bluuebunny/crossref_metadata_2025 huggingface dataset:
Efficiency in the Use of Hotellings T2
Authors: Jensen D. R. , Ramirez D. E.
Published: May 2007

Alternative scale models are compared with regard to the Pitman efficiency of Hotelling's T2 in tests for means. A basic decomposition identifies subspaces of the parameters in which one model is more efficient than another, or the two models have equal efficiency. Local and global bounds for relative Pitman efficiencies are given with reference to these subspaces. Applications include efficiency comparisons of marginal and conditional tests in a given model, and a comparison of the sensitivities of selected T2 tests regarding psychological profiles in treated and control groups of children.
Spectral Estimation by Variable Span Log Periodogram Smoothing: An Application to Annual Lynx Numbers
Authors: Solow Andrew R.
Published: May 2007

Spectral estimation is commonly based on smoothing the periodogram or its logarithm. In such a smoothing exercise, it is not entirely sensible to use the same bandwidth for all frequencies, since the smoothness of the underlying spectrum may vary. This note describes the use of a variable span smoother in estimating the log spectrum. An application to annual lynx data is presented.
An Approximate Solution to the Behrens‐Fisher Problem
Authors: Bhoj Dinesh S.
Published: May 2007

An approximate and practical solution is proposed for the Behrens‐Fisher problem. This solution is compared to the solutions considered by Mehta and Srinivasan (1970) and Welch's (1937) approximate t‐test in terms of the stability of the size and magnitude of the power. It is shown that the stability of the size of the new test is better than that of Welch's t when at least one of the sample sizes is small. When the sample sizes are moderately large or large the sizes and powers of all the recommended tests are almost the same.
Estimating Mean Landmark Triangles
Authors: Stoyan D. , Frenz M.
Published: May 2007

The paper deals with the statistical estimation of mean triangles of landmark data. For the model introduced by Bookstein (1986) three methods of estimating the “ideal” triangle are compared: the maximum likelihood method based on the exact distribution given in Mardia and Dryden (1989a), a moment method and an iterative algorithm yielding a mean triangle in the sense of Fréchet. These methods are compared by Monte Carlo simulation applied also to models with variances greater than those required for Bookstein's normal approximation.
An Estimation Procedure for the Joint Distribution of Spatial Direction and Thickness of Flat Bodies Using Vertical Sections Part I: Theoretical Considerations
Authors: Sandau Konrad
Published: May 2007

In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width is of interest. The fissures are mathematically generalized to flat bodies which form a stationary weighted surface process with the weight “thickness”. Because of stationarity a joint distribution of spatial direction and thickness exists in a “typical point” of the surface process. A suitable parametric family of distributions is assumed. The corresponding parameters can be estimated from measurements on the vertical sections. But on the sections only the visible thickness and the visible angle of a fissure can be measured. Therefore the joint distribution of these variables is expressed by the joint spatial distribution of spatial direction and thickness. This derived distribution depends on the same parameters. The Chi‐Square method is proposed for the parameter estimation. The estimation procedure is demonstrated using the Bingham‐Mardia distribution for the direction and the lognormal distribution for the thickness and by defining a way to correlate the mean thickness and the direction.
An Estimation Procedure for the Joint Distribution of Spatial Direction and Thickness of Flat Bodies Using Vertical Sections. Part II: An application in soil micromorphology
Authors: Sandau Konrad , Vogel Hans‐Jörg
Published: May 2007

In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width of these fissures is of interest. The fissures are mathematically generalized to flat bodies which are defined as stationary weighted surface processes with the weight “thickness”. In a typical point of the surface process suitable, joint parametric distributions of direction and thickness are assumed. The parameters have to be estimated from measurements on vertical sections which are taken from the soil. On these sections only a visible thickness and a visible angle can be observed. The joint distribution of these variables can be expressed by the joint distribution of spatial direction and thickness with the same parameters and in this indirect way the parameters can be estimated. The paper describes how to randomize the vertical section and how to measure the visible variables on the sections. The Chi‐Square method is proposed for the parameter estimation. Further it is discussed how to derive good starting values for the numerical procedure. All this is demonstrated in a simulation study using the Bingham‐Mardia distribution for the direction and the lognormal distribution for the thickness including a way to correlate the mean thickness and the direction. Finally an application in soil micromorphology is demonstrated for one soil horizon.
Sample Size Determination for Grouped Exponential Observations: A Cost Function Approach
Authors: Lui Kung‐Jong , Steffey Duane , Pugh Jamie K.
Published: May 2007

