bluuebunny/crossref_metadata_2025 huggingface dataset:
COMPUTER‐AIDED CONSTRUCTION OF SMALL (M, S)‐OPTIMAL INCOMPLETE BLOCK DESIGNS
Authors: Nguyen Nam‐Ky , Dey Aloke
Published: February 2008

A new exchange algorithm for the construction of (M, S)‐optimal incomplete block designs (IBDS) is developed. This exchange algorithm is used to construct 973 (M, S)‐optimal IBDs (v, k, b) for v= 4,…,12 (varieties) with arbitrary v, k (block size) and b (number of blocks). The efficiencies of the “best” (M, S)‐optimal IBDs constructed by this algorithm are compared with the efficiencies of the corresponding nearly balanced incomplete block designs (NBIBDs) of Cheng(1979), Cheng & Wu (1981) and Mitchell & John(1976).
RANDOMISATION AND THE 1975 SENATE BALLOT DRAW
Authors: CLARK R.M. , HARCOURT A.G.
Published: February 2008

“So the last shall be first, and the first last; for many be called, but few chosen.” Matthew 20:16

The “random” draw for positions on the Senate ballot papers in the 1975 election resulted in an apparently non‐random ordering, to the possible advantage of one particular party. This paper assesses the statistical significance of the 1975 draw and looks at possible causes of the evident non‐randomness. A simplified yet realistic mathematical model is used to describe conditions under which the so‐called donkey vote can have an effect on the final outcome of the election, thereby confirming the widely‐held belief that the order of parties on the Senate ballot paper is relevant. We examine other Senate elections between 1949 and 1983 for the existence of relevant non‐randomness similar to the 1975 result. Finally, we report briefly on our submission to the 1983 Joint Select Committee on Electoral Reform, which led to an improvement in the randomisation procedure.
EFFICIENT BLOCK DESIGNS FOR CORRELATED OBSERVATIONS
Authors: Martin R.J. , Eccleston J.A.
Published: February 2008

Current methods for the design of efficient incomplete block experiments when the observations within a block are dependent usually involve computer searches of binary designs. These searches give little insight into the features that lead to efficiency, and can miss more efficient designs. This paper aims to develop some approximations which give some insight into the features of a design that lead to high efficiency under a generalized least‐squares analysis for a known dependence structure, and to show that non‐binary designs can be more efficient for some dependence structures. In particular, we show how neighbour balance and end plot balance are related to the design efficiency for low‐order autoregressions, and that under moderate positive dependence, replication at lag two can sometimes increase efficiency.
DISTRIBUTION FREE MULTIPLE COMPARISONS FOR MONOTONICALLY ORDERED TREATMENT EFFECTS
Authors: Hayter Anthony J. , Stone Glenn
Published: February 2008

A method of calculating simultaneous one‐sided confidence intervals for all ordered pairwise differences of the treatment effectsj–i, 1 i < j k, in a one‐way model without any distributional assumptions is discussed. When it is known a priori that the treatment effects satisfy the simple ordering1k, these simultaneous confidence intervals offer the experimenter a simple way of determining which treatment effects may be declared to be unequal, and is more powerful than the usual two‐sided Steel‐Dwass procedure. Some exact critical points required by the confidence intervals are presented for k= 3 and small sample sizes, and other methods of critical point determination such as asymptotic approximation and simulation are discussed.
ALL THE GAUSSIAN WHITE NOISE SERIAL COVARIANCE MOMENTS TO ORDER FOUR
Authors: Anderson O.D.
Published: February 2008

Using a recursive method, we obtain all the cumulants, central moments, and moments about zero, up to order 4, for the mean‐corrected serial covariances from series realisations of length n, given a Gaussian white noise process. Some implicit higher order results are also derived.
CORRECTING FOR KURTOSIS IN DENSITY ESTIMATION
Authors: Ruppert D. , Wand M.P.
Published: February 2008

Using a global window width kernel estimator to estimate an approximately symmetric probability density with high kurtosis usually leads to poor estimation because good estimation of the peak of the distribution leads to unsatisfactory estimation of the tails and vice versa. The technique proposed corrects for kurtosis via a transformation of the data before using a global window width kernel estimator. The transformation depends on a “generalised smoothing parameter” consisting of two real‐valued parameters and a window width parameter which can be selected either by a simple graphical method or, for a completely data‐driven implementation, by minimising an estimate of mean integrated squared error. Examples of real and simulated data demonstrate the effectiveness of this approach, which appears suitable for a wide range of symmetric, unimodal densities. Its performance is similar to ordinary kernel estimation in situations where the latter is effective, e.g. Gaussian densities. For densities like the Cauchy where ordinary kernel estimation is not satisfactory, our methodology offers a substantial improvement.
ON THE DESIGN OF FIELD EXPERIMENTS UNDER A ONE‐DIMENSIONAL NEIGHBOUR MODEL
Authors: Gleeson Alan C. , Eccleston John A.
Published: February 2008

This paper examines the effect of randomisation restrictions, either to satisfy conditions for a balanced incomplete block design or to attain a higher level of partial neighbour balance, on the average variance of pair‐wise treatment contrasts under a neighbour model discussed by Gleeson & Cullis (1987). Results suggest that smaller average pairwise variances can be obtained by ignoring requirements for incomplete block designs and concentrating on achieving a higher level of partial neighbour balance. Field layout of the design, although often determined by practical constraints, e.g. size, shape of site, minimum plot size and experimental husbandry, may markedly affect average pairwise variance. For the one‐dimensional (row‐wise) neighbour model considered here, investigation of three different layouts suggests that for a rectangular array of plots, smaller average pairwise variances can generally be obtained from layouts with fewer rows and more plots per row.
ROBUST ESTIMATION AND HYPOTHESIS TESTS FOR FIRST‐ORDER THRESHOLD AUTOREGRESSIVE MODELS
Authors: Kulkarni P.M.
Published: February 2008

