bluuebunny/crossref_metadata_2025 huggingface dataset:
Validity of the F‐ratio Test for Replicated Latin Square Designs Under Relaxed Conditions
Authors: Monga  , Tardif S.
Published: May 2007

In a replicated latin square design, the F‐ratio test statistic enjoys a noncentral Fisher distribution under the assumption of i.i.d. normal errors. This paper shows that the latter distribution still holds if a certain correlation structure is introduced within the sets of errors associated with each latin square. The correlation structure is characterized by the fact that, put in form of matrices, these sets of errors have exchangeable rows and exchangeable columns.
Monthly Variability of Fibrocystic Breast Disease as Assessed by Palpation1
Authors: Pagano Marcello , Leviton Alan , Allred Elizabeth , Heydn Siegfried
Published: May 2007

Breast nodules in women afflicted with “fibrocystic breast disease” show a variability in time. This paper proposes a Markov chain to model this temporal change. The model seems to fit the available data very well, if different parameters are used for pre‐ und post‐menopausal women.
Statistical Model for Locating Fragile Points on Nucleic‐ACID Molecules
Authors: Liu Chui‐Yu , Liu Chui‐Yu
Published: May 2007

Breakage is an important behavioral characteristic of nucleic‐acid molecules. This paper concerns the problem of estimating the location of fragile (F) points on biological macromolecules such as DNA or RNA. We assume that the original length of the macromolecules is a random variable, breakage occurs more likely at some points of the macromolecules than others, and the number of breakages, except for those occurring at such points, is according to a Poisson process. Under these assumptions, the density function of the length of a randomly chosen segment has been derived. The Maximum Likelihood Estimation (MLE) is suggested for estimating the parameters. The model is applied to the data available on RNA of Avian Myeloblostosis Virus (AMV), and three possible F‐points have been located. The robustness of the model is discussed.
Some Inference Results in Modified Freund's Bivariate Exponential Distribution
Authors: Hanagal David D.
Published: May 2007

This paper obtains MLE of the parameters and large sample tests for independence as well as symmetry of two components in modified Freund's model of bivariate exponential distribution proposed by PROSCHAN and SULLO (1974). The Modified Freund's model is more general model than the other models like MARSHALL and OLKIN (1967), FREUND (1961) and BASU (1974) which are the sub‐models of Modified Freund's model. It satisfies the most important Loss of Memory Property (LMP) which implies the other three sub‐models also satisfy LMP. We also obtain the confidence interval for the parameters in the above model. We extend the above results in fixed time censored and random censored samples.
A Note on Robust Intensity Estimation for Point Processes
Authors: Särkkä A. , Särkkä A.
Published: May 2007

A robust intensity estimator based on independent marking is derived. A simulation study is made to convince that the new estimator works also in such cases where the usual estimators based on the distance methods do not work. Some truncated distributions are derived.
On Estimation of Relative Risk in Case Control Studies
Authors: Singh Padam , Aggarwal Abha Rani
Published: May 2007

An estimator of relative risk in a case control study has been proposed in terms of observed cell frequencies and the probability of disease. The bias of the usual estimator i.e odds ratio as compared to the new estimator has been workedout. The expression of Mean Square Error of proposed estimator has been derived in situations where probability of disease is exactly known and when it is estimated through an independent survey. It has been observed that there is a serious error using odds ratio as an estimate of relative risk when probability of disease is not negligible. In such situations the proposed estimator can be used with advantage.
A Within Year Growth Model for Crop Yield Forecasting
Authors: Jain R. C. , Agrawal Ranjana , Singh K. N.
Published: May 2007

Logistic growth model can be used to forcast total dry matter at maturity about one month before harvest in wheat and rice whereas forecast of head/panicle weight can be made about 15 days advance of harvest. Total dry matter as well as head weight at maturity were over estimated in general when partial data were used. Modified growth model worked well to adjust for over estimation in total dry matter and head weight at maturity.
Analysis of Survival Data with Two Dependent Competing Risks
Authors: Bagai Isha , Rao B. L. S. Prakasa
Published: May 2007

Here we consider a competing risks model where the two risks of interest are not independent. The dependence is due to the additive effect of an independent contaminating risk on two initially independent risks. The problem is identifiable when the three risks fllow independent exponential distributions and also when the two initial risks follow proportional hazards model. Procedures are suggested for estimation and testing hypotheses regarding the parameters of the three exponentials in the first can and the constant of proportionality in the second case, when the information available consists of the times to death and the causes of death of the individuals.
Statistical Comparison of Band Spectral Powers: An Aid in Stochastical Analysis of Brain Electrical Activity. Part 2: Construction of Confidence Intervals of Spectral Band Power and their Application in EEG‐Analysis
Authors: Schack B. , Wagner H. , Grieszbach G. , Witte H.
Published: May 2007