Calculating the required sample size for a desired power at a given type I error level, we often assume that we know the exact time of all subject responses whenever they occur during our study period. It is very common, however, in practice that we only monitor subjects periodically and, therefore, we know only whether responses occur or not during an interval. This paper includes a quantitative discussion of the effect resulting from data grouping or interval censoring on the required sample size when we have two treatment groups. Furthermore, with the goal of exploring the optimum in the number of subjects, the number of examinations per subject for test responses, and the total length of a study time period, this paper also provides a general guideline about how to determine these to minimize the total cost of a study for a desired power at a given α‐level. A specified linear cost function that incorporates the costs of obtaining subjects, periodic examinations for test responses of subjects, and the total length of a study period, is assumed, primarily for illustrative purpose.
On the Comparison of Umbrella Pattern Treatment Means with a Control Mean
Authors: Chen Y. I.
Published: May 2007

This paper is concerned with comparing several increasing dose levels (treatments) with a zero dose control when the prior information about the umbrella pattern treatment means is available. The problem of testing whether there is at least one treatment which is better than the control is considered. Multiple test procedures are then proposed for deciding treatments (if any) which are better than the control. Some approximate criticial values of the proposed tests are reported. The results of a Monte Carlo power study are presented.
Evaluation of Staging Systems for Colorectal Cancer
Authors: Le Chap T. , Grambsch Patricia M. , Zelterman Daniel , Lindgren Bruce R.
Published: May 2007

An alternative way to implement the Akaike Information Criterion (AIC) is proposed for the evaluation of staging systems for colorectal cancer.
Monte Carlo Investigations for Relative Efficiency of Stratified Random Sampling Scheme for Estimation of Relative Risk in Case‐Control Studies
Authors: Singh Padam , Gupta T. C.
Published: May 2007

Monte Carlo Investigations have been widely used in Sample Surveys in Comparing the efficiency of various methods when exact mathematical comparisons are not possible. In this paper the same has been used for comparing the efficiency of Stratified Random Sampling with respect to Simple Random Sampling for estimation of Relative Risk in Case‐Control Studies. The data used relate to a Case Control study on peptic ulcer. On the basis of Monte Carlo Investigations on 50 samples of size 10–20 (Cases and Controls), it has been observed that there is considerable gain in efficiency in using Stratified Random Sampling over Simple Random Sampling. The sensitivity of the results with the change in Sample Size has also been investigated.
A Power Transformation for Generalized Logistic Response Function with Application to Quantal Bioassay
Authors: El‐Saidi Mohammed A.
Published: May 2007

It is known that when the logistic response function is generalized by introducing shape parameters, the usual computational simplicity afforded by statistical softwares such as GLIM and S‐Plus may be lost. This fact is illustrated by Prentice (1976), Brown (1982), Stukel (1985, 1988), and El‐Saidi (1986). In this paper, we consider a power transformation of the generalized logistic model and show how the use of such transformation simplifies the computational difficulties associated with generalized logistic models. Furthermore, applying this technique to some data sets previously analyzed by D'Angio et al. (1981) and Brown (1982) shows an improvement in the fit in comparison to other models such as the logistic, the unstratified multiplicative model GMU and the additive model GA described by Storer et al. (1983).
On Moors' Randomized Response Model
Authors: Mangat N. S. , Singh Ravindra , Singh Sarjinder , Singh Balwant
Published: May 2007

This paper considers a modification of famous unrelated question randomized response model due to Moors' (1971). The estimator based on the proposed strategy is shown to be unbiased and always more efficient than the estimator for Moor's model.
Mixed Moment Estimation in Hermite Distribution and its Comparison with Other Estimation Procedures from Sample Size Considerations
Authors: Patel Y. C.
Published: May 2007

In this paper (1) expressions (correct to n−2 terms) for biases, variances, and covariances of the estimators a and b of Hermite distribution with probability generating function Exp[a(t–1) + b(t–1)] are obtained for two mixed moment estimates; (2) for the biases and variance‐covariances, approximate regions of the parameter space (a>0, b>0) have been outlined where a sample of size 100 can be considered as “safe” in the sense that contribution of second order terms in them is 5% of that from the first order term; (3) comparison of the biases and variance‐covariances of these two sets of estimators are made with those for the moment estimators, maximum likelihood estimates and the even point estimators for a sample of size 100 using the terms up to order n−2; (4) the comparisons based on n−2 terms in (3) have not only provided information on the estimation procedures included in the Hermite distribution, but also demonstrated the importance of higher order terms in the sampling properties of the various alternative techniques for the Hermite distribution.
Analysis of Counts involving Random Effects with Applications in Experimental Biology
Authors: Jansen J.
Published: May 2007

This paper is concerned with the analysis of count data with special reference to experimental biology and agricultural research. The model considered in this paper is obtained by extending a generalized linear model by introducing random effects with associated variance components on the scale of the linear predictor. Maximum likelihood estimation is discussed and compared with a method which uses a simplified version of the likelihood equations. Two practical applications are used to illustrate the methods.
A Stratified Product Limit Estimator for the Follow‐up Study in Cardio‐Thoracic Surgery
Authors: Chen C. L. , Laub Glenn W. , McGrath Lynn B.
Published: May 2007

