bluuebunny/crossref_metadata_2025 huggingface dataset:
MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS IN RENEWAL AND MARKOV‐RENEWAL PROCESSES
Authors: Basawa I. V.
Published: February 2008

Sampling procedures using randomized observation‐points are suggested for estimating parameters in renewal and Markov renewal models. The usual asymptotic properties of the maximum likelihood method are shown to hold. The method we suggest provides a solution to the ML estimation problem in either or both of the following situations: (i) observations on between‐event intervals are unavailable, (ii) the interval densities are unknown or difficult to evaluate while their Laplace‐Stieltjes transforms are known.
ON TESTS OF SYMMETRY FOR DISCRETE POPULATIONS
Authors: Shirahata Shingo
Published: February 2008

In this paper problems of tests of symmetry about the origin with discrete samples are considered. Recently Vorličková established the asymptotic normality of linear rank statistics and signed rank statistics in [5] and [6]. Here we propose statistics which are conditionally the sum of independent variables, including the locally most powerful tests for a one sided one parameter family. Their asymptotic distributions are derived under the null hypothesis and the contiguous rounding off location alternatives. We propose four types of signed rank tests and investigate their properties.
SELECTING THE m POPULATIONS WITH LARGEST MEANS FROM k NORMAL POPULATIONS WITH UNKNOWN VARIANCES
Authors: Chiu W. K.
Published: February 2008

This paper gives a two‐sample procedure for selecting the m populations with the largest means from k normal populations with unknown variances. The method is a generalization of a recent work by Ofosu [1973] and hence should find wider practical applications. The experimenter takes an initial sample of preset size N0 from each population and computes an unbiased estimate of its variance. From this estimate he determines the second sample size for the population according to a table presented for this purpose. The populations associated with the m largest overall sample means will be selected. The procedure is shown to satisfy a confidence requirement similar to that of Ofosu.
A NOTE ON THE DEMOGRAPHIC IMPACT OF CONTRACEPTION IN A MATHEMATICAL MODEL OF HUMAN REPRODUCTION
Authors: Rives Norfleet W.
Published: February 2008

The application of mathematical models of human reproduction to the study of reproductive behaviour as a function of contraceptive behaviour was pioneered by Perrin and Sheps (1963). More recent work in this area continues to focus on an examination of the birth rate as the principal dependent variable. This note suggests an alternative procedure for studying the demographic impact of contraception through the analysis of birth intervals. A mathematical model is formulated for the waiting time between successive live births, and a procedure is described for incorporating into the model certain contraceptive parameters. A controlled experiment is then performed to determine the effect of these parameters on expected child spacing patterns.
ON POINT MULTISERIAL CORRELATION1
Authors: Hamdan M. A. , Schulman R. S.
Published: February 2008

Abstract

We present a simple form for the estimator of the point multiserial correlation coefficient between a quantitative variate X and a qualitative variate 7. Given a bivariate sample grouped in the form of an r×c contingency table the estimator is based on finding the optimum Y‐scores which maximize the correlation coefficient. The resulting estimator is equivalent to Das Gupta's (1960) for ungrouped X‐values, with the advantage of simplicity in its calculation. Under the assumption of conditional normality, the significance of point multiserial correlation may be studied by an F‐test.
ON A PAPER BY DAVIES, PATE AND FROST CONCERNING MAXIMUM AUTOCORRELATIONS FOR MOVING AVERAGE PROCESSES1
Authors: Andeeson O. D.
Published: February 2008

The maximum possible autocorrelations, for moving average processes of order q, have recently been discussed. In this paper, we give the corresponding process parameter values when greatest (or least) autocorrelations are attained. The attainment of an individual autocorrelation bound often does not fully define the process, and for such cases we also investigate the possible conditional bounds for the remaining autocorrelations.
CERTAIN BOUNDS CONCERNING CHARACTERISTIC FUNCTIONS1
Authors: Daley D. J.
Published: February 2008

The largest value of the constant c for which

holds over the class of random variables X with non‐zero mean and finite second moment, is c=π.

Let the random variable (r.v.) X with distribution function F(·) have non‐zero mean and finite second moment. In studying a certain random walk problem (Daley, 1976) we sought a bound on the characteristic function

of the form

for some positive constant c. Of course the inequality is non‐trivial only provided that . This note establishes that the best possible constant c =π.

The wider relevance of the result is we believe that it underlines the use of trigonometric inequalities in bounding the (modulus of a) c.f. (see e.g. the truncation inequalities in §12.4 of Loève (1963)). In the present case the bound thus obtained is the best possible bound, and is better than the bound

(2) |1‐ϕ(θ)| ≥ |θEX|‐θ2EX2\2

obtained by applying the triangular inequality to the relation

which follows from a two‐fold integration by parts in the defining equation (*).

The treatment of the counter‐example furnished below may also be of interest.

To prove (1) with c=π, recall that sin u > u(1‐u/π) (all real u), so

Since |E sinθX|‐|E sin(‐θX)|, the modulus sign required in (1) can be inserted into (4).

Observe that since sin u > u for u < 0, it is possible to strengthen (4) to (denoting max(0,x) by x+)

To show that c=π is the best possible constant in (1), assume without loss of generality that EX > 0, and take θ > 0. Then (1) is equivalent to

(6) c < θEX2/{EX‐|1‐ϕ(θ)|/θ}

for all θ > 0 and all r.v.s. X with EX > 0 and EX2. Consider the r.v.

where 0 < x < 1 and 0 < γ < ∞.

