bluuebunny/crossref_metadata_2025_split huggingface dataset:
MINIMUM MSE ESTIMATION BY LINEAR COMBINATIONS OF ORDER STATISTICS1
Authors: Samanta M. 
Published: February 2008

SummaryIn this paper we assume that in a random sample of size ndrawn from a population having the pdf f(x; θ) the smallest r1 observations and the largest r2 observations are censored (r1≥0, r2≥0). We consider the problem of estimating θ on the basis of the middle n‐r1‐r2 observations when either f(x;θ)=θ‐1f(x/θ) or f(x;θ) = (aθ)1f(x‐θ)/aθ) where f(·) is a known pdf, a (<0) is known and θ (>0) is unknown. The minimum mean square error (MSE) linear estimator of θ proposed in this paper is a “shrinkage” of the minimum variance linear unbiased estimator of θ. We obtain explicit expressions of these estimators and their mean square errors when (i) f(·) is the uniform pdf defined on an interval of length one and (ii) f(·) is the standard exponential pdf, i.e., f(x) = exp(–x), x≥0. Various special cases of censoring from the left (right) and no censoring are considered.
A TEST OF HOMOGENEITY AGAINST SCALE ALTERNATIVES USING SUBSAMPLE EXTREMA1
Authors: Gore A. P. , Shanubhogue Ashok 
Published: February 2008

SummaryIn this paper a new class of non‐parametric tests for testing homogeneity of several populations against scale alternatives is proposed. For this, independent samples of fixed sizes are drawn from each population and from these samples, all possible sub‐samples of the same size are drawn and their maxima and minima are computed. Using these extreme the class of tests is obtained. Tests of this type have been offered for the two‐sample slippage problem by Kochar (1978). Under certain conditions, this class of tests is shown to be consistent against ‘difference in scale’ alternatives. The test has been compared with Bhapkar's V‐test (1961), Deshpande's D‐test (1965), Sugiura's Drs‐test (1965) and with a classical test given by Lehmann (1959, pp. 273–275). It is shown that some members of this proposed class of tests are more efficient than the first three tests in the case of uniform, Laplace and normal distributions, when the number of populations compared is small.
ON THE PERFORMANCE OF KOLMOGOROV‐SMIRNOV TESTS ON STABLE RANDOM VARIABLES1
Authors: Hua Tsushung A. 
Published: February 2008

SummaryThis paper provides two procedures to perform the Kolmogorov–Smirnov (K‐S) tests on stable random variables. One utilizes the integral representation of the cumulative distribution function of this random variable to perform the K‐S test; the other utilizes the Gil‐Pelaez‐Roseń transformation of data (Csörg(1983)) to test uniformity on (0,1) for the transformed sample. Both procedures are examined and evaluated by a simulation study.
ON RESOLVABLE INCOMPLETE BLOCK DESIGNS1
Authors: Sharma V. K. , Das M. N. 
Published: February 2008

summaryA 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

SummaryThis 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

SummaryThe 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

SummaryLet 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

SummaryThe 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

SummaryThe 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.
EXPRESSIONS FOR INVERSE MOMENTS OF POSITIVE QUADRATIC FORMS IN NORMAL VARIABLES
Authors: Jones M. C. 
Published: February 2008

SummaryA 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

summaryA 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

SummaryOften, 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.
A Note on the Predictors of Differenced Sequences
Authors: Peiris M. Shelton 
Published: February 2008

SummaryIn 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

SummaryA 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

SummaryThe 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

SummaryLet 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

SummaryAn 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

SummaryAn 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

summaryA 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

SummaryIn 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

SummaryA 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

SummaryAn 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

summaryExact 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

summaryA 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

summaryThe 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

summaryThe 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

summaryWhite 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

summaryA 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

summaryMultivariate 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

summaryThe 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

summaryThis 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

summaryThe 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

summaryMy 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

SummaryModifications 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

SummaryAdjusted 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.