We propose a stratified product limit estimator and compare the asymptotic results with those of the unstratified version. When the censoring mechanisms are unequal for different strata, the unstratified version may overestimate the total survival rate of a heterogeneous population. A numerical example in cardiac surgery is examined to demonstrate that this situation does occur in real applications. This overestimation also can be elucidated heuristically by some redistribution schemes for the censored data.
Testing in Normal Mixture Models with Some Information on the Parameters
Authors: Mangin Brigitte , Goffinet Bruno , Elsen Jean Michel
Published: May 2007

The aim of this paper is to study the distribution of the likelihood ratio for testing whether or not one is sampling from a mixture of two distributions or from a single distribution. We study the case where some information is available on the variation range of the parameters of populations. First we study the simplest case in which the difference between the mean of the two populations is known. We show certain distortions between theoretical and simulation results. Secondly, we show how this distortion spreads to the situation where this difference belongs to an interval. Finally, we give an example concerning the detection of major genes in animal population.
Estimation of a Conditional Mean in a Linear Regression Model
Authors: Bhoj Dinesh S. , Ahsanullah Mohammad
Published: May 2007

Consider the two linear regression models of Yij on Xij, namely Yij = βio + βil Xij + εij,j = 1,2,…,ni, i = 1,2, where εij are assumed to be normally distributed with zero mean and common unknown variance σ2. The estimated value of a mean of Y1 for a given value of X1 is made to depend on a preliminary test of significance of the hypothesis β11 = β21. The bias and the mean square error of the estimator for the conditional mean of Y1 are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.
Calculating the Sample Size in the Examination of Animals for the Presence of Residues Using Prior Information
Authors: Fuchs K. , Wernecke K. D. , Gölles J. , Köfer J.
Published: May 2007

The council of the European Economic Communities has issued a directive (86/469/EEC) for the examination of animals and fresh meat for the presence of residues of several hormones, drugs and environmental pollutants. The purpose of this paper is to compare the method used by the EEC with a Bayesian approach to calculate necessary sample size using prior information in different situations (assuming Beta‐, Normal‐ and Gamma‐distribution for the prior distribution). It has been shown that the Bayesian approach requires significantly smaller sample sizes for all levels of inspection. Furthermore, an example is given in the examination of pigs for the presence of residues of drugs in pork.
Use of the Maximum Likelihood Method in the Analysis of Phenotypic Stability
Authors: Piepho Hans‐Peter
Published: May 2007

The stability variance is an important estimator of phenotypic stability of genotypes. It may be estimated by method of moments and by maximum likelihood. We demonstrate by Monte Carlo simulation that, given a sufficient number of environments, maximum likelihood estimates (MLE's) are slightly better if ranking of genotypes is the experimenter's major aim. A likelihood ratio test is available for different hypotheses.
On the Estimation of Heritability from Unbalanced Data
Authors: Singh B.
Published: May 2007

The distribution and moments, of ANOVA estimator of heritability are given under unbalanced random model. These expressions are used to investigate the effect of unbalancedness on the bias and variance/MSE of the estimator and also the validity of certain approximations for its variance, numerically. The computed results reveal that the unbalancedness increases both the bias and variance/MSE of the estimator and the Smith‐approximation for the variance of the estimator provides better accuracy.
Confidence Intervals for the Mean of a Poisson Distribution: A Review
Authors: Sahai Hardeo , Khurshid Anwer
Published: May 2007

The paper provides a comprehensive review of methodology for setting confidence intervals for the parameter of a Poisson distribution. The results are illustrated by a numerical example.
Application of Discriminant Analysis to the Family Planning Data
Authors: Kumar Kuldeep , Sahai Ajit
Published: May 2007

The main strategy of family planning program in many over populated countries like India, China etc. is to bring down fertility by propagating various family planning devices like Tubectomy, IUD, Vasectomy, conventional contraceptives etc. Data was collected on various socio‐economic and demographic characteristics of the users of these devices. Based on it we have developed a discriminant function for these devices using the methodology given by Kumar (1983).
Estimation of Prevalence and Relative Risk in Repetitive Surveys
Authors: Lamba I. M. S. , Singh P.
Published: May 2007

The Theory of double sampling as proposed by Neyman (1938) and subsequently used for successive sampling by Jesson (1942), Yates (1960), Patterson (1950), Eckler (1955), Kuldroff (1963) and Tikkiwal (1960, 1967) has been explored to develop a general estimator which can be used for estimation of parameters such as mean, ratio or double ratio. A simple case of sampling on two occasions has only been considered but the logic can easily be extended for more than two occasions. The results show that the generalised estimator will be very useful for the applied statisticians.
Statistical Analysis of Nonrectangular Family Data
Authors: Kleffe J. , Province M. A. , Rao D. C.
Published: May 2007