Based on the result that the distribution of estimated spectral power in broad frequency bands can be approximated by x2‐distribution the accuracy of the approximation was tested by different models of stochastical processes. Two significance tests for comparison of spectral band powers on the basis of this approximation and the estimation of confidence intervals were developed and tested by application on EEG data. By means of these test statistics, a new basis for statistical comparison between EEG maps of groups as well as between maps of groups and single maps can be suggested.
A Simple Approach to Analyse Non‐Orthogonal Data
Authors: Subramani J.
Published: May 2007

The present paper deals with an alternative and simple procedure to analyse the non‐orthogonal data. The procedure is general in nature but has some advantages for the non‐orthogonal data due to some missing observations. The procedure is applied to (i) two way classification with unequal number of observations per cell; (ii) randomized block designs with some missing observations and (iii) balanced incomplete block designs and also illustrated with the help of numerical examples.
The S‐Distribution A Tool for Approximation and Classification of Univariate, Unimodal Probability Distributions
Authors: Voit Eberhard O.
Published: May 2007

In many statistical applications a data set needs to be evaluated but there is no solid information about which probability distribution might be most appropriate. Typical solutions to this problems are: to make assumptions that facilitate mathematical treatment; to use a family of distribution functions that contains all relevant distributions as special cases; or, to employ nonparametric methods. All three solutions have disadvantages since assumptions are usually difficult to justify, families of distributions contain too many parameters to be of practical use, and nonparametric methods make it difficult to characterize data in a succinct quantitative form. The S‐distribution introduced here is a compromise between the conflicting goals of simplicity in analysis and generality in scope. It is characterized by four parameters, one of which reflects its location, the second one its spread, and the remaining two its shape; transformation to a standard form reduces the number of free parameters to two. Cumulatives and densities are computed numerically in fractions of seconds, key features like quantiles and moments are easily obtained, and results can be presented in terms of parameter values. The S‐distribution rather accurately models different distribution functions, including central and noncentral distributions, and thus competes in flexibility with some distribution families. As an approximation, the S‐distribution provides a graphical method for demonstrating relationships between distributions, such as the relationships between central F, χ2 and χ−2 or central and noncentral t, χ‐1, and normal.
Comparison and Evaluation of Three Methods of Estimation of the Johnson Sb Distribution
Authors: Siekierski Krzysztof
Published: May 2007

Thre methods of estimating the parameters of the Johnson S6 distribution were tested by simulation. The maximum likelihood method, the method based on percentiles of a sample and the method based on moments of a transformed random variable were taken into consideration. Many sets of samples were generated differing in sizes and in the actual values of parameters, whereupon the parameters were estimated by the three methods. It was proved that if the sample is small or the skewness of the distribution is considerable, the maximum likelihood estimates can assume preposterous values. The method based on moments is recommended due to its simplicity and to the fact that the estimates, though usually biased, never assume absurd values.
Binary Longitudinal Data Analysis with Correlation a Function of Explanatory Variables
Authors: Darlington G. A. , Farewell V. T.
Published: May 2007

When binary responses are observed over time, the dependence between observations for an individual must be considered. If the focus of a study is to identify the relationship between the binary response and a set of explanatory variables then the dependence between observations may also depend on the explanatory variables. An extension of a model where dependence is assumed to be constant will be considered. A model previously proposed for dependent binary responses will be revisited and a robust estimate of the variance‐covariance matrix of coefficient estimates will be suggested to provide estimates of standard errors. The results of simulation studies investigating the properties of coefficient estimates will be discussed. An example based on a study of the AIDS epidemic and intravenous drug use behaviour will be analyzed to illustrate the techniques.
New Better than Used and Other Concepts for a Class of Life Distributions
Authors: Rao B. Raja , Damaraju C. V. , Rao Pro F. B. Raja , Damaraju C. V.
Published: May 2007

It is well‐known that the inequalities used in the definition of the New Better than Used (N. B. U.) and the New Better than Used in Expectation (N.B.U.E.) concepts, see BARLOW and PROSCHAN (1965, 1975) become equalities if, and only if, the life length of an organism follows an exponential distribution. It is proved in the present paper that these inequalities also reduce to equalities for the class of life distributions that have the “setting the clock back to zero” property. Simple examples of these distributions include the exponential, the linear hazard exponential and the Gompertz distributions. The General Krane distributions (Krane 1963) belong to this class, as well as a recent model introduced by CHIANG and CONFORTI (1989) of a survival distribution in which the hazard rate is a function of the accumulated effect of an individual's continuous exposure to the toxic material in the environment and his biological reaction to the toxin absorbed.