Results of Petrucelli & Woolford (1984) for a first‐order threshold autoregressive model are considered from a robust point of view. Robust estimators of the threshold parameters of the model are obtained and their asymptotic normality is proved. Testing the equality of the threshold parameters is considered using the robust analogues of Wald and score test statistics. Limiting distributions of these statistics are given under both null and alternative hypotheses.
EMPIRICAL BAYES ESTIMATION FOR FIRST‐ORDER AUTOREGRESSIVE PROCESSES
Authors: Kim Young‐Won , Basawa I.V.
Published: February 2008

Large sample properties of an empirical Bayes estimate for a first order autoregressive process are obtained with respect to both the empirical Bayes and the frequentist frameworks.
PITMAN NEARNESS COMPARISONS OF ESTIMATES OF TWO ORDERED NORMAL MEANS
Authors: Gupta Rameshwar D. , Singh Harshinder
Published: February 2008

Maximum likelihood estimates of ordered means of two normal distributions having common variance have been shown to be better than the usual maximum likelihood estimates (i.e. corresponding sample means) with respect to Pitman Nearness criterion. The maximum likelihood estimate of common variance taking into consideration the order restriction of the means is shown to have smaller mean square error than the unrestricted maximum likelihood estimate of the common variance. These two estimators have also been compared with respect to Pitman Nearness criterion.
BALANCED CHANGE‐OVER DESIGNS FOR AUTOCORRELATED OBSERVATIONS
Authors: Gill P.S.
Published: February 2008

Some aspects of design of change‐over experiments with autocorrelated observations are investigated. Williams' designs (1949, 1950) are seen to be balanced for autocorrelated observations.
BURR CRITICAL VALUE APPROXIMATIONS FOR TESTS OF AUTOCORRELATION AND HETEROSCEDASTICITY
Authors: Evans Merran A.
Published: February 2008

The paper evaluates the accuracy of Burr approximations of critical values and p‐values for test a of autocorrelation and heteroscedasticity in the linear regression model.
ON THE DERIVATION AND COMPUTATION OF THE CORNISH‐FISHER EXPANSION
Authors: Lee Yoong‐Sin , Lee Moy Chee
Published: February 2008

The paper gives a simple derivation based on elementary statistics for the Cornish—Fisher expansion. The method simplifies greatly the algebra in working out the polynomials involved both in the normalization and in the inverse expansions. The derivation also leads to recursive formulae which yield powerful algorithms for numerical computation of the expansion.
FITTING SPATIAL CORRELATION MODELS: APPROXIMATING A LIKELIHOOD APPROXIMATION
Authors: Kiiveri H.T.
Published: February 2008

The paper considers a class of spatial correlation models (stationary Gaussian processes) which includes (spatial) conditional autoregressive, simultaneous autoregressive, moving average and direct covariance models. Given observations on a finite rectangular lattice, a likelihood approximation for estimating the parameters in the spectral density of the model is discussed. The approximation consists of applying the trapezoidal rule, with a her grid of frequencies than the usual Fourier frequencies, to compute the integral in an appraximation due to Whittle (1954) and later modified by Guyon (1984). With this approximation, a Fisher scoring type algorithm has a simple form and in some casea reduces to iteratively reweighted least squares. Methods for computing the unbiased two‐dimensional periodogram required by the method are presented and the accuracy of the approximation is discussed. The asymptotic distribution of the parameter estimates computed from the likelihood approximation is also given.
A NOTE ON EVANESCENT PROCESSES
Authors: Pollett P.K. , Jones D. Vere
Published: February 2008

This note examines the connection between μ‐invariant measures for the transition function of a continuous‐time Markov chain and those of its q‐matrix, Q. The major result establishes a necessary and aufficient condition for a convergent μ‐invariant measure for Q to be μ‐inhant for the minimal transition function, P, under the assumption that P is honest. This corrects Theorem 6 of Vere‐Jones (1969) and the first part of Corollary 1 of Pollett (1986), both of which assert that the above conclusion holds in the absence of this condition. The error was pointed out by E.A. van Doom (1991) and the counterexample which be presented provides the basis for the present arguments. In determining where the error occurred in the original proof, we are able to identify a simple sufficient condition for μ‐invariance.
STATISTICAL CHALLENGES OF AIDS: (The 1990 Knibbs Lecture, Canberra, 27 November 1990)
Authors: Becker Niels G.
Published: February 2008

Issues that are central to the understanding and management of the HIV epidemic have generated numerous statistical challenges. This paper considers questions concerning the incubation period, the effects of treatments, pre diction of AIDS cases, the choice of surrogate end points for the assessment of treatments and design of strategies for screening blood samples. These issues give rise to a broad range of intriguing problems for statisticians. We describe some of these problems, how they have been tackled so far and what remains to be done. The discussion touches on topical statistical methods such as smoothing, bootstrapping, interval censoring and the ill‐posed inverse problem, as well as asking fundamental questions for frequentist statistics.
A SEMIPARAMETRIC MIXTURE MODEL FOR THE ANALYSIS OF COMPETING RISKS DATA
Authors: Kuk Anthony Y.C.
Published: February 2008