MINQUE (Minimum Norm Quadratic Unbiased Estimators) theory is applied to the problem of estimation of variance components in family data (siblings) with variable family size. Using this approach, the traditional iterative maximum likelihood estimators are shown to be asymptotically normal, even though the data come from non‐identical parent distributions. Asymptotic expressions are also obtained for the variance of the MINQUE estimators which hold even if the data are decidedly non‐normal (e.g. a mixture of normals). In the case of normal data, exact small‐sample variance estimates are derived. Simulations demonstrate the fast rate of convergence to asymptotic properties as the number of families increases. These desirable qualities suggest that the easy to compute MINQUE class of estimators may provide a useful alternative method for modelling familial aggregation.
Analysis of Rates Using a Generalized Poisson Regression Model
Authors: Singh Karan P. , Famoye Felix
Published: May 2007

In this paper a generalization of the Poisson regression model indexed by a shape parameter is proposed for the analysis of life table and follow‐up data with concomitant variables. The model is suitable for analysis of extra‐Poisson variation data. The model is used to fit the survival data given in Holford (1980). The model parameters, the hazard and survival functions are estimated by the method of maximum likelihood. The results obtained from this study seem to be comparable to those obtained by Chen (1988). Approximate tests of the dispersion and goodness‐of‐fit of the data to the model are also discussed.
Trend Test for Overdispersed Proportions
Authors: Chen James J.
Published: May 2007

The Cochran‐Armitage test has commonly been used for a trend test in binomial proportions. The quasi‐likelihood method provides a simple approach to model extra‐binomial proportions. Two versions of the score and Wald tests using different parameterizations for the extra‐binomial variance were investigated: one in terms of intercluster correlation, and another in terms of variance. The Monte Carlo simulation was used to evaluate the performance of the each version of the score test and the Wald test, and the Cochran‐Armitage test.

The simulation shows that the Cochran‐Armitage test has the proper size only for the binomial sample data, and the test is no longer valid when applied to the extra‐binomial data. The Wald test is more likely to exceed the nominal level than the score test under either intercluster correlation model or variance model. Both score tests performed very well even with the binomial data; the tests control the type I error and in the meantime maintain the power of detecting the dose effects. Based on the design considered in this paper, the two scores test are comparable. The score test based on the intercluster correlations model seems better controlling the Type I error but appears less powerful than that based on the variance model. An example from a developmental toxicity experiment is given.
A Method to Rank Multiple Trait Performance of Biological Entities
Authors: Arunachalam V.
Published: May 2007

Performance of biological entities are defined, in general by k inter‐dependent traits whose error variances are heterogeneous. A method of arriving at “Performance Scores” for the entities along with a multivariate test of significance of k‐trait differences is described. They are used to compute, for each entity, a “Performance Index” on which a ranking of the relative performance is obtained. The improvement in the present method over an earlier one is illustrated with a numerical example.
Multi‐Stage Markov Analysis of Progressive Disease Applied to Melanoma
Authors: Wanek Leslie A. , Goradia Tushar M. , Elashoff Robert M. , Morton Donald L.
Published: May 2007

A fundamental research goal in clinical studies of progressive, multi‐stage disease is to understand its natural history and its relationship with prognostic factors. Our current understanding of this topic is based on the use of two‐stage methods for event‐time analysis which neglect intermediate transition information. In contrast, a multi‐stage model utilizes all available data and provides more accurate insight into disease progression. We specify a forward‐flowing multi‐stage Markov model based on the discrete clinical stages of disease. By assuming the process to be Markovian, we avoid unnecessary complications to our numerical estimation procedure. Due to noncontinuous patient monitoring and the chronic nature of progressive disease, heavy right‐ and interval‐censoring exists in the transition data. We develop a modified ECM algorithm to numerically carry out the otherwise complicated parameter estimation for this process. We also identify significant prognostic factors relevant to each transition, along with the relative importance of each prognostic factor. The numerical estimation is stable, and the parameter estimates are maximum likelihood estimates (Meng, 1990). In general our forward‐flowing multi‐stage models provide a flexible framework for the study of the effects of prognostic factors on progression among several stages. We apply our Markov model to a dataset of malignant melanoma patients, and present an inferential discussion. Results from our multi‐stage Markov model provide an improved understanding of melanoma progression.
A Modified Chi‐Square Test for Testing Equality of Two Multinomial Populations Against an Ordering Restricted Alternative
Authors: Oluyede Broderick O.
Published: May 2007

A modified chi‐square test for testing the equality of two multinomial populations against an ordering restricted alternative in one sample and two sample cases is constructed. The relation between a concept of dependence called dependence by chi‐square and stochastic ordering is established. A tabulation of the asymptotic distribution of the test statistic under the null hypothesis is given. Simulations are used to compare the power of this test with the power of the likelihood ratio test of stochastic ordering of the two multinomial populations.
Multiple Testing for Detecting Efficient Dose Steps
Authors: Bauer P. , Budde M.
Published: May 2007