As a simple application of the result proved in the paper, the life expectancy of an organism at age γ0 involved in the N.B.U.E. concept is evaluated for the Gompertzian growth process and for the Chiang and Conforti model.
On a Class of Almost Unbiased Ratio Estimators
Authors: Biradar R. S. , Singh H. P.
Published: May 2007

A class of almost unbiased ratio estimators for population mean σ is derived by weighting sample σ = (1/n) σ yi, ratio estimators σ and an estimator, σ (yi/xi). It is shown that NIETO DE PASCUAL (1961) estimator is a particular member of the class and an optimum estimator in the class (in the minimum variance sense) is identified. The results are illustrated through two numerical examples.
Tables of the Critical Values for Simultaneous Tests
Authors: Enǎchescu D. , Ursianu Emiliana
Published: May 2007

A method for computing percentage points for the studentized maximum absolute deviate in normal samples is presented. Examples of the use of these points in the construction of simultaneous tests for a linear function of means, are given.
Effect of Selection on the Failure Rate Function
Authors: Suresh R. P.
Published: May 2007

Effect of selection procedures such as truncation and genotypic selection, are studied using selection differentials. These studies are mainly restricted to the study of mean or percentiles of the characteristics of interest. However, in situations where improvement on longetivity is itself of interest, in addition to studying mean or percentiles, one may study the reliability characteristics such as Failure Rate, Mean Residual Life etc., of the lifetimes of individuals. In this paper, we study the effect of genotypic selection when the distribution function of the lifetime is governed by a single locus with 2 alleles. We compute the difference in the failure rate function from one generation to the next generation for different values of n, the number of generations. We also obtain the limiting values of the failure rate function as n and compute the number of generations required for the failure rate to reach a value close enough to the limiting failure rate function. We also consider an example in a two‐loci case and study the effect of selection on the failure rate function.
EM Algorithm for Segregation Analysis
Authors: Achuthan N. R. , Krishnan T.
Published: May 2007

We consider the problem of estimating segregation ratios in families based on ascertainment through affected children, formulate it as an incomplete problem and work out the EM algorithm for maximum likelihood estimation of segregation ratios. We treat both the cases of known and unknown ascertainment probability. We also derive expressions for the covariance matrix of the estimators suitable for computing along with the EM algorithm. We illustrate the method with an example, compare the computational effort with that required in using the scoring method and argue that the EM algorithm is simpler.
A Modification of the Edgeworth Approximation in the AR (1) Model
Authors: Liu Shu‐Ing , Su Chien‐Chou , Chien‐Chou Shu‐Ing Liu
Published: May 2007

This paper considers the sampling distribution problem of the least squares estimator for the parameter of some special autoregressive models. The Edgeworth approximation has been derived and a modification is proposed to improve its accuracy. Comparisons with the exact distribution and the so called Edgeworth‐B approximation have been discussed. The results show that the proposed approximation performs more accurately than the Edgeworth‐B approximation, especially, when models are close to the non‐stationary boundary.
Estimation in a Continuous State Space Branching Process
Authors: Kale Mohan , Deshmukh S. R.
Published: May 2007

In some biological studies it is impossible to count the total number of individuals, but the size of the population can be measured by it's weight or volume. The probability of extinction of such populations is an interesting parameter, e.g. in modelling of epidemics. In this paper, the estimation of extinction probability and the moments of the offspring distribution is studied and the asymptotic properties of the estimators are discussed.
A Note on Errors‐in‐Variables in Panel Data
Authors: Mauldin Patrick D.
Published: May 2007

This Note expands the difference estimator developed by GRILICHES and HAUSMAN (1986) to the case of many independent variables, all having errors‐in‐variables.
Some Early Developments in Ratio Estimation
Authors: Sen A. R.
Published: May 2007

John Graunt (1662) was the first to estimate the ratioy/xwhereyrepresents the total population andxthe known total number of registered births in the same areas during the preceding year.

About 1765 Messance (Stephan, 1948) and Moheau (1778) published very carefully prepared estimates for France based on enumeration of population in certain districts and on the count of births, deaths and marriages as reported for the whole country. The districts from which the ratio of inhabitants to birth was determined only constituted a sample. Laplace (1786) prepared similar estimates in 1802 based on a two‐stage sampling plan.

Recently Hansen and Hurwitz (1943) showed that the ratio estimate (yi/ni)XofYis unbiased where allxi's are known and thenthcluster is selected with p.p.s. More recently Hájek (1949), Lahiri (1951), Midzuno (1952) and Sen (1952) developed independently the sampling ofnclusters with p.p.s to the totals of the sizes of the sample clustersS(xi).

Des Raj (1954) and Sen (1952, 1953) gave unbiased estimate of the variance of the estimator which was generally non‐negative for samples with smaller probabilities. Rao and Vijayan (1977) gave an unbiased estimator which is non‐negative for samples with larger probabilities. Hájek (1949) provided an almost unbiased estimator of the variance of the estimator.