This paper deals with the regression analysis of failure time data when there are censoring and multiple types of failures. We propose a semiparametric generalization of a parametric mixture model of Larson & Dinse (1985), for which the marginal probabilities of the various failure types are logistic functions of the covariates. Given the type of failure, the conditional distribution of the time to failure follows a proportional hazards model. A marginal like lihood approach to estimating regression parameters is suggested, whereby the baseline hazard functions are eliminated as nuisance parameters. The Monte Carlo method is used to approximate the marginal likelihood; the resulting function is maximized easily using existing software. Some guidelines for choosing the number of Monte Carlo replications are given. Fixing the regression parameters at their estimated values, the full likelihood is maximized via an EM algorithm to estimate the baseline survivor functions. The methods suggested are illustrated using the Stanford heart transplant data.
ESTIMATION OF GUARANTEE TIME AND MEAN LIFE AFTER WARRANTY FOR TWO‐PARAMETER EXPONENTIAL FAILURE MODEL
Authors: Khattree Ravindra
Published: February 2008

Suppose manufactured items have failure times distributed with the two‐parameter exponential density function à‐le‐(x‐μ)/à (x≥μ≥0). The paper considers estimation of the guarantee time μ and mean life after warranty à. Properties of various estimators are given for both separate and simultaneous estimation of μ and à. Criteria for comparing estimators are entropy loss, LINEX loss, and (generalized) Pitman nearness.
THE OPTIMAL TEST FOR SELECTING THE GREATER OF TWO BINOMIAL PROBABILITIES
Authors: Pollard Graham H.
Published: February 2008

The efficiency of a sequential test is related to the “importance” of the trials within the test. This relationship is used to find the optimal test for selecting the greater of two binomial probabilities,pαandpb, namely, the stopping rule is “gambler's ruin” and the optimal discipline whenpα+pb≤1 (≥ 1) is play‐the‐winner (loser), i.e. an α‐trial which results in a success is followed by an α‐trial (b‐trial) whereas an α‐trial which results in a failure is followed by α b‐trid (α‐trial) and correspondingly for b‐trials.
ON CHARACTERIZATIONS THROUGH MIXED SUMS
Authors: Pakes Anthony G.
Published: February 2008

Let X, X‘ and X“ be independent and have the same law, and let U be uniform on [0,1] and independent of X’ and XI”. A problem which has received considerable attention is to identify the laws of X for which X =c U(X‘+X“), the equality being in law. If X is positive it has an exponential law, and mixture solutions exist without the sign restriction. The problem has been extended to allow more summands on either side and to let U have a special beta law. In the positive case X then has a gamma law.

This problem is tackled in full generality by considering an integral equation for the characteristic function of X. Uniqueness results and necessary conditions are given. The general case is reduced to that where X is positive, and the solution of the corresponding integral equation is constructed under the necessary conditions. This is shown to characterize all possible laws of X when there is a single summand on the left and U has an arbitrary law on [0,1]. Examples are given and known particular results are sharpened.
CLASSIFICATION AND PROPORTION ESTIMATION
Authors: Bélanger J. , Gagnon D.
Published: February 2008

Assume that a number of individuals are to be classified into one of two populations and that, at the same time, the proportion of members of each population needs to be estimated. The allocated proportions given by the Bayes classification rule are not consistent estimates of the true proportions, so a different classification rule is proposed; this rule yields consistent estimates with only a small increase in the probability of misclassification. As an illustration, the case of two normal distributions with equal covariance matrices is dealt with in detail.
MINIMUM QUADRATIC DISTANCE ESTIMATION FOR A PARAMETRIC FAMILY OF DISCRETE DISTRIBUTIONS DEFINED RECURSIVELY
Authors: Luong Andrew , Garrido José
Published: February 2008

The distribution function of a random sum can easily be computed iteratively when the distribution of the number of independent identically distributed elements in the sum is itself defined recursively. Classical estimation procedures for such recursive parametric families often require specific distributional assumptions (e.g. Poisson, Negative Binomial). The minimum distance estimator proposed here is an estimator within a larger parametric family. The estimator is consistent, efficient when the parametric family is truncated, and can be made either robust or asymptotically efficient when the parametric family has infinite range. Its asymptotic distribution is derived. A brief illustration with Automobile Insurance data is included.
TRIMMED LIKELIHOOD ESTIMATION OF LOCATION AND SCALE OF THE NORMAL DISTRIBUTION
Authors: Bednarski T. , Clarke B.R.
Published: February 2008

Consideration of multivariate statistical procedures leads to description of robust methods of estimation of location and scale for real random variables. This paper outlines asymptotic theory for estimating location and scale by viewing it as a trimmed likelihood estimator. An appeal is made to results from empirical processes linking the proofs to compact differentiability of estimating functionals. The estimator for location does not depend on the scale estimate and is robust against asymmetric contamination. Coincidentally the location estimator denned at the normal distribution is similar to the least trimmed squares estimator. Simulations corroborate the asymptotic theory and illustrate robustness against asymmetric contamination.
AMEMIYA'S FORM OF THE WEIGHTED LEAST SQUARES ESTIMATOR
Authors: Koenker Roger , Machado José A.F. , Skeels Christopher L. , Welsh A.H.
Published: February 2008