Then EX=1, EX2=1+γx2,

From (4) it follows that |1‐ϕ(θ)| > 0 for 0 < |θ| <π|EX|/EX2 but in fact this positivity holds for 0 < |θ| < 2π|EX|/EX2 because by trigonometry and the Cauchy‐Schwartz inequality,

|1‐ϕ(θ)| > |Re(1‐ϕ(θ))| = |E(1‐cosθX)| = 2|E sin2θX/2|

(10) >2(E sinθX/2)2

(11) >(|θEX|‐θ2EX2/2π)2/2 > 0,

the inequality at (11) holding provided that |θEX|‐θ2EX2/2π > 0, i.e., that 0 < |θ| < 2π|EX|/EX2. The random variable X at (7) with x= 1 shows that the range of positivity of |1‐ϕ(θ)| cannot in general be extended.

If X is a non‐negative r.v. with finite positive mean, then the identity

shows that (1‐ϕ(θ))/iθEX is the c.f. of a non‐negative random variable, and hence

(13) |1‐ϕ(θ)| < |θEX| (all θ).

This argument fans if pr{X < 0}pr{X> 0} > 0, but as a sharper alternative to

(14) |1‐ϕ(θ)| < |θE|X||,

we note (cf. (2) and (3)) first that

(15) |1‐ϕ(θ)| < |θEX| +θ2EX2/2.

For a bound that is more precise for |θ| close to 0,

|1‐ϕ(θ)|2= (Re(1‐ϕ(θ)))2+ (Imϕ(θ))2 <(θ2EX2/2)2+(|θEX| +θ2EX2‐/π)2,

so

(16) |1‐ϕ(θ)| <(|θEX| +θ2EX2‐/π) + |θ|3(EX2)2/8|EX|.
QUADRAT SAMPLING AND THE ESTIMATION OF NEYMAN TYPE A AND THOMAS DISTRIBUTIONAL PARAMETERS1
Authors: Gleeson A. C. , Douglas J. B.
Published: February 2008

Computer simulation is employed to investigate the effects of quadrat size, sampling and estimation method, and cluster spread, density and size when estimating Neyman Type A and Thomas distributional parameters from quadrat samples. Results obtained indicate that quadrat size and cluster spread affect the estimates. Use of first order standard errors in selecting suitable quadrat sizes is discussed. Where clusters have non‐zero spread, the usual situation in practice, cluster density is generally overestimated and cluster size underestimated, which suggests the need for development of modified estimation procedures.
SOME EXPECTED VALUES FOR THE ERROR RATES OF THE SAMPLE QUADRATIC DISCRIMINANT FUNCTION1
Authors: McLachlan G. J.
Published: February 2008

The expected error rates of the sample quadratic discriminant function are studied in the context of two populations with different means and proportional covariance matrices. For the general case of all population parameters unknown the expected error rates are expressed in the form of asymptotic expansions which are evaluated numerically and tabulated for several combinations of the population parameters.
A SIMPLE PROCEDURE FOR SAMPLING πpswor1
Authors: Brewer Kenneth E. W.
Published: February 2008

The author's 1963 procedure for selecting two units per stratum πpswor is generalized to any feasible fixed number of sample units. Simple closed expressions are given for the working probabilities at each draw but the formula for the joint probabilities of inclusion of pairs of units is recursive and tedious to apply. The stability of the variance estimator is believed to be close to the optimum that can be obtained using the Horvitz‐Thompson estimator of total in situations where that estimator itself is optimal. Some suggestions are made for rotation of the sample.
BALANCED DESIGNS FOR ROW‐AND‐COLUMN EXPERIMENTS WITH TWO NON‐INTERACTING SETS OF TREATMENTS, ONE SET NOT BEING APPLIED TO ALL THE ROWS1
Authors: Preece D. A. , Hall W. B.
Published: February 2008

This note gives and discusses balanced row‐and‐column designs for experiments with two non‐interacting sets of treatments, one set not being applied to all the rows. These designs are potentially useful for occasions when trees that have tested one set of experimental treatments are needed for testing a second set before the residual effects of the first have become negligible, but when the experimenter wishes to apply the second set to only some of the rows. The designs are appropriate if the residual and new effects do not interact.
THE DESIGN OF SURVEYS FOR PLANNING PURPOSES1
Authors: Holt D. , Smith T. M. F.
Published: February 2008

The paper is in the form of a dialogue between Fred, a young mathematical statistician with a model building view of survey design and analysis and Harry, an experienced survey statistician who prefers the traditional sampling distribution basis. The two essentially different philosophical approaches are brought out in their conversation which is concerned with a proposed traffic noise survey. Harry has been commissioned to design a survey to evaluate the effect of various sources of traffic noise on people for future planning purposes, the underlying theme of the paper is the concept of the population for which inferences are required and the different approaches which the two statisticians take to achieving this.
THE RELATIONSHIP BETWEEN A CLASS OF ASYMPTOTICALLY NORMAL ESTIMATORS AND GOODNESS OF FIT TESTS1
Authors: Talus G. M. , Chesson P. L.
Published: February 2008

This paper considers a class of asymptotically normal estimators denned implicitly in terms of asymptotically normal statistics. The estimators are used as a basis for a general goodness of fit test where asymptotic null and non‐null distributions are obtained. Certain standard tests are obtained as special cases of these results.
AN IMPROVED APPROACH TO INVERTING THE AUTOCOVARIANCE MATRIX OF A GENERAL MIXED AUTOREGRESSIVE MOVING AVERAGE TIME PROCESS1
Authors: Anderson O. D.
Published: February 2008