The paper discusses situations where Hájek's estimator of variance should be preferred to the Rao‐Vijayan estimator and vice versa.
On the Information Matrix of Exponential Mixture Models with Long‐term Survivors
Authors: Ghitany M. E.
Published: May 2007

The aim of this paper is to study the properties of the asymptotic variances of the maximum likelihood estimators of the parameters of the exponential mixture model with long‐term survivors for randomly censored data. In addition, we study the asymptotic relative efficiency of these estimators versus those which would be obtained with complete follow‐up. It is shown that fixed censoring at timeTproduces higher precision as well as higher asymptotic relative efficiency than those obtainable under uniform and uniform‐exponential censoring distributions over (0,T). The results are useful in planning the size and duration of survival experiments with long‐term survivors under random censoring schemes.
Estimation of Incidence from Age Wise Prevalence
Authors: Lamba I. M. S. , Singh Padam
Published: May 2007

A method used by various researchers for estimation of incidence from prevalence data of a stable population for irreversible stable diseases has been validated. For this purpose a followup data was generated by life table distribution techniques with known mortality and incidence rates. The results show that the method as such cannot be used to estimate the true incidence from prevalence data of a crossectional study from stable population. The remote situation where the method will work has been discussed. A method has also been presented for situations where the known method fails i.e. duration of irreversible disease is less than the age of effected persons in a stable population.
Precision Estimation in Zelen's Single‐Consent Design
Authors: Matts J. P. , McHugh R. B.
Published: May 2007

The precision of a treatment contrast, as conventionally estimated in Zelen's Single‐Consent Design, is shown under randomization theory to be positively biased. The magnitude of this bias is demonstrated and a new statistic is derived which is a consistent estimator of the precision. Confidence interval estimation for the treatment contrast is also presented.
A Note on Quantile Estimation for Curtailed Experiments
Authors: Trajstman A. C.
Published: May 2007

There may be experiments where due to misadventure or logistic or ethical reasons final measurements on all experimental units cannot be obtained. If at least 50% of the final measurements have been taken estimates of the lower quantiles and the median can be obtained. For such curtailed experiments it is shown how quantiles, above those that can be estimated directly from the data set, can be estimated indirectly by exploiting a property of symmetric distributions. The performance of the indirect quantile estimator is compared with that of the direct quantile estimator and conditions for the indirect estimator to have smaller variance than the direct estimator are presented. It is also shown how the indirect estimator may be pooled with the direct estimator to obtain an improved estimate of the upper quantiles.

When it cannot be assumed that the data come from a symmetric distribution transformations to symmetry may be performed and the indirect estimation technique used on the transformed data; back transformations then yield the estimates of the upper quantiles.
Randomization Analysis of Incomplete Data in Some Basic Designs
Authors: Dash S. P. , Bourghawi Suad M. , El‐Amaari Ali
Published: May 2007

The first two randomization moments of W = Tt.S.S./(Tt.S.S. + Error S.S.) are derived in case of (a) a completely randomized design with one observation missing using (I) Yates method of fitting constants and (II) the available observations only and in case of (b) a randomized block design in which one treatment is tested twice by mistake in a block and another treatment is not tested at all in that block using (I) all the available observations and (II) the data after deleting the observation due to the treatment tested by mistake in place of another treatment in a block.

It is concluded that in each of the two cases for a completely randomized design, the F‐test is unbiased whereas in each of the two cases for a randomized block design the F‐test is in general not unbiased. However, if one treatment is tested twice by mistake in randomly chosen plots of some block, the F‐test is unbiased in both cases for a randomized block design.

For a completely randomized design the F‐test is found to be a good approximation to the corresponding randomized test if N ≧ 80 in case (I) whereas in case (II) this approximation is of the same accuracy as that of case (I) if N ≧ 90. For a randomized block design it is seen that in case (I), the F‐test provides a good approximation to the corresponding randomization test if v≧r≧7 and in case (II) this approximation is of the same accuracy if r≧6 and r(v‐1)≧45.

The analysis of several uniformity trial data shows that for values of “N” in the neighbourhood of 50 the agreement of the first two moments of “W” under the randomization theory and normal theory are reasonably close in all the four cases considered.
A Guide to Bivariate Ideas of Quantal Response Analysis, as Applied in Biometrics and Econometrics
Authors: Hutchinson T. P.
Published: May 2007

A review is provided of the several bivariate generalisations of quantal response analysis that have appeared in the biometric and econometric literatures. There are three main types: (i) where a binary outcome is the result of two stimulants, and thus the bivariate distribution of the thresholds for response is relevant; (ii) where three or more alternative outcomes may arise from a single stimulant; and (iii) where the response itself is bivariate (i.e., two types of response may simultaneously be observed).
On Assessment of Bioequivalence for Drugs with Negligible Plasma Levels
Authors: Liu Jen‐Pei , Chow Shein‐Chung
Published: May 2007

In bioavailability studies, bioequivalence between drug products is usually determined based on some pharmacokinetic responses such as area under the blood or plasma concentration‐time curve and maximum concentration. For some drug products, however, we may have negligible plasma levels because their intended routes of administration. In this case, assessment of bioequivalence between drug products of this kind may be established using clinical endpoints such as therapeutic response and time to the onset of a therapeutic response. In this paper, we propose two procedures which modify the method of generalized estimating equations (Liang and Zeger, 1986) and the proportional hazard models for paired failure times to assess bioequivalence between two drug products under the structure of a standard two‐sequence, two‐period crossover design. An example concerning a bioequivalence trial for albuterol metered dose inhaler indicated for acute bronchospasm (Herson, 1991) is used to illustrate the proposed procedures.
Regression Models for Clinical Trials with Correlated Categorical Responses
Authors: Burnett R. T. , Shedden J. , Broekhoven L.
Published: May 2007