Amemiya's estimator is a weighted least squares estimator of the regression coefficients in a linear model with heteroscedastic errors. It is attractive because the heteroscedasticity is not parametrized and the weights (which depend on the error covariance matrix) are estimated nonparametrically. This paper derives an asymptotic expansion for Amemiya's form of the weighted least squares estimator, and uses it to discuss the effects of estimating the weights, of the number of iterations, and of the choice of the initial estimate. The paper also discusses the special case of normally distributed errors and clarifies the particular consequences of assuming normality.
NONPARAMETRIC ESTIMATION FOR COMPETING RISKS
Authors: Froda S. , Luong A.
Published: February 2008

This paper considers the estimation of the ratio of two scale parameters when the data are censored. It emphasises characteristics of the asymptotic variance under censoring from a practical point of view. The estimator proposed by Padgett & Wei (1982) for the two‐sample scale model is extended to the competing risks model. Asymptotic properties of the estimator are studied via its influence function. The use of influence functions permits a unified treatment of both models. Examples show and illustrate that under both models the variance can become infinite under some circumstances.
UPPER BOUNDS FOR LATINIZED DESIGNS
Authors: Williams E.R. , John J.A.
Published: February 2008

Upper bounds axe derived for the efficiency factor of a class of resolvable incomplete block designs known as latinized designs. These designs are particularly useful in glasshouse and field trials, and can be readily extended to two‐dimensional blocking structures. Existing bounds for resolvable designs axe also reviewed and a comparison is made between the third moment bounds discussed by Jarrett (1989) and the second moment bounds of Tjur (1990).
NEIGHBOUR ANALYSIS WITH ADJUSTMENT FOR INTERPLOT COMPETITION
Authors: Pithuncharurnlap M. , Basford K.E. , Federer W.T.
Published: February 2008

In field experiments involving a large number of experimental plots, a neighbour analysis can be used to control environmental variation by estimating the trend within blocks. The effect of interplot competition is another important source of variation which has an influence on the estimation of treatment contrasts. To reduce the effect of the variation from these sources and to improve the precision of comparison between treatments, a spatial model is proposed for incorporating both trend effect and interplot competition. It is a modification to the residual maximum likelihood neighbour analysis of Gleeson & Cullis (1987) using the two neighbouring treatment effects to estimate interplot competition. A real example is used to illustrate this methodology. The results indicate that the extended model gives no appreciable difference in standard error of mean differences compared with the model taking into account the trend effect only. However, the rankings of estimated treatment means do differ. More research using both real and simulated data is required before such models that incorporate trend and competition effects can be confidently recommended.
NONPARAMETRIC ESTIMATION OF ANGULAR DISTRIBUTIONS FROM CARTESIAN OBSERVATIONS WITH ERROR
Authors: Horgan G.W. , Haslett J.
Published: February 2008

If angular data are obtained from Cartesian observations, then any measurement error in these observations will produce a particular error structure in the angular data. The paper shows how non‐parametric density estimation by orthogonal series may be performed in this case.
INVERSE SAMPLING FOR DOMAIN ESTIMATION IN A STRATIFIED POPULATION
Authors: Mukerjee Rahul , Basu Sujit K.
Published: February 2008

For a stratified population under inverse sampling, we propose and study an unbiased estimator for the mean of units belonging to a domain with specific features. An alternative, simpler, ratio‐type estimator is also considered. Empirical studies show that strategies based on inverse sampling can be superior to a more traditional strategy based on stratified simple random sampling with a fixed number of draws in each stratum.
ROBUST ESTIMATION UNDER TYPE II CENSORING
Authors: Akritas Michael G. , Basak Indrani , Lee Myung Hwi
Published: February 2008

The properties of robust M‐estimators with type II censored failure time data are considered. The optimal members within two classes of ψ‐functions are characterized. The first optimality result is the censored data analogue of the optimality result described in Hampel et al. (1986); the estimators corresponding to the optimal members within this class are referred to as the optimal robust estimators. The second result pertains to a restricted class of ψ‐functions which is the analogue of the class of ψ‐functions considered in James (1986) for randomly censored data; the estimators corresponding to the optimal members within this restricted class are referred to as the optimal James‐type estimators. We examine the usefulness of the two classes of ψ‐functions and find that the breakdown point and efficiency of the optimal James‐type estimators compare favourably with those of the corresponding optimal robust estimators. From the computational point of view, the optimal James‐type ψ‐functions are readily obtainable from the optimal ψ‐functions in the uncensored case. The ψ‐functions for the optimal robust estimators require a separate algorithm which is provided. A data set illustrates the optimal robust estimators for the parameters of the extreme value distribution.
KERNEL DENSITY ESTIMATION WHEN THE BANDWIDTH IS LARGE
Authors: Jones M.C.
Published: February 2008

The performance of kernel density estimation, in terms of mean integrated squared error, is investigated in the opposite of the usual situation, namely when the bandwidth is large. This affords noteworthy insights including the special role taken by the normal density function as kernel and a tie‐in with ‘semiparametric’ approaches to density estimation.
INTERRELATIONSHIPS BETWEEN lP‐ISOTROPIC DENSITIES AND lP‐ISOTROPIC SURVIVAL FUNCTIONS, AND DE FINETTI REPRESENTATIONS OF SCHUR‐CONCAVE SURVIVAL FUNCTIONS
Authors: Hayakawa Yu
Published: February 2008