Anderson (1976b) showed how the exact inverse of a mixed process could be obtained by a single adjustment to an approximate inverse. A similar approach is demonstrated here, but this time approximate inverses are found in a much neater manner, using an idea implicit in Tiao and Ali (1971).
TECHNIQUES OF COVARIANCE STRUCTURAL ANALYSIS1
Authors: Mukherjee Bishwa Nath
Published: February 2008

The paper delineates the scope and important features of covariance structural analysis in which some pattern can be postulated a priori for the covariance matrix. The coverage given also includes a brief review of the published work in this area with illustration of statistical tests based, on principles of maximum likelihood and union‐intersection. Few results on the computational ease under the assumption of particular covariance structures are reported. A few unsolved problems in the area of structural analysis are briefly mentioned.
ROUGH ANALYSIS AND SPURIOUS ACCURACY
Authors: Finch Peter D.
Published: February 2008

General aspects of rough and ready statistical procedures are illustrated by a crude analysis of survivorship in a medical trial. It is argued that more sophisticated procedures yield a possibly spurious accuracy since their trustworthiness is no greater than that of premises whose validity cannot be established from the data at hand.
A HEURISTIC TECHNIQUE FOR TESTING FOR THE PRESENCE OF INTERACTION IN NONREPLICATED FACTORIAL EXPERIMENTS
Authors: Millken George A. , Rasmuson Dale
Published: February 2008

Abstract  This paper suggests univariate and multivariate techniques for investigating interaction in nonreplicated factorial experiments. The tests can detect certain types of interaction, but they are not powerful against all possible alternative hypotheses. The two‐way factorial experiment is discussed in some detail and an example is used to demonstrate the procedure. The procedure is compared to other tests for interaction. These comparisons show that the procedure can detect some types of interaction which other tests cannot. Likewise other tests can detect interaction this procedure cannot.
NON‐EXISTENCE OF AN EXACT β‐CONFIDENCE INTERVAL FOR A SCALE PARAMETER*
Authors: Chen Hubert J.
Published: February 2008

Abstract There are given k (≥22) independent distributions with c.d.f.'sF(x;θj) indexed by a scale parameter θj, j = 1,…, k. Let θ[i](i = 1,…, k) denote the ith smallest one of θ1,…, θk. In this paper we wish to show that, under some regularity conditions, there does not exist an exact β‐level (0≤β1) confidence interval for the ith smallest scale parameter θibased on k independent samples. Since the log transformation method may not yield the desired results for the scale parameter problem, we will treat the scale parameter case directly without transformation. Application is considered for normal variances. Two conservative one‐sided confidence intervals for the ith smallest normal variance and the percentage points needed to actually apply the intervals are provided.
TWO SEQUENTIAL PROCEDURES FOR PARTITIONING A SET OF ONE‐PARAMETER EXPONENTIAL POPULATIONS WITH RESPECT TO A CONTROL
Authors: Perng S. K. , Groves John D.
Published: February 2008

Abstract  This article suggests two sequential procedures for partitioning a set of one parameter exponential populations with respect to a control. The procedures guarantee that the probability of correct decision exceeds a preassigned value P
SEQUENTIAL SEARCHING SCHEMES FOR AN OPTIMAL DOSAGE
Authors: Wei Lee‐Jen
Published: February 2008

For a certain chemotherapy an optimal dosage is defined as the highest possible dose which is still not “too toxic.” A linear regression is assumed between toxicity and dosage. Sequential searching processes for an optimal dosage are proposed utilizing Bayesian techniques. Simulations are performed to indicate the effectiveness of the new schemes.
BOUNDS FOR THE AVERAGE SAMPLE NUMBER FUNCTION FOR A BINOMIAL SEQUENTIAL TEST
Authors: Billard L.
Published: February 2008

Recently, Billard (1977) developed a partial sequential procedure for comparing a null hypothesis against a two‐sided alternative hypothesis when the parameter under test is that of the binomial distribution. In that paper, approximations to the operating characteristic and average sample number function were derived. In this note, bounds to the average sample number function are derived. Using numerical results a comparison of the approximations, bounds and empirical values is made.
466 AND ALL THAT
Authors: Wood J. T.
Published: February 2008

This paper describes a complex long‐term citrus experiment conducted at Griffith, New South Wales, over a period of 35 years. The design has a number of interesting features. Information on certain interactions is spread over several strata of the analysis of variance and the addition of new treatment factors, in 1955 and 1971 raised difficult problems.
UPPER BOUNDS FOR EFFICIENCY FACTORS IN BLOCK DESIGNS
Authors: Williams E. R. , Patterson H. D.
Published: February 2008

Upper bounds are derived for efficiency factors in block designs with particular types of variety or block concurrence matrices. These bounds compare favorably with existing upper bounds.
THE MINIMUM OF HIGHER ORDER GAPS
Authors: Cressie Noel
Published: February 2008

A large body of theory exists for statistics based on gaps or spacings. A natural generalization to gaps of higher order leads to statistics for testing uniformity which have higher power. In particular the null and alternative distributions of the minimum gap statistic are derived and the power of the test is seen to increase withm.
MODELS AND DESIGNS FOR EXPERIMENTS WITH MIXTURES
Authors: Becker Niels
Published: February 2008