Regression models for correlated categorical data are presented in which the covariance is a function of measured effects. The regression and covariance parameters are estimated by extended least square methods. A numerical example of a clinical trial comparing two antiemetic treatment regimes for patients receiving chemotherapy is given to illustrate the approach.
Incorporating Prior Beliefs in Treatment Allocation for Clinical Trials
Authors: Faraggi David , Reiser Benjamin
Published: May 2007

Recently Faraggi and Reiser (1991) introduced a general dynamic treatment allocation scheme which incorporates the permuted block allocation procedure and the Begg Iglewicz procedure as special cases. A drawback of previous allocation methods is that they did not allow incorporation of prior knowledge of the relative importance of the prognostic factors. In this paper we extend our allocation model to incorporate the weighting of prognostic factors. A simulation study examines the effects of this procedure and an example of its implementation is given.
Configural Frequency Analysis as a Parametric Method for the Search of Types and Antitypes
Authors: Spiel Christiane , Von Eye Alexander
Published: May 2007

The article introduces Parametric Configural Frequency Analysis (CFA). It is argued that there are two types of parameters that can be of importance in CFA models. The first is effect parameters that are estimated from the data. This type of parameter is involved in almost all models of Classical, nonparametric CFA. The second type involves a priori or distributional parameters that can be used for estimation of expected frequencies. These parameters are specified a priori rather than estimated from data. A combination of models from Classical CFA and Parametric CFA is introduced as Semi‐Parametric CFA. Data examples illustrate the new CFA models in comparison with the Classical CFA. Interpretational issues are discussed.
Adaptive Quantile Estimation and its Application in Analysis of Biological Signals
Authors: Grieszbach G. , Schack B.
Published: May 2007

Quantiles and their estimations are the basis for solving numerous problems of statistics. The paper presents adaptive recursive estimation methods for this statistical parameter. Its specifical properties are investigated and the possibilities of applications in computer assisted analysis of biological signals are demonstrated even satisfying real time requirements.
Interaction Biases in Two‐Period Crossover Studies: A Modified Analysis to Test with More Sensitivity
Authors: Cleophas Ton J. M.
Published: May 2007

The two‐period crossover trial is considered the most powerful means of determining the efficacy of new drugs. However, this study design is frequently invalidated by treatment‐by‐period interaction. If, for example, the effect of the first treatment period carries on into the next one, then it influences the response to the latter period (carryover effect). A second problem is, that the standard approach (Hills‐Armitage analysis) for interaction bias has a low statistical sensitivity. The author recently described an alternative method entitled the clinical approach because it looks at the clinical performance of the separate treatment groups and not, as the standard approach, at the means of the groups. It may be hypothesized that this alternative approach is statistically more sensitive than the standard in situations where there is interaction in just one of the treatment groups. The present study uses two examples and a mathematical model. It shows that in case of single‐group interaction the clinical approach can, indeed, detect carryover effect at a 30% lower level than the standard. On the other hand, however, the standard approach does so even at a 40% lower level than the clinical in case of two‐group interaction. I conclude that one approach supplements the other and that they be used in future studies simultaneously.
Association, Symmetry and Diagonal Models for Occupational Mobility and Other Similar Square Contingency Tables Having Ordered Categorical Variables
Authors: Lawal H. Bayo
Published: May 2007

This paper examines various association, symmetry and “diagonal band” class models for both the British and Danish social mobility data. Composite models are also fitted to these data and the variety of models considered ensures that for most square tables, parsimonious models within the class of models examined in this study can always be found that will adequately describe such tables. The models considered in this study, which have been described in various forms by Goodman (1984), Upton (1985) and Tomizawa (1986) can suit most square tables having ordered classificatory variables. A model selection procedure is also examined.
Estimation of Partial Regression Coefficient
Authors: Singh Padam , Talwar Harsh Kumari
Published: May 2007

A sampling scheme providing unbiased partial regression coefficient has been proposed. The proposed sampling scheme is not only unbiased but also superior to simple random sampling and that due to Singh and Bathla (1990) for estimation of partial regression coefficient.
Drug Addiction ‐ Pushers Generated from the Addicts
Authors: Billard L. , Dayananda P. W. A.
Published: May 2007

This work develops a model for the spread of drug addiction in a closed population of size N. The spread of addiction is considered as an epidemic process where the addicts mix homogeneously within the population. There is an additional group (or pushers) with whom the susceptibles interact, but who are generated from the addicts. State probabilities and moments are obtained for this stochastic process. An extension to a generalized model is also made.
Estimation of Difference of Population Means with Missing Observations
Authors: Bouza C. N. , Prabhu‐Ajgaonkar S. G.
Published: May 2007