Interrelationships between lP‐isotropic densities and lP‐isotropic survival functions are studied. We obtain representations for densities whose survival functions are lP‐isotropic and for survival functions whose densities are lP‐isotiopic. The former are mixtures of products of Weibull densities and the latter are mixtures of products of Gamma survival functions. Based on a theorem proved by Cooke, we show that de Finetti representations for Schur‐concave survival functions that have the same level sets as a product measure can be represented as mixtures of products of increasing failure rate survival functions.
ON CROSS‐VALIDATION FOR SMOOTHING SPLINES IN THE CASE OF DEPENDENT OBSERVATIONS
Authors: van der LINDE ANGELIKA
Published: February 2008

Cross‐validation, as a popular tool for choosing a smoothing parameter, is generalized to the case of dependent observations. A general version of the ‘deletion theorem’ for representation and simplified calculation of cross‐validatory criteria is given. Finally cross‐validation is discussed in terms of penalized likelihoods as a method for model choice analogous to the Akaike information criterion.
RATES OF CONVERGENCE IN SEMI‐PARAMETRIC MODELLING OF LONGITUDINAL DATA
Authors: MOYEED R.A. , DIGGLE P.J.
Published: February 2008

We consider the problem of semi‐parametric regression modelling when the data consist of a collection of short time series for which measurements within series are correlated. The objective is to estimate a regression function of the form E[Y(t) |x] =x'ß+μ(t), where μ(.) is an arbitrary, smooth function of timet, andxis a vector of explanatory variables which may or may not vary witht.For the non‐parametric part of the estimation we use a kernel estimator with fixed bandwidthh.Whenhis chosen without reference to the data we give exact expressions for the bias and variance of the estimators for β and μ(t) and an asymptotic analysis of the case in which the number of series tends to infinity whilst the number of measurements per series is held fixed. We also report the results of a small‐scale simulation study to indicate the extent to which the theoretical results continue to hold whenhis chosen by a data‐based cross‐validation method.
APPLICATIONS OF ROBUST ESTIMATION FOR VARIANCE COMPONENTS MODELS:THE DETECTION OF MAJOR GENE EFFECTS IN FINGER RIDGE COUNTS IN NORMAL AND FRAGILE X FAMILIES
Authors: Huggins Richard M. , Loesch Danuta Z.
Published: February 2008

A diagnostic technique is proposed to detect major gene effects and other systematic departures from a model for the trait means in the presence of outliers. The technique is based on the examination of residuals from fitting variance components models to quantitative pedigree data using robust statistical procedures. The approach is demonstrated using the total ridge count and ridge count of the middle finger from 54 extended families affected with the Fragile X syndrome, and a sample of 217 normal pedigrees.
CHARACTERIZATIONS OF SHIFT‐INVARIANT DISTRIBUTIONS BASED ON SUMMATION MODULO ONE
Authors: Wilms Roel J.G. , Thiemann Jan G.F.
Published: February 2008

Let X1Y1,…, Yn be independent random variables. We characterize the distributions of X and Yj satisfying the equation {X+Y1++Yn}=dX, where {Z} denotes the fractional part of a random variable Z. In the case of full generality, either X is uniformly distributed on [0,1), or Yj has.a shifted lattice distribution and X is shift‐invariant. We also give a characterization of shift‐invariant distributions. Finally, we consider some special cases of this equation.
BAHADUR SLOPES FOR COMPARISONS OF TESTS BASED ON RESAMPLING
Authors: Jing Bing‐Yi
Published: February 2008

LetX1,…,Xnbe random variables symmetric about θ from a common unknown distribution Fθ(x) =F(x–θ). To test the null hypothesisH0:θ= 0 against the alternativeH1:θ > 0, permutation tests can be used at the cost of computational difficulties. This paper investigates alternative tests that are computationally simpler, notably some bootstrap tests which are compared with permutation tests. Of these the symmetrical bootstrap‐f test competes very favourably with the permutation test in terms of Bahadur asymptotic efficiency, so it is a very attractive alternative.
ON TESTS FOR INTERACTION IN A NONREPLICATED TWO‐WAY LAYOUT
Authors: Piepho Hans‐Peter
Published: February 2008

The paper proposes tests for interaction in a two‐way table with one observation per cell. The power of these tests is independent of the additive main effects in the linear model. This is an advantage compared to a test suggested earlier, which has low power if main effects are very variable.
ESTIMATING TEMPORAL FARM INCOME DISTRIBUTIONS USING SPATIAL SMOOTHING TECHNIQUES
Authors: Kokic Philip N. , Moon Lynelle , Gooday Jane , Chambers Ray L.
Published: February 2008

The Australian Bureau of Agricultural & Resource Economics (ABARE) has conducted the annual Australian Agricultural and Grazing Industries Survey, covering the broadacre sector, in a consistent format since 1978/79. In this period the incomes of farmers have fluctuated considerably. Interest has focused on temporal income variation because of its relationship to the inherent riskiness of farming. Part of these income fluctuations can be explained by changing commodity prices and by highly variable climatic conditions. This paper outlines a method of measuring the magnitude of this income variation and how it relates to other variables. Due to rotation within the sample of farms surveyed, data are limited for determining the income variability of any particular farm. This paper, using spatial locations of surveyed farms, shows how kernel smoothing techniques can be adapted to estimate the distribution of a farm's income. This analysis uses data collected from 1978/79 to 1991/92. Summary information from these distributions is cross‐tabulated against several other variables. This shows that income variability is strongly related to the production mixture of farming businesses.
A PERMUTATION PAIRED TEST ALLOWING FOR MISSING VALUES
Authors: Maritz J.S.
Published: February 2008