Properties such as the tensile strength of an alloy of. different metals and the freezing point of a mixture of liquid chemicals, depend on the proportions (by weight or volume) of the components present and not on the total amount of the mixture. In choosing a model to relate such a property to the proportions of the various components of the mixture, there arise intriguing difficulties due to the fact that proportions sum to unity. It is demonstrated how to construct models which allow for the possibility of inactive components (components that do not affect the property at all) or components with additive effects. The design of experiments to fit such models to data is then discussed with a view to determining whether a given component is inactive or has an additive effect. The optimal allocation of observations to simplex‐lattice designs is considered for one of these models. The construction ofD‐optimal designs for these models is an open problem.
CLASSIFICATION, DISTRIBUTIONS AND ADMISSIBILITY IN AUTOREGRESSIVE PROCESS
Authors: Bandyopadhyay Shibdas
Published: February 2008

The problem considered here is to classify a unit into one of two populations based on a vector of measurements on the unit. The observation vector is assumed to follow an auto‐regressive process. Samples from the process are used to construct classification rules. The distributions of some classification statistics are obtained. The admissibility of some classification rules is established.
A NEW APPROXIMATION FOR FISHER'S Z
Authors: Chaubey Yogendra P. , Mudholkar Govind S.
Published: February 2008

As the sample size increases, the coefficient of skewness of the Fisher's transformationz= tanh‐1r, of the correlation coefficient decreases much more rapidly than the excess of its kurtosis. Hence, the distribution of standardized z can be approximated more accurately in terms of thetdistribution with matching kurtosis than by the unit normal distribution. Thistdistribution can, in turn be subjected to Wallace's approximation resulting in a new normal approximation for the Fisher's z transform. This approximation, which can be used to estimate the probabilities, as well as the percentiles, compares favorably in both accuracy and simplicity, with the two best earlier approximations, namely, those due to Ruben (1966) and Kraemer (1974).

Fisher (1921) suggested approximating distribution of the variance stabilizing transform z=(1/2) log ((1 +r)/(1r)) of the correlation coefficient r by the normal distribution with mean = (1/2) log ((1 + p)/(lp)) and variance =l/(n3). This approximation is generally recognized as being remarkably accurate when||Gr|is moderate but not so accurate when||Gr|is large, even whennis not small (David (1938)). Among various alternatives to Fisher's approximation, the normalizing transformation due to Ruben (1966) and atapproximation due to Kraemer (1973), are interesting on the grounds of novelty, accuracy and/or aesthetics. If r̄= r/√ (1r2) and r̄|Gr = |Gr/√(1|Gr2), then Ruben (1966) showed that (1) gn(r,|Gr) ={(2n5)/2}1/2r̄r{(2n3)/2}1/2r̄|GR, {1 + (1/2)(r̄r2+r̄|Gr2)}1/2is approximately unit normal. Kraemer (1973) suggests approximating (2) tn(r, |Gr) = (r|GR1) √ (n2), √(11r2) √(1|Gr2) by a Student'stvariable with(n2)degrees of freedom, where after considering various valid choices for |Gr1she recommends taking |Gr1= |Gr*, the median of r given n and |Gr.
A TEST OF THE LOCATION PARAMETER OF THE EXPONENTIAL DISTRIBUTION
Authors: Wong P. G.
Published: February 2008

In this paper, we propose a procedure for testing the location parameter of the exponential distribution for certain alternative hypotheses, which could result in the early rejection of the null hypothesis. This is a consequence of the monotone property of the test statistic which is based on the extremal quotient. The test being scale‐free does not require the scale parameter to be known.
ON THEIL'S METHOD IN DISTRIBUTION‐FREE REGRESSION
Authors: Maritz J. S.
Published: February 2008

Theil's (1950) method for inference about the slope of a straight line can be regarded as based on the median of all estimates of the slope derived from pairs of observations. The possibility of employing similar procedures for distribution‐free inference about the intercept is investigated, and it is shown that, in certain circumstances, efficiencies close to 1 can be achieved with an exactly distribution‐free procedure.
A NON‐SEQUENTIAL INVENTORY MODEL WITH VARIABLE SUPPLY
Authors: Panda Radha Madhab
Published: February 2008

In this paper an attempt has been made to determine an optimum order quantity for a two‐period inventory model where demands for each period are completely known, but the supply in each period is a stochastic one with mean equal to the corresponding order size.
ON THE SEQUENTIAL ESTIMATION OF THE PROBABILITY OF SUCCESS
Authors: Alvo Mayer , Cabilio Paul
Published: February 2008

Let x1x2, x3,be a sequence of independent Bernoulli trials with common success probabilityp. We consider the problem of estimation ofpusing a sequential Bayes theoretic approach when the cost per observation isc, and the loss of estimation is squared error loss. A heuristic procedure is suggested, a bound on its Bayes risk is computed, and asymptotic results are exhibited.
THE BIAS IN PERIODOGRAM ORDINATES AND THE ESTIMATION OF ARMA MODELS IN THE FREQUENCY DOMAIN
Authors: Pukkila T.
Published: February 2008

The paper has its origin in the finding that the frequency‐domain estimation of ARh4A models can produce estimates which may be remarkably biased. Both of the frequency‐domain estimation methods considered in the paper are based on the frequency‐domain likelihood function, which depends on the periodogram ordinates of the time series. It is found that, as estimates of the spectrum ordinates, the corresponding periodogram ordinates may contain a rather remarkable bias, which again causes bias in the estimates of parameters produced by a frequency‐domain estimation method of an ARMA model. The bias is reduced by tapering the observed time series. An example is given of estimation experiments for simulated time series from a pure autoregressive process of order two.
TWO STAGE SELECTION PROBLEM FOR NORMAL POPULATIONS WITH UNEQUAL VARIANCES
Authors: Bfinger Eve
Published: February 2008