Sampling strategies for estimating difference of population means are proposed. The original sample is fragmented into three subsamples. The use of a purposive device permits to measure only one of the variables in two samples. Bootstrap procedures are employed to evaluate distribution of the errors of estimators.
On the Frequency Distribution of a Product
Authors: Finney David J.
Published: May 2007

Biometric interest often attaches to the product of two directly determined variables. In sugar production, for example, the yield of the desired commodity is the product of the total weight of cane or beet from unit area and the sugar content per unit weight. In crop and animal production, there are many analogous situations where experimental or other information may come from field plots or individual animals and the success of inferences or decisions is related to the frequency distribution of such a product. The voluminous published literature relating to frequency distributions appears to contain little that is directly relevant. It therefore seems worth placing on record results recently obtained for the third and fourth moments of a product in the simple case of both variables being Normally distributed.
On Connectedness of a Two‐way Elimination of Heterogeneity Design
Authors: Siatkowski I.
Published: May 2007

For some subclass of a two‐way elimination of heterogeneity design, necessary and sufficient conditions are established for row‐connectedness and column‐connectedness of a design to imply its connectedness.
The Discrete Distribution Used for the Log‐rank Test Can Be Inaccurate
Authors: Soper K. A. , Tonkonoh N.
Published: May 2007

When the number of tumors is small, a significance level for the Cox‐Mantel (log‐rank) test Z is often computed using a discrete approximation to the permutation distribution. For j = 0,…, J let Nj(t) be the number of animals in group j alive and tumor‐free at the start of time t. Make a 2 × (1+J) table for each time t of the number of animals Rj(t) with newly palpated tumor out of the total Nj(t) at risk. There are a total of say K tables, one for each distinct time t with observed death or newly palpated tumor. The usual discrete approximation to the permutation distribution of Z is defined by taking tables to be independent with fixed margins Nj(t) and ΣRj(t) for all t.

However, the Nj(t) are random variables for the actual permutation distribution of Z, resulting in dependence among the tables. Calculations for the exact permutation distribution are explained, and examples are given where the exact significance level differs substantially from the usual discrete approximation. The discrepancy arisis primarily because permutations with different Z‐scores under the exact distribution can be equal for the discrete approximation, inflating the approximate P‐value.
Bias in the Logarithm of Microbial Density Estimates from Serial Dilutions
Authors: Garthright Wallace E.
Published: May 2007

The bias in the most‐probable‐number (MPN) estimate of microbial densities derived from serial dilutions might be less important than it has appeared to be. For many purposes, bias in the logarithm of the MPN is more important than bias in the MPN, and the bias in the logarithm is much less. The lesser bias has been reduced by using the theorems of Salama, Koch, and Tolley. Formulas and tables are provided.
Use of Quantal Method for Estimation of Agricultural Production
Authors: Deo Sheela S. , Pandit Satish J.
Published: May 2007

The usual analysis of quantal response data occurring in diverse fields such as economics, medicine, psychology and toxicology use probit and logit models or their extensions with generalised least squares or the principle of likelihood as the method of statistical inference. The quantal method was first used for estimation of agricultural production by S. M. Vidwans (1991). He has collected the data on yield rate of rabi jowar from the farmers for year 1981 in four villages in Shirur taluka and three villages in Daund taluka of Pune district of Maharashtra in India. The probit regression line is fitted. The fit is not good. The estimation is done using truncation of data. Here we observed that a second degree polynomial is a good fit to the data. This will give correct prediction of agricultural production with smaller standard error.
Prediction of New Cases of Disease or Infection for Small Subgroups
Authors: Solomon P. J. , Wilson S. R.
Published: May 2007

For health planning, a common requirement is to predict future numbers of cases of a disease or infection for which just a few cases have been observed so far. In this paper, the subgroup prediction method is extended to accommodate, from a practical view, two commonly occurring features of epidemic data, namely, variable periods of observation and nonexponential epidemic growth. A table is provided which considerably simplifies application of the method. The work was motivated by a consulting project in connection with the Australian AIDS epidemic, for which some results are presented.
Testing Equality of Coefficients of Variation of Two Populations
Authors: Bhoj Dinesh S. , Ahsanullah Mohammad
Published: May 2007

The test statistics are proposed for testing the equality of the coefficients of variation of two normal populations based on independent samples. The asymptotic distributions of the statistics are approximated by well‐known distributions. The empirical sizes and powers of these statistics are computed and compared.
A Selection Procedure for Selecting Good Exponential Populations
Authors: Gill Amar Nath , Sharma Suresh Kumar
Published: May 2007

Consider k independent exponential populations with location parameters μ1,…, μk and a common scale parameter or standard deviation θ. Let μ(k) be the largest of the μ's and define a population to be good if its location parameter exceeds μ(k) –Δ1. A selection procedure is proposed to select a subset of the k populations which includes the good populations with probability at least P*, a pre‐assigned value. Simultaneous confidence intervals, that can be derived with the proposed selection procedure, are discussed. Moreover, if populations with locations below μ(k) –δ2, (δ2 > δ1) are “bad”, a selection procedure is proposed and a sample size is determined so that the probability of omitting a “good” population or selecting a “bad” population is at most 1 – P*.
Some Remarks on the Estimation of the Pair‐Correlation Function for Point Processes
Authors: Doguwa Sani I. , Kukoyi Khalid O.
Published: May 2007

