Improved error bounds for genetic distances from DNA sequences

The genetic distance between two DNA sequences may be measured by the average number of nucleotide substitutions per position that has occurred since the two sequences diverged from a common ancestor. Estimates of this quantity can be derived from Markov models for the substitution process, while the variances are estimated using the delta method and confidence intervals calculated assuming normality. However, when the sampling distribution of the estimator deviates from normality, such intervals will not be accurate. For simple one-parameter models of nucleotide substitution, we propose a transformation of normal confidence intervals, which yields an almost exact approximation to the true confidence intervals of the distance estimators. To calculate confidence intervals for more complicated models, we propose the saddlepoint approximation. A simulation study shows that the saddlepoint-derived confidence intervals are a real improvement over existing methods.     

On the Estimation of the Population Mean with Known Coefficient of Variation

For the estimation of population mean a class of estimators has been proposed when the coefficient of variation is known and its efficiency is compared with the usual unbiased estimator and the estimators suggested by various researchers. The properties of the proposed class of estimators have been also discussed in the case of normal population.     

Non-Iterative Least Squares Estimation of Missing Values in Cross-Over Designs Without Residual Effect

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.     

A Monte Carlo Study of Robustness of Pretest and Shrinkage Estimators in Pooling Coefficients of Variation

Pooling data, when justified, is advantageous for estimating the true parameter. In this paper the problem of estimating the coefficient of variation is considered when it is a priori suspected that two coefficients of variation are the same. Various estimators based on pretest and shrinkage rules are considered. A comparison through the Simulated Mean Squared Error (SMSE) criterion is carried out among various proposed estimators of the target coefficient of variation. The relative simulated efficiencies of the restricted, shrinkage restricted and shrinkage pretest estimators are studied. It is found that the proposed estimators are quite robust when the sample sizes are not too large. The result of Monte Carlo study indicates that the proposed shrinkage pretest estimator is efficient than the usual estimator in a wider range.     

Improved Generalized Ratio-Cum-Product Estimation

In this paper, a generalized ratio-cum-product estimator for estimating the ratio (product) of two population means using auxiliary information on two other variables is given of which the estimators by SINGH (1969) and SHAH and SHAH (1978) are particular cases. The estimator is regeneralized when the covariance between two auxiliary variables is known.     

Estimation of the Parameters of two Parallel Regression Lines Under Uncertain Prior Information

The problem of parallelism for bi‐linear regression lines arises in many real life investigations. For two linear regression models with normal errors, the estimation of the slope as well as the intercept parameters is considered when it is apriori suspected that the two lines are parallel. Three different estimators are defined by using both the sample data and the non‐sample uncertain prior information. The relative performances of the unrestricted, restricted and preliminary test estimators are investigated based on the analysis of the bias, and risk functions under quadratic loss. An example based on a medical study is used to illustrate the method.     

A comparison of two bias-corrected covariance estimators for generalized estimating equations

Mancl and DeRouen (2001, Biometrics57, 126-134) and Kauermann and Carroll (2001, JASA96, 1387-1398) proposed alternative bias-corrected covariance estimators for generalized estimating equations parameter estimates of regression models for marginal means. The finite sample properties of these estimators are compared to those of the uncorrected sandwich estimator that underestimates variances in small samples. Although the formula of Mancl and DeRouen generally overestimates variances, it often leads to coverage of 95% confidence intervals near the nominal level even in some situations with as few as 10 clusters. An explanation for these seemingly contradictory results is that the tendency to undercoverage resulting from the substantial variability of sandwich estimators counteracts the impact of overcorrecting the bias. However, these positive results do not generally hold; for small cluster sizes (e.g., <10) their estimator often results in overcoverage, and the bias-corrected covariance estimator of Kauermann and Carroll may be preferred. The methods are illustrated using data from a nested cross-sectional cluster intervention trial on reducing underage drinking.     