In the comparison of various dose levels it can often be assumed that the parameters to be tested follow an order restriction. Two closed multiple test procedures for detecting the highest dose level still providing a shift in the response distribution as compared to the adjacent lower dose level is proposed. One is based on one sided comparisons between neighbouring doses, the other uses Helmert‐type contrast statistics. If a sequence of testing is fixed in advance the multiple test can be suitably modified. The power of the procedures is simulated under the assumption of normally distributed responses for various constellations of the dose means. It is compared with the power of a general Holm‐type procedure discussed in BUDDE & BAUER (1989).
Tests for Equality of Several Binomial Populations Against an Order Restricted Alternative and Model Selection for One‐Dimensional Multinomials
Authors: Oluyede Broderick O.
Published: May 2007

The problem of testing the equality of several binomial population against an order restricted alternative and model selection for one‐dimensional multinomials is studied. Test procedures are proposed. The asymptotic distribution of the test statistics are obtained. Comparisons are made with other test statistics including the likelihood ratio test for stochastic ordering. Also alternatives which does not depend on the distribution of test statistic is proposed.
Tests of Occupancy Rates for Clustered Populations: Case Where the Cluster Sizes are Known
Authors: Vaillant J.
Published: May 2007

A modified chi‐squared statistic Z is proposed for testing hypotheses about category occupancy rates for individuals distributed by clusters, when the cluster sizes are observed. This statistic is the Pearson chi‐square statistic based on the individuals' counts divided by 1 +M* whereM* is the mean number of other individuals per cluster per individual. The kind of alternative hypothesis for which the Z‐based test compares favourably in power with the Pearson chi‐square test based on the cluster frequencies is given. However, we prove that this latter test is more powerful than the former one as long as the equidistribution of the random choice vectors is assumed.
Error Normality Testing in a Model of Two‐Way Nested Classification
Authors: Brzeskwiniewicz Henryk , Wagner Wiesław
Published: May 2007

The paper deals with the construction of a normality test for the verification of the assumption about normal distribution of random errors in a fixed model of two‐way nested classification. For this purpose adequate linear transformations and orthogonal observable random vectors have been presented. To the adjusted residual vector obtained after these transformations, the D'Agostino normality test has been applied.
Robustness of Shrunken Predictors in Stratified Populations
Authors: Bouza C. N.
Published: May 2007

The effect of assuming an inadequate superpopulation model in stratified sampling is studied when a shrinkage technique is used. The robustness is close related with the balance of the strata samples. This theoretical problem is present in studies of ecology. The results obtained enable to estimate the abundance of plankton when salinity is the auxiliary variable and expert's advise, in coast experimental stations networks, is used for fixing the superpopulation model.
Asymptotic Normality of Parameter Estimators for Some Nearest Neighbour Models
Authors: Dobek A.
Published: May 2007

For auto‐regression models and first and second differences models it is shown that the REML estimators of unknown parameters are asymptotically normal when the number of observations tends to infinity.
Tests of Significance for Combined Measures of Plant Stability and Performance
Authors: Nassar R. , Léon J. , Hühn M.
Published: May 2007

Of significance in plant breeding is to develop varieties that are stable and have optimum performance, such as high yield, in different target environments. As such, selection should be on a measure that combines stability and performance. In this study, we examine the distributions for three nonparametric and three parametric measures for combined stability and performance and show that the F statistic from an analysis of variance may be used to test for differences among genotypes with regard to these measures. Recommendations are made based on the size and power of the F statistic for each of the measures. Application of the theoretical results is demonstrated using data on 14 varieties of oats in 18 locations.
Assessing the Diagnostic Utility of a Test
Authors: Viana M. A. G. , Farewell V.
Published: May 2007

Given the sensitivity and specificity of a binary test, Lindley and Novick's criterion of diagnostic utility is characterized by the range R of prevalence values in which opposing test results are in correct correspondence to opposing posterior odds on the disease. If the utility range of a new test includes the utility range R of an alternative test, then the new test is uniformly at least as useful as the standard, for all prevalence levels in R. A descriptive interpretation of the criterion is suggested and its statistical analysis is discussed.
Discriminant Analysis and its Application to Medical Data
Authors: Jain S. , Jain R. K.
Published: May 2007

Discriminant procedures are often used to classify data based on observed characteristics of the response variables. This paper discusses the validation techniques in the use of discriminant function approach. Numerical example is used to illustrate its application.
Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient
Authors: Bhoj Dinesh S. , Ahsanullah Mohammad
Published: May 2007

Consider the two linear regression models of Yij on Xij, namely Yij = βio + βij, Xij + Eij = 1, 2,…, ni, i = 1, 2, where Eij are assumed to be normally distributed with zero mean and common unknown variance σ2. The problem of estimating the conditional mean of Y1 for a given value of X1 is considered when it is a priori suspected that β10 = β20 and β11 = β21. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β10 = β20 and β11 = β21.
Subset Selection for Normal Means in a Two‐Way Design
Authors: Wu K. H. , Cheung S. H.
Published: May 2007