The paper discusses the Dudewicz‐Dalal modification of a Stein‐type two sample procedure for the goal of selecting the population with the largest mean from k normal populations with unknown variances. Largest k values are obtained such that a procedure based on sample means is preferred to the Dudewicz‐Dalal procedure. The more general goal of choosing those populations with the t largest means is also considered.
ON ESTIMATING THE MEAN OF A FINITE POPULATION SAMPLED ON TWO OCCASIONS WITH VARYING PROBABILITIES
Authors: Chaudhltri A. , Arnab R.
Published: February 2008

The problem considered is one of estimating the current value of a finite population mean from two samples selected with varying probabilities on the current and a previous occasion. Following the generalized least squares approach of Gurney and Daly (1965) we extend the works of Sin& (1968) and others to obtain two sampling strategies which are respectively more efficient than the ones suggested earlier by Raj (1965) and Chotai (1974).
SUPPLEMENTARY BIBLIOGRAPHY OF DESIGNS FOR EXPERIMENTS IN THREE DIMENSIONS
Authors: Preece D. A.
Published: February 2008

This bibliography supplements the list given by Preece (1975) of combinatorial and statistical publications on (a) designs for comparative experiments in three space dimensions, and (b) other related designs. The reader is referred to the original bibliography for details of the scope of the listing.

This supplementary bibliography includes a few publications overlooked previously, as well as recent additions to the literature.

Once again, many Soviet items are included. As previously, the system adopted for transliteration from Russian is that used by Mathematical Reviews.
ORTHOGONAL EXPANSIONS AND U‐STATISTICS
Authors: Eagleson G. K.
Published: February 2008

Lancaster's work on the orthogonal expansions of multivariate distributions is used to show how recent work on the asymptotic distribution of degenerate, two‐dimensional U‐statistics can be extended to higher dimensional U‐statistics, to the so‐called two‐sample case and to U‐statistics based on a sample of dependent random variables.
FIXED VERSUS RANDOM SAMPLING OF CERTAIN CONTINUOUS PARAMETER PROCESSES
Authors: McDunnough Philip , Wolfson David B.
Published: February 2008

Let {Z(t)} be a stochastic point process. When {Z(t)} is Poisson and it is desired to estimate the intensity A, it is shown that the optimal (in terms of Fisher information) discrete sampling scheme is to sample {Z(t)} at predetermined fixed time points. On the other hand, when {Z(t)} is a pure birth process and a maximum likelihood estimator of the birth rate is desired, it is sometimes better to sample at random time points, according to a renewal process. An application of these ideas is given in the estimation of bacterial density in a liquid, by the method of dilutions.
DETECTING NATURAL SELECTION: THE STEPWISE MUTATION MODEL WITH HETEROSIS
Authors: Watterson G. A. , Anderson R.
Published: February 2008

The problem of testing whether heterozygotes have a selective advantage is considered, assuming the stepwise mutation model for electrophoretic alleles. The population is observed for a number of generations, and the likelihoods of the changes in allele frequencies under the heterozygote advantage model and under the strict neutrality model are compared. It is shown by simulation that statistical tests based on the likelihoods have little power to detect selection if only a few generations of data are available.

Many population genetic models, including the stepwise mutation model, have been formulated as diffusion processes in continuous time. The paper gives expressions for the likelihoods of multivariate diffusions observed over a time interval.
RELAXING ASSUMPTIONS IN THE ONE SAMPLE t‐TEST
Authors: Cressie Noel
Published: February 2008

This paper reviews what is currently known about the behaviour of the t‐statistic when one is no longer sampling from a normal distribution. Suppose Y is a batch of data on which the t‐test is performed. Briefly then, heavy‐tailed components of Y give a light‐tailed t, positive correlation among Y gives a heavy‐tailed t, and positively skewed components of Y give a negatively skewed t. The emphasis is on understanding why one gets this type of behaviour, although some numerical tables are presented to illustrate the conclusions.
THE EXACT DISTRIBUTION OF THE BELL‐DOKSUM TEST OF INDEPENDENCE
Authors: Spurr Barrie D.
Published: February 2008

An expression for the exact distribution of the Bell‐Doksum test of independence based upon the use of order statistics from normally distributed random samples is derived and a table of critical values is provided. Two extensions of the theory are considered and possible applications to Poisson processes and queueing theory are noted.
TWO‐STAGE PROCEDURES FOR TESTING HOMOGENEITY OF MEANS AGAINST ORDERED ALTERNATIVES IN ONE‐WAY ANOVA WITH COMMON UNKNOWN VARIANCE
Authors: Marcus Ruth
Published: February 2008

In this paper we present two‐stage procedures for testing the equality of normal means against ordered alternatives in one‐way ANOVA with common and unknown variance. The procedures proposed are analogous to Williams's and Bartholomew's single‐stage methods. A table of percentiles needed for implementation is provided. Some Monte Carlo results for estimating the power of both procedures are given.
GOODNESS OF FIT STATISTICS BASED ON THE SPACINGS OF COMPLETE OR CENSORED SAMPLES
Authors: Tiku M. L.
Published: February 2008