The paper presents a paired test of the equality of two means, allowing for incomplete pairs. It is a permutation test depending on minimal distributional assumptions. The test may be performed on original data or after transformation of the data. Transformation to ranks is illustrated.
ON NON‐NEGATIVE UNBIASED ESTIMATION OF QUADRATIC FORMS IN FINITE POPULATION SAMPLING
Authors: Vijayan K. , Mukhopadhyay P. , Bhattacharyya S.
Published: February 2008

The paper investigates non‐negative quadratic unbiased (NnQU) estimators of positive semi‐definite quadratic forms, for use during the survey sampling of finite population values. It examines several different NnQU estimators of the variance of estimators of population total, under various sampling designs. It identifies an optimal quadratic unbiased estimator of the variance of the Horvitz‐Thompson estimator of population total.
ESTIMATING THE ANGLE BETWEEN THE MEAN DIRECTIONS OF TWO SPHERICAL DISTRIBUTIONS
Authors: Lewis Toby , Fisher Nicholas I.
Published: February 2008

This paper considers the problem of calculating a confidence interval for the angular difference between the mean directions of two spherical random variables with rotationally symmetric unimodal distributions. For large sample sizes, it is shown that the asymptotic distribution of 1 – cos α, where α is the sample angular difference, is approximately exponential if the true difference is zero, and approximately normal for a ‘large’ true difference; a scaled beta approximation is determined for the general case. For small sample sizes, a bootstrap approach is recommended. The results are applied to two sets of palaeomagnetic data.
SPLINE SMOOTHER AS A DYNAMIC LINEAR MODEL
Authors: MOYEED R.A.
Published: February 2008

The paper shows how a finite dimensional representation of a cubic smoothing spline can be put in the framework of a dynamic linear model. The formulation provides an updating scheme when observations do not occur sequentially in time or space.
TWO‐MOMENT SCALING FORMULAE FOR AGGREGATING EXAMINATION MARKS
Authors: Daley D.J.
Published: February 2008

Three different methods are presented for deriving linear transformations of raw examination marks in order to construct ostensibly fair’ average or aggregate marks for students taking possibly different subsets of subjects from the curriculum. All methods are based on the same linear model, which in the case of a balanced dataset (that is, if all students have marks in all subjects) is closely related to a simple principal component representation.
A ONE‐SIDED TRIMMED MEAN ESTIMATOR FOR THE MEAN OF POSITIVELY SKEWED DISTRIBUTIONS
Authors: Chen Ling
Published: February 2008

This article proposes estimating the mean of positively skewed distributions by a one‐sided trimmed mean estimator, called the upper‐mean, and uses it to assess soil contact exposures at sites with toxic contamination. An optimal upper‐mean is found by maximising the probability of the estimator falling in a target range. Monte Carlo studies are conducted for several positively skewed distributions and for a distribution obtained from real data. The simulation results show that the upper‐mean is a better estimator than the upper 95% confidence limit estimator currently used, because it is more probable that the estimator is covered by the target range.
SOME RESAMPLING PROCEDURES UNDER SYMMETRY
Authors: Jing BinG‐Yi
Published: February 2008

This paper investigates the properties of bootstrap and related methods assuming that the underlying distribution is symmetric but otherwise unknown. In particular it studies the percentile‐t, nonparametric tilting and empirical likelihood and finds that the performance of percentile‐t and non‐parametric tilting methods can be improved by incorporating the symmetry into the resampling procedure. However, for symmetric empirical likelihood, the Bartlett correctability no longer holds, although use of bootstrap calibration restores the good coverage properties typically associated with Bartlett correction. This surprising result shows that Bartlett correctability is a very delicate property.
AN ALGORITHM FOR THE DESIGN OF 2? FACTORIAL EXPERIMENTS ON CONTINUOUS PROCESSES
Authors: Saunders I.W. , Eccleston J.A. , Martin R.J.
Published: February 2008

Saunders & Eccleston (1992) presented an approach to the design of 2‐level factorial experiments for continuous processes. It determined sets of contrasts between the observations that could be well estimated, and then selected a design so that those contrasts estimated the parameters of interest. This paper shows that a well‐estimated contrast must have a large number of changes of sign or level, and also be ‘paired’ in a particular sense. It develops an algorithm which constructs designs that must have a large number of changes of sign, evenly spread among the contrasts and optimal or near optimal. When such designs exist they are often preferable to those produced by the reverse foldover algorithm of Cheng & Steinberg (1991).
A STATISTICAL MODEL FOR DUPLICATE TOURNAMENTS IN GAMES OF LUCK AND SKILL
Authors: Yu Philip L.H. , Cowan Richard
Published: February 2008

Many games played between two contestants start with a random deal, which introduces luck from the deal. The concept of ‘duplication’, commonly employed in Bridge tournaments, can be used to nullify that luck in a tournament. This paper poses a model for the contest between any two players and analyses the model for a tournament which employs the duplication principle. Two example tournaments on a new game are analysed.
THE IMPACT OF METHOD CHOICE ON META‐ANALYSIS
Authors: Mengersen K.L. , Tweedie R.L. , Biggerstaff B.
Published: February 2008

