bluuebunny/crossref_metadata_2025_split huggingface dataset:
ESTIMATION OF LLUCH'S EXTENDED LINEAR EXPENDITURE SYSTEM FROM CROSS‐SECTIONAL DATA1
Authors: Powell Alan 
Published: February 2008

AbstractComplete sets of demand relations may be fitted using varying types of sample information and varying a priori specifications. In this paper the identification and estimation of Lluch's extended linear expenditure system (ELES) from cross‐sectional data alone is investigated. Under the most favourable conditions of data availability, all of the parameters of the ELES model are identified, and are estimable by the method of reduced form least squares. This is the case where observations on permanent income are available for the consuming units of the cross section and where, in addition, prices are recorded (even though they do not vary from one consuming unit to the next). Under the least favourable conditions only the marginal budget shares are identified. This corresponds to the case where no data on permanent income, or on savings, are available. The conventional ordinary least squares estimators of the marginal budget shares are, under these conditions, biased and inconsistent. Expressions are developed for the large‐sample biases.
WAITING TIME IN THE COUPON‐COLLECTOR'S PROBLEM1
Authors: Nath Harmindar B. 
Published: February 2008

SummaryThe coupon collector's problem is generalized by allowing unequal proportions of the various types of coupons. The upper tail probabilities are used to find the probability distribution of the waiting time. The probability generating function is expressed in terms of the hypergeometric functions and therefrom the mean and the variance are derived.
ON TESTING THE EQUALITY OF LOCATION PARAMETERS IN k CENSORED EXPONENTIAL DISTRIBUTIONS
Authors: Khatri C. G. 
Published: February 2008

SummaryKumar and Patel (1971) have considered the problem of testing the equality of location parameters of two exponential distributions on the basis of samples censored from above, when the scale parameters are the same and unknown. The test proposed by them is shown to be biased for n1≠n2, while for n1=n2 the test possesses the property of monotonicity and is equivalent to the likelihood ratio test, which is considered by Epstein and Tsao (1953) and Dubey (1963a, 1963b). Epstein and Tsao state that the test is unbiased. We may note that when the scale parameters of k exponential distributions are unknown the problem of testing the equality of location parameters is reducible to that of testing the equality of parameters in k rectangular populations for which a test and its power function were given by Khatri (1960, 1965); Jaiswal (1969) considered similar problems in his thesis. Here we extend the problem of testing the equality of k exponential distributions on the basis of samples censored from above when the scale parameters are equal and unknown, and we establish the likelihood ratio test (LET) and the union‐intersection test (UIT) procedures. Using the results previously derived by Jaiswal (1969), we obtain the power function for the LET and for k= 2 show that the test possesses the property of monotonicity. The power function of the UIT is also given.
MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS IN RENEWAL AND MARKOV‐RENEWAL PROCESSES
Authors: Basawa I. V. 
Published: February 2008

SummarySampling 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

SummaryIn 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

SummaryThis 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

SummaryThe 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

AbstractWe 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

SummaryThe 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

SummaryThe 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\2obtained 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

SummaryComputer 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

SummaryThe 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

SummaryThe 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

SummaryThis 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

SummaryThe 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

SummaryThis 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

SummaryAnderson (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).
BOUNDS FOR THE AVERAGE SAMPLE NUMBER FUNCTION FOR A BINOMIAL SEQUENTIAL TEST
Authors: Billard L. 
Published: February 2008

SummaryRecently, 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

SummaryThis 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.
MODELS AND DESIGNS FOR EXPERIMENTS WITH MIXTURES
Authors: Becker Niels 
Published: February 2008

SummaryProperties 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

SummaryThe 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

SummaryAs 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

AbstractIn 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

SummaryTheil'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.
ON THE SEQUENTIAL ESTIMATION OF THE PROBABILITY OF SUCCESS
Authors: Alvo Mayer , Cabilio Paul 
Published: February 2008

AbstractLet 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

SummaryThe 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

SummaryThe 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

SummaryThe 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

SummaryLancaster'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.