Doguwa (1990) proposed kernel based pair‐correlation function estimators for Point processes. These estimators transport a part of the probability mass into the negative or left, to a hard‐core distance. The reflection technique is used to provide an alternative estimator of the pair‐correlation function, which drastically reduces the bias inherent in these estimators for the case of random and clustered point patterns. However, the drastic reduction in bias, is at the cost of a much larger variance.
The Design and Use of Variance Component Models in the Analysis of Human Quantitative Pedigree Data
Authors: Schork Nicholas J.
Published: May 2007

The use of variance components and multivariate linear models in genetics applications has a long history that dates back to (at least) Fisher's seminal 1918 paper “The correlation between relatives on the supposition of Mendelian inheritance” [Phil. Trans. 52: 399–433]. Although extensions and elaborations of Fisher's insights have been offered in recent times, relatively few studies exist which examine the theoretical and operational properties variance component models possess in complicated genetic analysis settings. In this paper variance component models, as well as some of their properties (e.g., power, efficiency, and sample size considerations) are discussed in the context of each of the following genetic analysis settings: 1. the detection of general polygenic additive and dominance effects; 2. the detection of genetic effects in the presence of environmental effects (and vice versa); 3. the detection of pleiotropic gene action; 4. aspects of the detection of genotype by environment interaction; and 5. sequential tests for general hypotheses framed in the context of settings 1 through 4. Exposition of the proposed methods and results are facilitated through a special emphasis placed on pedigree covariance structure modeling.
Analysis of Partially Balanced Incomplete Block Designs with Standards
Authors: Brzeskwiniewicz Henryk
Published: May 2007

The paper presents a detailed analysis of variance of PBIB designs supplemented by one or more standard treatments. Comparisons were carried out of treatment effects within the group of standard and test treatments and between the two groups. The analysis is supplemented by an example.
An Integrated Formulation for Comparing Treatments with Binary Response with a Control
Authors: Hsu Lifang
Published: May 2007

The problem of comparing k(≧2) bernoulli rates of success with a control is considered. An one‐stage decision procedure is proposed for either (1) choosing the best among several experimental treatments and the control treatment when the best is significantly superior or (2) selecting a random size subset that contains the best experimental treatment if it is better than the control when the difference between the best and the remaining treatments is not significant. We integrate two traditional formulations, namely, the indifference (IZ) approach and the subset selection (SS) approach, by seperating the parameter space into two disjoint sets, the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best experimental treatment for a correct selection (CS1) but in the IZ we define any selected subset to be correct (CS2) if it contains the best experimental treatment which is also better than the control. We propose a procedure R to guarantee lower bounds P1* for P(CS1≧PZ) and P2* for P(CS2≧IZ) simultaneously. A brief table on the common sample size and the procedure parameters is presented to illustrate the procedure R.
Partial Distributional Canonical Discriminant Analysis
Authors: Feldmann Uwe
Published: May 2007

A canonical discriminant technique is proposed which is unrelated to particular distributional assumptions. This approach allows for a data generated choice between ordered, partially ordered and unordered outcomes and remains identifiable in each dimension of the canonical model. The concepts of allocatability and distinguishability of categories are investigated. Maximum likelihood parameter estimation is conducted and inferential tests for the assessment of the dimensionality of the canonical model are derived. The model is applied to the perioperative prediction of risk of death from peritonitis, using real data.
The Power of the Mantel‐Haenszel Test when Adjustment is by the True or Estimated Propensity Score
Authors: Drake Christiana , McQuarrie Allan
Published: May 2007

The power of the Mantel‐Haenszel test for no treatment effect in the case of binary exposure and response variates was examined through simulation studies when subclasses were formed on the basis of the true and estimated propensity scores and by direct stratification on two continuous covariates. The power of these tests was also compared to the score test in a misspecified logistic regression model. In general adjustment by the true propensity score was most likely to reject a false null hypothesis, the score test was more likely to reject a false null hypothesis than the Mantel‐Haenszel test when adjustment is by the estimated propensity score or subclassification on the covariates. There was litte difference in the observed powers of the Mantel‐Haenszel tests between adjustment by the estimated propensity score and subclassification on the covariates.
Exact Test of Uniform Association in a 2 × 3 Table
Authors: Tomizawa Sadao
Published: May 2007

In a similar approach to Fisher's exact test of independence (null association) for a 2 × 2 table, this note gives an exact test of uniform association for a 2 × 3 table.
Estimation of Several Missing Values in F‐Square Designs
Authors: Subramani J. , Aggarwal M. L.
Published: May 2007