Estimating the Tumour Onset Distribution Using Kernel Estimators

Kernel estimators are used to obtain new estimators for the tumour onset distribution and its density. Asymptotical properties of the estimators are studied and confidence tests are constructed.     

Temporal Patterns of Variable Relationships in Person-Oriented Research: Prediction and Auto-Association Models of Configural Frequency Analysis

Longitudinal Configural Frequency Analysis (CFA) seeks to identify, at the manifest variable level, those temporal patterns that are observed more frequently (CFA types) or less frequently (CFA antitypes) than expected with reference to a base model. This article discusses, compares, and extends two base models of interest in longitudinal data analysis. The first of these, Prediction CFA (P-CFA), is a base model that can be used in the configural analysis of both cross-sectional and longitudinal data. This model takes the associations among predictors and among criteria into account. The second base model, Auto-Association CFA (A-CFA), was specifically designed for longitudinal data. This model takes the auto-associations among repeatedly observed variables into account. Both models are extended to accommodate covariates, for example, stratification variables. Application examples are given using data from a longitudinal study of domestic violence. It is illustrated that CFA is able to yield results that are not redundant with results from log-linear modeling or multinomial regression. It is concluded that CFA is particularly useful in the context of person-oriented research.     

Estimation of Variance Components Based on a Diallel Model Involving Maternal and Maternal Interaction Effects

For a diallel model (TOPHAM, 1966) estimators of variance components are obtained by adopting the general approach outlined by SEELY (1969, 1970, 1971), SEELY and ZYSKIND (1971) and YUAN (1977) in the case of unbalanced data.     

Parameter Estimation for Partially Complete Time and Type of Failure Data

The theory of competing risks has been developed to asses a specific risk in presence of other risk factors. In this paper we consider the parametric estimation of different failure modes under partially complete time and type of failure data using latent failure times and cause specific hazard functions models. Uniformly minimum variance unbiased estimators and maximum likelihood estimators are obtained when latent failure times and cause specific hazard functions are exponentially distributed. We also consider the case when they follow Weibull distributions. One data set is used to illustrate the proposed techniques. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Estimation of Population Mean in Stratified Sampling

When stratified random sampling is used for the estimation of population mean, use of ‘Combined ratio estimator’ is well known. Some improved estimators for population mean are proposed which are better than ‘Combined ratio estimator’ and some other well known existing ones, from the point of view of bias and mean square error. An empirical illustration is given.     

Could we obtain better estimates of plot species richness from multiple‐observer plant censuses?

Question: Could we better estimate plot species richness by asking several botanists to survey the same plots and using non‐parametric estimators of richness? Location: Two French deciduous forests. Methods: Using replicated, independent censuses made by 11 professional botanists on the same eight 100‐m² forest plots, the relative performance of different richness estimators (Lincoln‐Petersen, Jackknife 1&2, Chao 1&2, Bootstrap, Chao Mth, Darroch) and the variation in their performance with the number of botanists involved (teams with two to eight botanists) were investigated. The sensitivity of these estimators to the presence of misidentifications in the data was also assessed. Results: When misidentifications are removed, Chao Mth estimators converged fastest to true richness, but none of the tested estimators correctly accounted for differences in exhaustiveness between the teams. Finally, all estimators were highly sensitive to misidentifications. Conclusions: Richness estimators are of little help in the presence of misidentifications and are ineffective at removing between‐team discrepancies, thus strongly limiting their usefulness in practice. Methods are presented to show how surveys can be designed to remove misidentifications and limit between‐team discrepancies. A sensible sampling design for 100‐m² plots in temperate forests would involve triplets of botanists and correcting data with the Chao N1. Pairs of botanists would already significantly improve the richness estimates, but such estimates would still be biased low. However, further research is needed to design new richness estimators that are more robust to observer effects.     

Configural Frequency Analysis as a Parametric Method for the Search of Types and Antitypes

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.     