This paper focusses mainly on three crucial choices identified in recent meta‐analyses, namely (a) the effect of using approximate statistical techniques rather than exact methods, (fa) the effect of using fixed or random effect models, and (c) the effect of publication bias on the meta‐analysis result. The paper considers their impact on a set of over thirty studies of passive smoking and lung cancer in non‐smokers, and addresses other issues such as the role of study comparability, the choice of raw or adjusted data when using published summary statistics, and the effect of biases such as misclassification of subjects and study quality. The paper concludes that, at least in this example, different conclusions might be drawn from metaanalyses based on fixed or random effect models; that exact methods might increase estimated confidence interval widths by 5–20% over standard approximate (logit and Mantel‐Haenszel) methods, and that these methods themselves differ by this order of magnitude; that taking study quality into account changes some results, and also improves homogeneity; that the use of unadjusted or author‐adjusted data makes limited difference; that there appears to be obvious publication bias favouring observed raised relative risks; and that the choice of studies for inclusion is the single most critical choice made by the modeller.
MISSING VALUES, IMPUTATION AND ERROR RATE ESTIMATORS IN DISCRIMINANT ANALYSIS
Authors: Bello A.L.
Published: February 2008

Error rate is a popular criterion for assessing the performance of an allocation rule in discriminant analysis. Training samples which involve missing values cause problems for those error rate estimators that require all variables to be observed at all data points. This paper explores imputation algorithms, their effects on, and problems of implementing them with, eight commonly used error rate estimators (three parametric and five non‐parametric) in linear discriminant analysis. The results indicate that imputation should not be based on the way error rate estimators are calculated, and that imputed values may underestimate error rates.
A NOTE ON ARMA PARAMETERISATION*
Authors: Hannan E.J. , Kavalieris L.
Published: February 2008

This paper considers the relationship between ARMA parameterisations of models fory(t)andAy(t), whereAis invertible andy(t)is a vector time series (t = 0,±1,…). An ARMA model for the transformed seriesAy(t)may have fewer parameters than a model fory(t).This paper shows that such a saving is illusory because the apparently saved parameters are exactly balanced by the number of new parameters appearing inA.
TESTS FOR SEASONAL DIFFERENCING WITH AN UNKNOWN BREAK‐POINT
Authors: Ng T.M. , Li W.K.
Published: February 2008

Some Lagrange multiplier tests for seasonal differencing are proposed; their main objective is to avoid over‐differencing due to structural change. The null hypothesis is either the presence of both regular and seasonal unit roots or the presence of a seasonal unit root. Alternative hypotheses allow for stationarity around a possible structural change where the break‐point is unknown. The location of the structural change is estimated using the proposed procedures, the asymptotic distribution of the test statistics under the null hypothesis is derived and some useful percentiles are tabulated. An illustrative example based on the Canadian Consumer Price Index is presented.
DISTRIBUTION‐FREE CONFIDENCE PROCEDURE FOR UMBRELLA ORDERINGS
Authors: Pan Guohua
Published: February 2008

Responses in a one‐factor experiment with A; ordered treatments follow an umbrella, ordering if they consist of two piecewise monotone segments, i.e. increasing and then decreasing, or the converse. This paper proposes a non‐parametric distribution‐free confidence procedure for umbrella orderings, the aim being to identify the treatments that correspond to the optimal effects. It uses a method that joins the seemingly unrelated theories of U‐statistics and isotonic regression. A random confidence subset of the ordered treatments is constructed, such that it contains all the unknown peaks (optimal treatments) of an umbrella ordering with any prespecified confidence level. The paper demonstrates that the proposed confidence procedure is nonparametric distribution‐free and, further, that the proposed procedure naturally implies a test for umbrella alternatives. Since the proposed confidence procedure is always more informative than tests for umbrella alternatives, it should be used in their place in practice. An example illustrates the proposed procedure.
INDEPENDENCE DISTRIBUTION‐PRESERVING NONNEGATIVE‐DEFINITE COVARIANCE STRUCTURES FOR THE SAMPLE VARIANCE
Authors: Young Dean M. , Lehman Leah M. , Meaux Laurie M.
Published: February 2008

This paper explicitly characterizes the general nonnegative‐definite covariance structure for a multivariate normal random vector such that the univariate sample variance is distributed exactly as if the sample observations are normal independent and identically distributed (i.i.d.). This work extends the results of Baldessari (1965) and Stadje (1984) who have characterized the general positive‐definite covariance matrix such that the univariate sample variance is distributed exactly as if the sample observations are normal i.i.d.
REGRESSION ANALYSIS USING SCRAMBLED RESPONSES
Authors: Singh Sarjinder , Joarder A.H. , King Maxwell L.
Published: February 2008

This paper investigates the general linear regression modelY = Xβ+eassuming the dependent variable is observed as a scrambled response using Eichhorn & Hayre's (1983) approach to collecting sensitive personal information. The estimates of the parameters in the model remain unbiased, but the variances of the estimates increase due to scrambling. The Wald test of the null hypothesis H0:β=β0, against the alternative hypothesis Ha:β#β0, is also investigated. Parameter estimates obtained from scrambled responses are compared to those from conventional or direct‐question surveys, using simulation. The coverage by nominal 95% confidence intervals is also reported.
MULTI‐FACTOR BALANCED BLOCK DESIGNS WITH COMPLETE ADJUSTED ORTHOGONALITY FOR ALL PAIRS OF TREATMENT FACTORS
Authors: Preece D.A.
Published: February 2008