A goodness‐of‐fit statistic Z is defined in terms of the spacings generated by the order statistics of a complete or a censored sample from a distribution of the type (l/s̀)f((x‐μ)/s̀), μ and s̀ unknown. The distribution of Z is studied, mostly through Monte Carlo methods. The power properties of Z for testing Exponential, Uniform, Normal, Gamma and Logistic distributions are discussed; Z is shown to be more powerful than the Smith & Bain (1976) correlation statistic, except for testing Uniform, Normal and Logistic (symmetric distributions) against symmetric alternatives. The statistic Z is generalized to test the goodness‐of‐fit from κ 2 independent complete or censored samples.
TESTING THE LARGEST OF A SET OF CORRELATION COEFFICIENTS
Authors: Moran P. A. P.
Published: February 2008

A previous paper which studied the distribution of the smallest distance between N independent random points on the surface of a sphere is generalised to higher dimensions in order to study the distribution of the largest sample correlation coefficient between a set of independent normally distributed variables. Inclusion‐exclusion arguments provide accurate bounds for the tail of this distribution, and by another argument more exact bounds are also found, one of which is an improvement on the result in the previous paper. Bounds are also found for the power of the test against the alternative hypothesis that one only of the population correlation coefficients is non‐zero. The test is also shown to be the likelihood ratio test against the latter alternative.
AN APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATOR FOR CHAIN BINOMIAL MODELS
Authors: Saunders I. W.
Published: February 2008

Using the Poisson approximation to the Binomial distribution, we construct an approximate maximum likelihood estimator (MLE) for a class of chain binomial models. Our estimator proves to have properties which may make it preferable to the exact WLE.
An Application of Discrimination When Covariance Matrices are Proportional
Authors: Dargahi‐Noubary G. R.
Published: February 2008

In the context of time series, a situation is considered which leads to the discrimination between two normal populations having unequal means and proportional covariance matrices. It is then shown that this has an application to the important problem of earthquake‐explosion differentiation. The latter is done by introducing a non‐stationary model for seismic records of P‐waves from these two kinds of events.
A Note on the Canonical Correlations From Contingency Tables
Authors: O'Neill M. E.
Published: February 2008

Explicit formulae are obtained for the asymptotic variances and covariances of canonical correlations which correspond to non‐zero theoretical correlations in (p+ 1) x (q+1) contingency tables, withp≤q. The moments of the roots of a central Wishart matrix distributed as Wp(q;I) are also given in general, with means, variances and covariances tabulated forp= 2, 3, 4: these may apply to canonical correlations corresponding to zeros.
Asymptotic Properties of an Estimate of the Prediction Error Variance
Authors: Hong‐Zhi An
Published: February 2008

An estimate of the variance of the prediction error for a linear stationary time series is constructed by using only a part, ŷ0, ŷ1,…, ŷM, of the sample autocovariance sequence, whereMincreases withT, the length of the time series observed.Mincreases asTα(α <14). Under a higher moment condition, but not assuming Gaussianity, the estimate obtained is shown to be strongly consistent and asymptotically normal. The asymptotic variance of the estimation error is also obtained.
A Theorem on Products of Random Variables, With Application to Regression
Authors: Maller R. A.
Published: February 2008

It is shown that the product of two independent random variables in the domain of attraction of the normal distribution is also in the domain of attraction of the normal distribution, while if the product is in the domain of attraction of the normal distribution and one of the variables has finite variance, the other is in the domain of attraction of the normal distribution. This result is applied to prove the asymptotic normality of the regression coefficient in a linear regression when the error variance is not necessarily finite.
Sequential Estimation of Expectations in the Presence of Trend2
Authors: Theodorescu Radu , Wolff Hans
Published: February 2008

A sequence of independent random variables {Zn:n≥ 1} with unknown probability distributions is considered and the problem of estimating their expectations {Mn+1: n≥ 1} is examined. The estimation of Mn+1 is based on a finite set {zk:1≤k≤n}, each zk being an observed value of Zk, 1 ≤k≤n, and also based on the assumption that {Mn:n≥ 1} follows an unknown trend of a specified form.
Simultaneous Confidence Intervals for Monotone Contrasts of Normal Means
Authors: Marcus Ruth
Published: February 2008

The one‐way ANOVA model is considered. The variances are assumed to be either equal but unknown or unequal and unknown. Two‐stage procedures for generating simultaneous confidence intervals (SCI) for the class of monotone contrasts of the means are presented. The intervals are of fixed length and independent of the unknown variances.
A Characterization of a Matric‐Variate Exponential Distribution
Authors: Richards Donald St. P.
Published: February 2008

Suppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω1+Ω2 | S>Ω2) = Pr(S>Ω1) implies that S has a Wishart distribution on m+ 1 degrees of freedom.
A Note on the Effect of Autocorrelation on Multiple Regression Statistics
Authors: Praetz Peter
Published: February 2008

This note discusses the effect of autocorrelated distrubances when they are not modelled on the statistics used in drawing inferences in the multiple linear regression model. It derives biases for the F and R2 statistics and evaluates them numerically for an example. The note concludes with a few brief reflections for empirical research on the causes, detection and treatment of autocorrelation.
On Level Crossing Analysis of Queues
Authors: Shanthikumar J. G.
Published: February 2008

In this note we introduce a new level crossing analysis and using it derive an integral equation for the steady state waiting time in the GI/G/1 Queue. For the GI/M/1 queue we derive the rates of up‐ and down‐crossings of the virtual delay process and two integral equations, one for the steady state time spent in the system and the other for the steady state waiting time in the queue. Also, the steady state probability distributions of the time spent in the system and the waiting time in the queue are obtained by solving these integral equations.
Sampling on Two Occasions With Varying Probabilities
Authors: Arnab R.
Published: February 2008