A comparison of non-iterative and iterative estimators of heterogeneity variance for the standardized mortality ratio

This paper continues work presented in B?hning et al. (2002b, Annals of the Institute of Statistical Mathematics 54, 827-839, henceforth BMSRB) where a class of non-iterative estimators of the variance of the heterogeneity distribution for the standardized mortality ratio was discussed. Here, these estimators are further investigated by means of a simulation study. In addition, iterative estimators including the Clayton-Kaldor procedure as well as the pseudo-maximum-likelihood (PML) approach are added in the comparison. Among all candidates, the PML estimator often has the smallest mean square error, followed by the non-iterative estimator where the weights are proportional to the external expected counts. This confirms the theoretical result in BMSRB in which an asymptotic efficiency could be proved for this estimator (in the class of non-iterative estimators considered). Surprisingly, the Clayton-Kaldor iterative estimator (often recommended and used by practitioners) performed poorly with respect to the MSE. Given the widespread use of these estimators in disease mapping, medical surveillance, meta-analysis and other areas of public health, the results of this study might be of considerable interest.     

Robust Estimators on Laboratory Measurements of Fat and Protein in Milk

A total of 57 estimators of location were compared on data from routine laboratory measurements of fat and protein content in milk. Measurements in milk delivered from farmers to 6 different Norwegian dairies were used as a basis for a Monte Carlo study. The results indicated that the better robust estimators give an important increase in precision relative to the sample mean.     

Determination of Number and Size of Spherical Particles from Extraction Replicas

For spherical particles randomly dispersed in the space of a specimen the estimators of the parameters of the space structure from the measurements obtained from extraction replicas are given. First an arbitrary form of the probability density function f(x) of the diameter X and then the generalized RAYLEIGH and lognormal distributions of X are considered. Unbiased estimators of the space parameters and of parameters of these distributions are found. The variances of these estimators are given and unbiased estimators of these variances are determined.     

Robust estimation of population size in closed animal populations from capture-recapture experiments

In this paper the problem of finding robust estimators of population size in closed K-sample capture-recapture experiments is considered. Particular attention is paid to models where heterogeneity of capture probabilities is allowed. First, a general estimation procedure is given which does not depend on any assumptions about the form of the distribution of capture probabilities. This is followed by a detailed discussion of the usefulness of the generalized jackknife technique to reduce bias. Numerical comparisons of the bias and variance of various estimators are given. Finally, a general discussion is given with several recommendations on estimators to be used in practice.     

Asymptotic Normality of Parameter Estimators for Some Nearest Neighbour Models

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.     

Semiparametric frailty models for zero‐inflated event count data in the presence of informative dropout

Recurrent events data are commonly encountered in medical studies. In many applications, only the number of events during the follow‐up period rather than the recurrent event times is available. Two important challenges arise in such studies: (a) a substantial portion of subjects may not experience the event, and (b) we may not observe the event count for the entire study period due to informative dropout. To address the first challenge, we assume that underlying population consists of two subpopulations: a subpopulation nonsusceptible to the event of interest and a subpopulation susceptible to the event of interest. In the susceptible subpopulation, the event count is assumed to follow a Poisson distribution given the follow‐up time and the subject‐specific characteristics. We then introduce a frailty to account for informative dropout. The proposed semiparametric frailty models consist of three submodels: (a) a logistic regression model for the probability such that a subject belongs to the nonsusceptible subpopulation; (b) a nonhomogeneous Poisson process model with an unspecified baseline rate function; and (c) a Cox model for the informative dropout time. We develop likelihood‐based estimation and inference procedures. The maximum likelihood estimators are shown to be consistent. Additionally, the proposed estimators of the finite‐dimensional parameters are asymptotically normal and the covariance matrix attains the semiparametric efficiency bound. Simulation studies demonstrate that the proposed methodologies perform well in practical situations. We apply the proposed methods to a clinical trial on patients with myelodysplastic syndromes.