A new series of multi‐factor balanced block designs is introduced. Each of these designs has the following properties: (i) each of its k– 1 treatment factors is disposed in a cyclic or multi‐cyclic balanced incomplete block design with parameters (v,b,r,k,Λ) = (a(k‐l) + 1,a2(k‐1) +a, ak, k, k) (a > 1); (ii) the incidence of any one of the treatment factors on any other is balanced; and (iii) after adjustment for blocks only, the relationship between any two of the treatment factors is that of adjusted orthogonality. The treatment factors are thus orthogonal to one another in the within‐blocks stratum of the analysis of variance. The designs provide a benchmark with which other designs may be compared.
DISPERSION CONTROL FOR MULTIVARIATE PROCESSES – SOME COMPARISONS
Authors: Tang Pak F. , Barnett Neil S.
Published: February 2008

Tang & Barnett (1996) present some techniques for monitoring and controlling the dispersion of multivariate normal processes based on subgroup data. The current paper compares the proposed techniques and various competing procedures. Simulation results indicate that the proposed techniques are superior to existing procedures.
ESTIMATION OF QUANTILES FOR A FRÉCHET‐TYPE DISTRIBUTION
Authors: Hasofer A.M. , Wang J.Z.
Published: February 2008

Estimation of high quantiles of a distribution in the domain of attraction of the Fréchet distribution is based on the extremal distribution of theklargest order statistics. The problem is treated by a local maximum likelihood method on a three parameter model. The estimators are shown to be asymptotically consistent for the whole range of the tail index parameter.
IMPROVED INFERENCE FROM RECAPTURE EXPERIMENTS WITH BEHAVIOURAL RESPONSE THROUGH MODELLING and AUXILIARY EXPERIMENTATION
Authors: Chaiyapong Y. , Lloyd C.J.
Published: February 2008

Allowing for behavioural response in a recapture experiment involves a large reduction in the precision of estimating the unknown population size. Unless the number of individuals captured is very large, the model is of little use in practice. This paper studies the extent to which this efficiency loss can be reduced by modelling the behavioural response. The most dramatic improvements in efficiency are obtained by estimating the rate of the behavioural response from an intensive study of a small subset of the population. In many practical situations this may be a cost‐ and time‐effective alternative to intensively sampling the entire population.
MODEL‐BASED VARIANCE ESTIMATION IN SURVEYS WITH STRATIFIED CLUSTERED DESIGN
Authors: Longford N.T.
Published: February 2008

A model‐based method for estimating the sampling variances of estimators of (sub‐)population means, proportions, quantiles, and regression parameters in surveys with stratified clustered design is described and applied to a survey of US secondary education. The method is compared with the jackknife by a simulation study. The model‐based estimators of the sampling variances have much smaller mean squared errors than their jackknife counterparts. In addition, they can be improved by incorporating information about the unknown parameters (variances) from external sources. A regression‐based smoothing method for estimating the sampling variances of the estimators for a large number of subpopulation means is proposed. Such smoothing may be invaluable when subpopulations are represented in the sample by only few subjects.
ESTIMATION FOR THE GENERAL SAMPLE SELECTION MODELS
Authors: Wang You‐Gan , Yin Ming
Published: February 2008

summary

Consider a general regression model with an arbitrary and unknown link function and a stochastic selection variable that determines whether the outcome variable is observable or missing. The paper proposes U‐statistics that are based on kernel functions as estimators for the directions of the parameter vectors in the link function and the selection equation, and shows that these estimators are consistent and asymptotically normal.
TWO‐SAMPLE NONPARAMETRIC TILTING METHOD
Authors: Jing Bing‐Yi , Robinson John
Published: February 2008

summary

Efron introduced the one‐sample nonparametric tilting method for constructing confidence intervals. The method enjoys some good features such as being range‐respecting and having internal studentizing and good coverage accuracy. This paper presents a two‐sample version of the one‐sample non‐parametric tilting method for dealing with two independent sample problems, whereby each of the two individual samples is ‘tilted’ separately by different amounts. The paper shows that careful choice of the two tilting parameters produces second‐order accurate confidence limits. Further, saddlepoint approximations can be used to avoid extensive Monte Carlo simulations, and it turns out that the approximations are exceptionally easy to apply with the tilting parameters. Numerical examples illustrate the two‐sample nonparametric tilting method.
FOURIER SERIES ESTIMATION FOR LENGTH BIASED DATA
Authors: Jones M.C. , Karunamuni R.J.
Published: February 2008

summary

This paper proposes and investigates Fourier series estimators for length biased data. Specifically, two Fourier series estimators are constructed and studied based on ideas of Jones (1991) and Bhattacharyya et al. (1988) in the case of kernel density estimation. Approximate expressions for mean squared errors and integrated mean squared errors are obtained and compared, and some simulated examples are investigated. The Fourier series estimator based on the proposal of Jones seems to have the more desirable properties of the two. The paper concludes with some comments that put this work in a wider context.
ON CHARACTERIZING DISTRIBUTIONS VIA LINEARITY OF REGRESSION FOR ORDER STATISTICS
Authors: Wesolowski Jacek , Ahsanullah Mohammad
Published: February 2008

summary

Let X1Xn be a random sample from an absolutely continuous distribution with the corresponding order statistics X1:n≤X2:n≤Xn:n. A complete solution of the problem, posed in 1967 by T. Ferguson, of determining the distribution by linearity of regression of Xk+2:n with respect to Xk:n is given. The only possible distributions are of the exponential, power and Pareto type. A linear regression relation for exponents of order statistics is also considered.