Subset selection procedures for normal means are extended to a two‐way layout. Suppose the same c treatments exist in each of r 2 groups. We first examine the case where a standard treatment is present and introduce a method of selecting, in each of the r groups, a subset which contains all treatments with means at least as large as the mean of the standard treatment. The same subset need not be selected in each group. We then consider the case without a standard treatment and develop procedures for selecting, in each of the r groups, a non‐empty subset which includes the treatment with the largest mean. In each case, the probability of simultaneous correct selection in all r groups is constrained to be at least as large as a specified constant P*. It is demonstrated that the percentage points needed for the implementation of these new procedures can be obtained from already existing tables or algorithms. The use of the procedures is illustrated with the reanalysis of two real data sets (JUGDUTT, 1988; SINGH et al., 1991).
Unbiasedness of the Estimator of the Function of Expected Value in the Mixed Linear Model
Authors: Klaczyński K. , Molińska A. , Moliński K.
Published: May 2007

The traditional method for estimating the linear function of fixed parameters in mixed linear model is a two‐stage procedure. In the first stage of this procedure the variance components estimators are calculated and next in the second stage these estimators are taken as true values of variance components to estimating the linear function of fixed parameters according to generalized least squares method.

In this paper the general mixed linear model is considered in which a matrix related to fixed parameters and or/a dispersion matrix of observation vector may be deficient in rank. It is shown that the estimators of a set of functions of fixed parameters obtained in second stage are unbiased if only the observation vector is symmetrically distributed about its expected value and the estimators of variance components from first stage are translation‐invariant and are even functions of the observation vector.
The Tomato Salad Problem Reconsidered
Authors: Fleischer Karlheinz
Published: May 2007

One problem in microscopy is the estimation of the distribution of sizes of cellular particles (assumed to be spheres) from the distribution of their profiles in a thin tissue sample (tomato salad problem). Because the exact formula of the solution derived by BACH (1959) is difficult to evaluate, SCHUBERT/VOSS (1974, 1975) provided an iterative procedure and a random search procedure to approximate the solution. This paper shows that neither of both procedures must be carried out, because there is a simple iterative procedure which gives precise results.
The S‐Distribution: Approximation of Discrete Distributions
Authors: Voit Eberhard O. , Yu Shuiyang
Published: May 2007

The S‐distribution is defined by the ordinary differential equation dF/dX = α(Fg — Fh Fo = F(Xo), where F is the cumulative distribution of the random variable X, and α, g, h, and Fo are parameters. The S‐distribution was recently described in this journal as a tool for the approximation and classification of univariate, unimodal continuous probability distributions. This article shows that the S‐distribution rather accurately models the commonly used univariate discrete distributions.
Weighted Multivariate Regression Estimates Solved by Random Effects Approach
Authors: Volaufová Júlia , Komornik Jozef
Published: May 2007

The paper deals with the random effects model, where the expectation vector and the covariance matrix of the effect influencing the population are to be estimated. The iterated estimator of expectation vector is derived, based on the invariant estimator of the combined covariance matrix, and some of its statistical properties are shown.
Non‐Iterative Least Squares Estimation of Missing Values in Cross‐Over Designs Without Residual Effect
Authors: Subramani J.
Published: May 2007

In the present study an attempt has been made to esttimate several missing values in cross‐over designs. When the observations are missing in a particular pattern, explicit expressions are given for the estimators of the missing values. This procedure is illustrated with the help of a numerical example.
An Alternative Approach to Estimation in Two‐Phase Sampling Using two Auxiliary Variables
Authors: Smoo J. , Smoo L. N. , Mohanty S.
Published: May 2007

Using two‐phase sampling mechanism, two alternative estimators in the presence of the available knowledge on second auxiliary variable z are considered, when the population mean of the main auxiliary variable × is unknown. The suggested estimators are found to be more eficient than the ratio‐type and regression‐type estimators suggested by KIREGYERA (1980, 1984).
Evaluation of the Kullback‐Leibler Discrepancy for Model Selection in Open Population Capture‐Recapture Models
Authors: Burnham Kenneth P. , Anderson David R. , White Gary C.
Published: May 2007

The objective of this paper is to introduce the logical basis of AIC‐based model selection to persons analyzing capture‐recapture data and to explore the key theorettical aspect of AIC based model selection, for open‐model capture‐recapture, needed for AIC to perform well in this context. Almost all previous work on AIC assumes a Gaussian model; that assumption does not hold for capture‐recapture models. Assuming the Cormack‐Jolly‐Seber model as the true model, we used numerical methods to evaluate the expectation of the log‐likelihood relative to Akaike's target predictive log‐likelihood. The use of this particular target criterion was motivated by the idea of using the Kullback‐Leibler discrepancy for model selection, for which Akaike found the bias of the sample log‐likelihood was asymptoticallyK, whereK= the number of estimated (by MLE) parameters. In some sense, then, AIC is a bias‐adjusted log‐likelihood. For a set of 81 plausible cases, we evaluated this bias almost exactly. The ratio of this bias to the first order theory (bias ofK) and to second order theory (K+ a sample size adjustment) is essentially 1 for these 81 cases. Thus, AIC should be a suitable basis for model selection in open model capture‐recapture.
The Influence of Noise and Non‐Normality on Biserial Correlation Coefficients
Authors: Dünki Rudolf M.
Published: May 2007