In estimating the current value of a finite population total from two consecutive surveys with samples chosen with varying probabilities, we demonstrate through examples the intuitively expected superiority of strategies when current unmatched samples are chosen from the complements of the current matched sub‐samples, over the usual ones where these are chosen from the entire population.
Variations in Household Telephone Access: Implications for Telephone Surveys
Authors: Jones Roger
Published: February 2008

The growing proportion of households that have telephones and the increasing cost of face‐to‐face interviewing have led to greater interest in the use of telephone surveys in Australia over recent years. However about 20 per cent of private households do not have a telephone service, which could give rise to significant biases in population estimates derived from telephone surveys if no adjustment is made to take account of the differences between those with and without telephone access. This paper examines these differences and suggests ways in which their possible effects might be overcome.
Nonparametric Tests for Intercept in Linear Regression Problems
Authors: Rao K. S. Madhava , Gore A. P.
Published: February 2008

In this paper we demonstrate how various hypotheses of interest about the intercept parameter in one‐sample, two‐sample and several‐sample linear regressions could be tested by simple adaptations of familiar nonparametric procedures, when an experimenter has the liberty to choose the values of the independent variable. Asymptotic Relative Efficiencies of the proposed procedures are discussed.
Jackknifing in Categorical Data Analysis
Authors: Parr William C. , Tolley H. Dennis
Published: February 2008

Estimation of nonlinear functions of a multinomial parameter vector is necessary in many categorical data problems. The first and second order jackknife are explored for the purpose of reduction of bias. The second order jackknife of a function g(.) of a multinomial parameter is shown to be asymptotically normal if all second order partials ∂2g(p)∂dpi∂pj obey a Hölder condition with exponent α>1/2. Numerical results for the estimation of the log odds ratio in a 2times2 table demonstrate the efficiency of the jackknife method for reduction of mean‐square‐error and the construction of approximate confidence intervals.
Contiguity of Probability Measures
Authors: Scott David J.
Published: February 2008

The notion of contiguity of probability measures is a very useful one, providing a generally applicable method of calculating the asymptotic power of a sequence of tests and thus a means of comparing competing tests. This paper attempts to give an account of the basic results of contiguity theory which is self‐contained and accessible to statisticians to whom the theory is of use. In addition, the relationship between contiguity and mutual contiguity is explored.
Some Remarks on The Paper by Theodorescu and Wolff: “Sequential Estimation of Expectations in the Presence of Trend”
Authors: Pakes Anthony G.
Published: February 2008

Recently Theodoresu and Wolff have proposed a sequence of random variables for estimating a sequence of constants satisfying a certain recurrence equation. Their problem, which is similar to some arising in stochastic approximation theory, was solved by using techniques from this theory. The present paper shows that the theory of sums of independent random variables is a more natural tool for tackling this problem.
Remark on Construction of Efficiency‐Balanced Designs
Authors: Kageyama Sanpei
Published: February 2008

In this note, all the efficiency‐balanced block designs constructed by utilizing two methods of Dey & Singh (1980) are completely presented within a practical range of parameters.
On the Extinction Time of a Continuous time Markov Branching Process
Authors: Narayan Prakash
Published: February 2008

Several authors have studied and derived bounds for the mean extinction time of a discrete branching process. In this note, we obtain the mean and variance of the extinction time, given extinction of a continuous time Markov branching process. We also obtain bounds for the mean extinction time in terms of moments of the offspring distribution.
Stochastic Multigrade Population Models in Continuous Time
Authors: Agrafiotis G. K.
Published: February 2008

A continuous time stochastic model for the analysis of wastage in a hierarchically structured multigrade population system, with non‐homogeneous Poisson input, is developed in this paper. Special cases of the model are discussed and the distribution of the grade sizes at any time is obtained through the use of straightforward probabilistic arguments.
Some Methods of Construction of Gd‐Rc and Rectangular‐rc Designs
Authors: Agrawal H. L. , Prasad Jagdish
Published: February 2008

A number of methods of construction of GD‐RC and RectanguIar‐RC designs, based upon the series A of BIB‐RC designs, using the method of Kronecker product, are developed.
Series Expansion for a Hypergeometric Function of Matrix Argument with Applications
Authors: Gupta Rameshwar D. , Richards Donald St P.
Published: February 2008

A series expansion is obtained for the confluent hypergeometric function of the second kind when the argument is a 2 times 2 positive definite matrix. Applications are made to the distributions of Hotelling's generalized T02 statistic, and the smallest latent root of the covariance matrix.
The Joint Treatment of Exact and Stochastic Restrictions
Authors: Shonkwiler J. S.
Published: February 2008

In regression analysis both exact and stochastic extraneous information may be represented via restrictions on the parameters of a linear model which then may be estimated by applying constrained generalized least squares. It is shown that this estimator can be recast as a computationally simpler estimator that is a combination of the ordinary least squares estimator and the discrepancy between the OLS estimator and both types of restrictions. The variance of the restricted parameters is explicitly shown to depend on the variance of the extraneous information.
Robustness Against Inequality of Variances
Authors: Brown B. M.
Published: February 2008