The present study deals with the estimation of several missing values in F‐square designs. The estimating equations for the non‐iterative least squares estimation of Missing Values and explicit expressions for the estimators of the particular patterns of Missing Values are presented. This procedure is illustrated with the help of a numerical example.
Non‐Iterative Least Squares Estimation of Missing Values in Hyper‐Graeco‐Latin Square Designs
Authors: Subramani J.
Published: May 2007

In this paper an attempt has been made to obtain explicit expressions for the estimators of the several missing values in hyper‐graeco‐latin square designs. Further it has been shown that the estimates of the missing values in latin square designs and graeco‐latin square designs are obtained as a particular case of the estimates of the missing values in hyper‐graeco‐latin square designs.
Estimation of Relative Risk in Case Control Studies Through Logistic Regression Analysis
Authors: Aggarwal Abha Rani , Singh Padam
Published: May 2007

Multiple logistic regression analysis is used to estimate the relative risk in case control studies. The estimators obtained are valid when disease is rare. In this paper an estimator of relative risk in a case control study has been proposed using logistic regression results when the incidence of disease is not small. The bias of the usual estimator through logistic regression as compared to the new estimator has been worked out. The expression of Mean Square Error of proposed estimator has been derived in situations when the incidence of disease is known exactly as well as when estimated through an independent survey. It has been observed that there is a significant bias using the conventional estimator of relative risk when incidence of disease is high. In such situations the proposed estimator can be used with advantage.
Trunk‐Top Relations in a Siberian Pine Forest
Authors: Gavrikov V. L. , Grabarnik P. Ya. , Stoyan D.
Published: May 2007

In this paper we study relations between trunks and tops of pines in natural Siberian forests. By statistical methods we show that the tops tend to deviate in the direction away from the nearest neighbour tree or from a summary of the trees in a given neighbourhood. In an alternative approach we show that the tops deviate into the direction of the empty space near the trunk position defined by the corresponding Voronoi polygon.
Symmetric Bernoulli Distributions and Generalized Binomial Distributions
Authors: Qu Y. , Greene T. , Piedmonte M. R.
Published: May 2007

The generalized binomial distribution is defined as the distribution of a sum of symmetrically distributed Bernoulli random variates. Several two‐parameter families of generalized binomial distributions have received attention in the literature, including the Polya urn model, the correlated binomial model and the latent variable model. Some properties and limitations of the three distributions are described. An algorithm for maximum likelihood estimation for two‐parameter generalized binomial distributions is proposed. The Polya urn model and the latent variable model were found to provide good fits to sub‐binomial data given by Parkes. An extension of the latent variable model to incorporate heterogeneous response probabilities is discussed.
Asymptotic Confidence Intervals for the Relative Relapse Rate Under Random Censorship
Authors: Hentzschel Jürgen
Published: May 2007

In the present paper we determine asymptotic confidence intervals of relative relapse rates (RRR) in the case of stochastically right censorship. A practical problem which promotes this discussion is the investigation of the efficiency of a test medicine: The quotient of the mortality rates (called the RRR) of two groups of acute leukemia patients is used as its indicator whereby the patients of one group received the remedy. With this task we will pursue a recent paper by Rao et al. (1991) who assumed the Weibull distribution to be the model for relapse times in both groups. Furthermore, the observed samples are stochastically right censored with censoring distributions of Weibull type, too. We construct asymptotic confidence intervals for the distribution parameters on the basis of the ml estimator and a pseudo‐ml estimator from which the intervals for RRR follow. For the benefit of accuracy in the case of finite samples a bias correction is proposed. By means of a numerical example with the Freireich data (Freireich (1964)) the resulting intervals are compared with those of the approximative methods in Rao et al. (1991).
Comparisons of Some Chi‐Squared Goodness‐of‐Fit Test Statistics in Sparse One‐Way Multinomials
Authors: Lawal H. Bayo
Published: May 2007

The behavior of Pearson's X2 test, the likelihood ratio test Y2 and the two of its derivatives, G2 and Gk2, the Freeman‐Tukey test (FT) and the Cressie and Read test Statistic I(2/3) are examined in this study. Estimated attained α levels based on 1000 simulated samples when the approximating distribution is χk‐12, are computed for these tests for the various values of k, n and seven null hypotheses. Results from estimated power computations indicate that none of the test statistics has a clear advantage over any others, and that the choice of which test to use must therefore rest mainly on the performances with regards to the attained α levels when the χ2 approximation is invoked. In this respect, the log‐normal approximation proposed by Lawal and Upton (1980) is strongly recommended. This is closely followed by the I(2/3).
Distribution‐free Estimation of a Monotonic pth Quantile Function
Authors: Strömberg U.
Published: May 2007

When analyzing biological data sets, a frequent problem is to estimate the pth quantile of a distribution, when that quantile is assumed to depend on a covariate; in the present paper the dependence of the quantile on the covariate is assumed to be monotonic. Some properties of an isotonic pth quantile regression, considered as an estimator of an increasing pth quantile function, are presented.