The estimation of any biserial correlation coefficient is biased if noise‐like processes are overlaid. We've carried out a computer simulation to study this effect. The effect can be described in a universal way. Additionally, we've varied the type of distribution within the simulation and compared this effect with the effect of noise. Based on this comparison, we've been able to draw some conclusions on the use of biserial correlation coefficients.
Model Building and Analysis for Block Designs with Nested Rows and Columns
Authors: Mejza Iwona , Mejza Stanislaw
Published: May 2007

The paper deals with two main problems: it gives a unified approach to model building for observations obtained in a block design with nested rows and columns and it provides the analysis of variance for such data. Also, some statistical properties of the design are examined.
On Probability of Heritability Estimates from Full‐Sib Analysis Exceeding Unity Based on Underlying Theoretical Distribution
Authors: Prabhakaran V. T. , Sharma B. S.
Published: May 2007

A procedure for obtaining the theoretical probability of heritability (h2) estimates from full‐sib analysis exceeding unity is described. Probability densities useful in the evaluation of these probabilities are also derived. These are used for obtaining the probabilities for several combinations of sire/dam numbers and three levels of h2 (0.10, 0.25, 0.50) assuming additive genetic model and two full‐sibs per mating.
On a Statistical Model of Mortality in Chicken
Authors: Ravindranathan N.
Published: May 2007

In this paper a statistical model for analysing mortality pattern among chicken is developed. The model is used to infer the mortality characteristics in four strains of white leghorn birds.
A Locally Most Powerful Test for Detecting a Treatment Effect in the Presence of Nonresponders
Authors: Razzaghi Mehdi , Nanthakumar A.
Published: May 2007

A problem that frequently occurs in many biological experiments is when some subjects in the treatment group may be unaffected by the treatment. For this reason, the distribution of responses in the treatment group is expressed as a two‐component mixture, where Lehmann alternatives are used to relate the distributions of affected and unaffected patients. A distribution‐free approach is proposed for testing the hypothesis of no treatment effect against the alternative that a subset of the treated subjects respond to the treatment. The test is locally optimal and structured on the basis of the empirical distribution of the untreated subjects. The properties of the test are discussed and the power function is derived. It is shown that the power increases with the proportion of responders in the experiment.
Conjugate and Other Distributional Methods in Configural Frequency Analysis
Authors: Wood Phillip K. , Sher Kenneth J. , Eye Alexander Von
Published: May 2007

Configural Frequency Analysis (CFA) is being increasingly used by psychologists and other researchers to test for the presence of combinations of categorical variables which occur more frequently or less frequently than expected under a particular model of chance. Configurations which occur more frequently than chance are known as “Types”‐Configurations which are conspicuous by their absence or rarity are known as “Antitypes”. Most configural frequency test theory consists of binomial tests applied to the cells of a cross‐tabulation table. The wide variety of statistical tests described in papers and books on CFA are approximations to the binomial test, due to the computational intensity associated with performing binomial tests directly (VON EYE, 1990b). This paper advocates direct computation of binomial probabilities instead of the usual approximations used in CFA. Mathematical relationships of the binomial distribution with the F and incomplete beta distributions are described which enable the researcher to efficiently compute binomial probabilities using functions available in common statistical software. The classical inference approach adopted by traditional CFA makes it difficult to make conclusions regarding the likely prevalence rates of types or antitypes in the reference population. It is also not possible to exploit additional information about the sample which, while not known precisely, is known with a degree of confidence and can aid in the identification of types and antitypes. A Bayesian conjugate distributions approach based on the incomplete beta distribution is proposed. Bayesian extensions of this model to both classical CFA and a sequential CFA analysis advanced by KIESER and VICTOR (1991) are described.
Adaptive Methods of Trend Detection and Their Application in Analysing Biosignals
Authors: Schack B. , Grieszbach G.
Published: May 2007

In the study estimations of the linear trend and its slope of discrete deterministic and stochastic signals are introduced, which are based on adaptive methods of mean estimation. Because of its simple recursive nature both the trend and the slope estimation may be realized in real time and thus they may be used for on‐line procedures e.g. in monitoring systems of intensive care units. The adaptive estimation functions are self‐learning, that means they are able to adapt automatically to the new conditions after structure changes of the time series and thus may be also used for detecting points of structure fracture. The properties of the adaptive trend‐ and slope estimations are demonstrated by some characteristic simulation examples and the possibilities of their applications for analysing biological signals are investigated in three different medical cases.
A Bootstrap Method for Using Imputation Techniques for Data With Missing Values
Authors: Bello A. L.
Published: May 2007

