) proved the existence of non‐similar tests which can be more powerful than best similar tests. They used Student's problem of testing for a non‐zero mean given a random sample from the normal distribution with unknown variance as an example. This raises the question: should we use a non‐similar test instead of Student's t test? Questions like this can be answered by comparing the power of the test with the power envelope. This paper discusses the difficulties involved in computing power envelopes. It reports an empirical comparison of the power of the t test and the power envelope and finds that the two are almost identical especially for sample sizes greater than 20. These findings suggest that, as well as being uniformly most powerful (UMP) within the class of similar tests, Student's t test is approximately UMP within the class of all tests. For practical purposes it might also be regarded as UMP when moderate or large sample sizes are involved.
DISTRIBUTION‐FREE TESTS BASED ON SUB‐SAMPLE EXTREMA FOR TESTING AGAINST POSITIVE DEPENDENCE
Authors: Kochar Subhash C. , Gupta R.P.
Published: February 2008

A class of distribution‐free tests based on U‐statistics has been proposed for testing the null hypothesis of independence against positive quadrant dependence. The tests are based on U‐statistics and the Kendall's‐tau test belongs to this class.
A MONTE CARLO COMPARISON OF ELLIPTICAL‐THEORY AND OTHER TESTS FOR EQUALITY OF COVARIANCE MATRICES
Authors: Pervaiz Muhammad Khalid , Skinner C.J.
Published: February 2008

A Monte Carlo study of the size and power of tests of equality of two covariance matrices is carried out. Tests based upon normality assumptions, elliptical distribution assumptions as well as distribution‐free tests are compared. Samples are generated from normal, elliptical and non‐elliptical populations. The elliptical‐theory tests, in particular, have poor size properties for both elliptical distributions with moderate sample sizes and for non‐elliptical distributions.
EMPIRICALLY ACCELERATED CONVERGENCE OF THE SPACINGS STATISTICS TO NORMALITY
Authors: Mudholkar Govind S. , Smethurst Philip A.
Published: February 2008

If the asymptotic normality of a statistic is inadequate for approximating its distribution in practice, then the statistic may be transformed in order to improve the approximation by accelerating the convergence to normality. We treat a goodness‐of‐fit statistic, the sum of the logarithms of generalized uniform spacings introduced by Cressie (1976, 1978), in this spirit. Specifically, we apply the method of maximum likelihood to simulations of the statistic in order to estimate a power transformation, as in Box & Cox (1964), and hence develop a small sample normal approximation. This approximation provides a more versatile method of applying the statistic than currently available tables of percentiles.
THE RATE OF CONVERGENCE IN THE NORMAL APPROXIMATION FOR THE WILCOXON R‐ESTIMATOR
Authors: Hall Peter , Welsh A.H.
Published: February 2008

We exploit the fact that the Wilcoxon score R‐estimator of the slope in a linear regression model minimises Gini's mean difference of the residuals to obtain a Berry‐Esseen rate of convergence result for the Wilcoxon R‐estimator.
ON BOOTSTRAP HYPOTHESIS TESTING
Authors: Fisher Nicholas I. , Hall Peter
Published: February 2008

We describe methods for constructing bootstrap hypothesis tests, illustrating our approach using analysis of variance. The importance of pivotalness is discussed. Pivotal statistics usually result in improved accuracy of level. We note that hypothesis tests and confidence intervals call for different methods of resampling, so as to ensure that accurate critical point estimates are obtained in the former case even when data fail to comply with the null hypothesis. Our main points are illustrated by a simulation study and application to three real data sets.
A METHOD FOR DETERMINING THE ASYMPTOTIC EFFICIENCY OF SOME SEQUENTIAL PROBABILITY RATIO TESTS
Authors: Pollard Graham
Published: February 2008

This paper gives a method for decomposing many sequential probability ratio tests into smaller independent components called “modules”. A function of some characteristics of modules can be used to determine the asymptotically most efficient of a set of statistical tests in which a, the probability of type I error equals β, the probability of type II error. The same test is seen also to give the asymptotically most efficient of the corresponding set of tests in which a is not equal to β. The “module” method is used to give an explanation for the super‐efficiency of the play‐the‐winner and play‐the‐loser rules in two‐sample binomial sampling. An example showing how complex cases can be analysed numerically using this method is also given.
ESTIMATING THE ROOT OF A NONPARAMETRIC REGRESSION FUNCTION IN A ROBUST FASHION
Authors: He Xuming
Published: February 2008

For a nonparametric regression model y = m(x)+e with n independent observations, we analyze a robust method of finding the root of m(x) based on an M‐estimation first discussed by Härdle & Gasser (1984). It is shown here that the robustness properties (minimaxity and breakdown function) of such an estimate are quite analogous to those of an M ‐estimator in the simple location model, but the rate of convergence is somewhat limited due to the nonparametric nature of the problem.
A CONDITIONAL DERIVATION OF RESIDUAL MAXIMUM LIKELIHOOD
Authors: Verbyla A.P.
Published: February 2008

Patterson & Thompson (1971) introduced residual maximum likelihood estimation in the case of unbalanced incomplete block designs. Harville (1974) and Cooper & Thompson (1977) give alternative derivations of the likelihood function. The purpose of this note is to provide another derivation of the likelihood function which may be useful in teaching.