Various asymptotic‐based criteria are used to assess the robustness against inhomogeneity of variance of various standard and/or distribution‐free tests in the two sample problem. The extent of robustness is influenced greatly by the equality or not of the two sample sizes, conforming to an earlier principle of G. E. P. Box. With equal sample sizes, t‐tests and related trimmed‐mean‐like tests are robust, but otherwise, the sign test emerges clearly as the most robust test to variance inequality.
Estimable Versions of Griffiths' Measure of Association
Authors: Bolyai Sándor Csörgö , Hall Peter
Published: February 2008

Many techniques have been proposed for measuring the degree of association between a pair of random variables X and Y. However, the measures often suffer from two drawbacks: they are difficult to calculate when the joint distribution of (X, Y) is known, and difficult to estimate when the joint distribution is unknown. In the present paper we present two modifications of a measure proposed by Griffiths (1972), and show that they exhibit neither of these deficiencies.
Distribution‐Free Methods in Regression1
Authors: Brown B. M. , Maritz J. S.
Published: February 2008

A modification to the least‐squares estimating equations in simple linear regression, leading to exact distribution‐free inference about slope, is outlined. The modification involves a general residual‐transformation iψ and the cases of ψ— sign, rank, and the identity are discussed in some detail.

It is also shown how exact inference about individual parameters in regressions with more than one design variable can be carried out by a restricted permutation argument coupled with a suitable design.
Difficulties of Interpretation With Markov Chain Models
Authors: Finch Peter D.
Published: February 2008

Questions such as “how useful is a Markov chain model!” and “what does it tell us about a real process?” are discussed. The relevance of context is stressed and it is argued that good data fits are not enough by themselves. It is suggested that a descriptive data analytic interpretation of the modelling process might sometimes be more appropriate than the usual probabilistic interpretation.
RECENT TRENDS IN ASYMPTOTIC OPTIMAL INFERENCE FOR DEPENDENT OBSERVATIONS1
Authors: Basawa I. V.
Published: February 2008

An overview of some recent developments in the area of asymptotic inference for non‐ergodic type stochastic processes is presented. Both local and global formulations of the asymptotic model are given, and non‐local optimality results are reviewed. Recent results on conditional inference are briefly discussed. Some open problems and possibilities for new developments are also mentioned.
CATASTROPHE PROCESSES WITH CONTINUOUS STATE‐SPACE1
Authors: Brockwell P. J. , Gani J. M. , Resnick S. I.
Published: February 2008

Some continuous state‐space models for the size of a population subject to catastrophes are examined. Inputs to the population constitute a compound Poisson process, and catastrophes, which are of random magnitudes, occur at a rate which is dependent on the population size. Necessary and sufficient conditions for the existence of stationary distributions are investigated and in special cases the stationary distributions are found explicitly. The time‐dependent behaviour of a process with linear catastrophe rate and truncated exponential catastrophe sizes is also studied.
ESTIMATION OF PARAMETERS IN THE MARGINAL FISHER DISTRIBUTION1
Authors: Clark R. M.
Published: February 2008

The Fisher distribution is frequently used as a model for the probability distribution of directional data, which may be specified either in terms of unit vectors or angular co‐ordinates (co‐latitude and azimuth). If, in practical situations, only the co‐latitudes can be observed, the available data must be regarded as a sample from the corresponding marginal distribution. This paper discusses the estimation by Maximum Likelihood (ML) and the Method of Moments of the two parameters of this marginal Fisher distribution. The moment estimators are generally simpler to compute than the ML estimators, and have high asymptotic efficiency.
AN ESTIMATION PARADOX ARISING IN POPULATION GENETICS THEORY1
Authors: Ewens W. J.
Published: February 2008

We consider a stochastic process describing the evolution of a certain population. A sample is taken from this population in some given generation and is to be used for estimation purposes. It is shown that if one wishes to estimate, from the sample, the actual value of a certain population quantity F in the current generation, estimation using a statistic f is preferred to estimation using a different statistic k, whereas, if one wishes to estimate the mean value of F relative to the stochastic process describing the population evolution, estimation using k is preferred to estimation using f.
A GALTON‐WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTS WITH ESSENTIALLY CONSTANT OFFSPRING MEANS AND TWO RATES OF GROWTH1
Authors: MaCphee I. M. , Schuh H.‐J.
Published: February 2008

A Galton‐Watson process in varying environments (Zn), with essentially constant offspring means, i.e. E(Zn)/mn→α∈(0, ∞), and exactly two rates of growth is constructed. The underlying sample space Ω can be decomposed into parts A and B such that (Zn)n grows like 2non A and like mnon B (m > 4).
THE WEIGHTED MEDIAN AND MULTIPLE REGRESSION1
Authors: Seneta E.
Published: February 2008

This paper reviews the iterative use of the weighted median to estimate the parameter vector in the classical linear model when the fitting criterion is (i) least absolute deviation sum (LAD); and (ii) the Cauchy criterion. The implications of the Cauchy criterion, little developed hitherto, are compared and contrasted with results for the better‐known LAD procedure. Since the weighted median is essentially an estimation technique for the simplest regression model, its use in these contexts illustrates the central role in statistical theory that is played by regression analysis, a focal area of the work of E. J. Williams (1959).
DISTRIBUTIONS IN R WITH ROTATIONAL SYMMETRIES1
Authors: Watson G. S.
Published: February 2008

Let X ∈ R be a random vector with a distribution which is invariant under rotations within the subspaces Vj (dim Vj. = qj) whose direct sum is R. The large sample distributions of the eigenvalues and vectors of Mn= n‐1Σnl xixi are studied. In particular it is shown that several eigenvalue results of Anderson & Stephens (1972) for uniformly distributed unit vectors hold more generally.