Bootstrap is a time‐honoured distribution‐free approach for attaching standard error to any statistic of interest, but has not received much attention for data with missing values especially when using imputation techniques to replace missing values. We propose a proportional bootstrap method that allows effective use of imputation techniques for all bootstrap samples. Five detcnninistic imputation techniques are examined and particular emphasis is placed on the estimation of standard error for correlation coefficient. Some real data examples are presented. Other possible applications of the proposed bootstrap method are discussed.
Testing the Independence of Competing Risks: An Application to the Analysis of Breast Cancer Recurrence
Authors: Assel Bernard , Fourquet Alain , Hoang Thu , Myasnikova Catherine , Yaicovlev Andrej
Published: May 2007

As evidenced by the results of data analysis the contralateral breast cancer recurrence is most likely to originate from subclinical tumor foci that preexist at the time of treatment This raises the natural question as to whether the rtcumnas in the contralateral breast evolve independently of those in the ipsilateral breast It is common knowledge in the theory of competing risks that this problem can not be solved within the nonparaoretric framework. To overcome the obstacle om needs to proceed from a biologically‐based parametric model of tumor latency. We explore this possibility with a model proposed earlier (HOANG et al., 1992). When incorporated into a family of joint distributions with given marginal distributions for the tumor latency times, the model allows testing the independencc hypothesis by the likelihood ratio test Our analysis of data on the ipsilateral and contralateral breast recurrence, though being conclusive only under the model assumptions, suggests that the dependence of risks is negligible for the two typcs of local failure.

AMS 1980 subject classification
Measures of Imbalance for Higher Order Designs
Authors: Marqués Lydia Lera
Published: May 2007

In this paper we consider a generalization of the measures of imbalance given by AHRENS and PINCUS (1981) considering the cases: m‐fold hierarchical model and m‐way classification model in order to quantify the degree of imbalance in an unbalanced design. These measures of imbalance satisfy the same properties as those for the one‐way classification model.
Mean Figures and Mean Shapes Applied to Biological Figure and Shape Distributions in the Plane
Authors: Ziezold Herbert
Published: May 2007

Fundamental propositions for mean figures and mean shapes in the plane are proved by using complex numbers. A test of equality of two figure or shape distributions is introduced and applied to data from larvae of mussels and from saurian heads.
Zero‐Altered and other Regression Models for Count Data with Added Zeros
Authors: Heilbron David C.
Published: May 2007

On occasion, generalized linear models for counts based on Poisson or overdispersed count distributions may encounter lack of fit due to disproportionately large frequencies of zeros. Three alternative types of regression models that utilize all the information and explicitly account for excess zeros are examined and given general formulations. A simple mechanism for added zeros is assumed that directly motivates one type of model, here called the added‐zero type, particular forms of which have been proposed independently by D. LAMBERT (1992) and in unpublished work by the author. An original regression formulation (the zero‐altered model) is presented as a reduced form of the two‐part model for count data, which is also discussed. It is suggested that two‐part models be used to aid in development of an added‐zero model when the latter is thought to be appropriate.
Lower Confidence Limits for the Positive Linear Combination of two Variances
Authors: Anbupalam T. , Ponnuswamy K. N. , Srinivasan M. R.
Published: May 2007

An alternative method for determining the approximate lower confidence limits for the positive linear combination of two variances based on an approach similar to BULMER (1957) has been proposed. The probability coverage of the proposed alternative limits has been compared with the other existing methods.
Proportionality of Diagonal Blocks with Blockwise Independence
Authors: Gupta A. K. , Chao C. C.
Published: May 2007

In this paper, the tests of similarities among group covariance matrices and the differences among block covariance matrices within a group under repeated measurement model are studied. There are nine hierarchical nested structures of covariance matrices which have been tested. The likelihood ratio tests have been derived for these nine hierarchically structured models. An algorithm for determining the numerical solution of the corresponding maximum likelihood equations is also given.
On Countable Mixtures of Bivariate Binomial Distributions
Authors: Papageorgiou H. , David Katerina M.
Published: May 2007

A unified treatment is given for mixtures of bivariate binomial distributions with respect to their index parameter(s). The use of probability generating functions is employed and a number of interesting properties including probabilities, factorial moments, factorial cumulants and conditional distributions are derived. Five classes of such mixtures are examined and several well known bivariate discrete distributions are used as illustrative examples. Biological applications are indicated including the fit of three bivariate distributions to an actual set of human family data.
Testing Multivariate Normality in Series Experiments of Incomplete Blocks by Generalized Shapiro‐Wilk Test
Authors: Wagner Wieslaw , Brzeskwiniewicz Henryk
Published: May 2007

In this paper, we verify our assumption about multivariate normality in series experiments of incomplete blocks by the generalized Shapiro‐Wilk test. This test utilizes transformations of mean yields of the investigated varieties and the generated random variables according to Durbin's randomization principle.