Boolean Models: Maximum Likelihood Estimation from Circular Clumps

This paper deals with the problem of making inferences on the maximum radius and the intensity of the Poisson point process associated to a Boolean Model of circular primary grains with uniformly distributed random radii. The only sample information used is observed radii of circular clumps (DUPAC, 1980). The behaviour of maximum likelihood estimation has been evaluated by means of Monte Carlo methods.     

A Note on Maximum Likelihood Ratio Test of No Outliers in Regression Models

A derivation of the maximum likelihood ratio test for testing no outliers in regression models is given using the method of WETHERILL (1981, pp. 106–107) for estimating the regression parameters. This method is essentially similar to the one outlined in BARNETT and LEWIS (1978, p. 263), although by our detailed derivation it is easier to see that the maximum likelihood estimate of θ of model (3) under the hypothesis that the i^th observation in an outlier is the same as that obtained from model (1) when the i^th observation is removed.     

A Modified “Best Maximum Likelihood” Estimator of Line Regression with Errors in Both Variables: An Application for Estimating Genetic Admixture

The problem of estimation when both variables are subject to error in a linear regression model has been discussed in the literature and it has wide applications in econometrics and other social sciences. In this paper we consider the relaxation of the assumption of homoscedasticity and introduce the covariance structure of errors of measurements in the analysis to obtain a Modified Best Maximum Likelihood (MBML) estimator of the regression coefficient. We also provide an application of the above modification to estimate the extent of genetic contribution of a parental population in an admixed population. With data on frequencies of “unique” African and Caucasian alleles in US Blacks, it is shown that US Blacks have 30.9·2.2 percent genes that are of Caucasian origin.     

Fitting Survival Data to a Piecewise Linear Hazard Rate in the Presence of Covariates

This paper extends the work of KODLIN (1967), who proposed a method for analyzing patient survival data wherein the hazard rate was linearly related to the survival time. The present paper extends Kodlin's model to permit maximum likelihood estimation of the parameters so that covariate effects are included and the slope and intercept parameters are allowed to change over fixed intervals of the time domain of study. An illustration of the method using multiple myeloma data is given and the results are compared with those of Kodlin's model, the Feigl-Zelen, Zippin-Armitage model, the exponential model, and Cox's proportional hazards model.     

Estimation of the mean function with panel count data using monotone polynomial splines

We study nonparametric likelihood-based estimators of the meanfunction of counting processes with panel count data using monotonepolynomial splines. The generalized Rosen algorithm, proposedby Zhang & Jamshidian (2004), is used to compute the estimators.We show that the proposed spline likelihood-based estimatorsare consistent and that their rate of convergence can be fasterthan n^1/3. Simulation studies with moderate samples show thatthe estimators have smaller variances and mean squared errorsthan their alternatives proposed by Wellner & Zhang (2000).A real example from a bladder tumour clinical trial is usedto illustrate this method.     

可交换条件下多维结构回归模型总体平均处理效应的估计

在可交换条件下,当响应变量为多维时,利用结构回归模型研究总体平均处理效应的估计。     

Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure

We propose a method to estimate the regression coefficients in a competing risks model where the cause-specific hazard for the cause of interest is related to covariates through a proportional hazards relationship and when cause of failure is missing for some individuals. We use multiple imputation procedures to impute missing cause of failure, where the probability that a missing cause is the cause of interest may depend on auxiliary covariates, and combine the maximum partial likelihood estimators computed from several imputed data sets into an estimator that is consistent and asymptotically normal. A consistent estimator for the asymptotic variance is also derived. Simulation results suggest the relevance of the theory in finite samples. Results are also illustrated with data from a breast cancer study.     

Inference for the Break Point in Segmented Regression with Application to Longitudinal Data

This paper considers inference for the break point in the segmented regression or piece‐wise regression model. Standard likelihood theory does not apply because the break point is absent under the null hypothesis. We use results by Davies for this type of non‐standard set‐up [Biometrika 64 (1977), 247–254 and 74 (1987), 33–43] to obtain a test for the null hypothesis of no break point. A confidence interval can be constructed provided replicate data are available. The methods are exemplified using two longitudinal datasets, the one from ecology, the other from pharmacology.     

Numerical non-identifiability regions of the minimal model of glucose kinetics: superiority of Bayesian estimation

The so-called minimal model (MM) of glucose kinetics is widely employed to estimate insulin sensitivity (S(I)) both in clinical and epidemiological studies. Usually, MM is numerically identified by resorting to Fisherian parameter estimation techniques, such as maximum likelihood (ML). However, unsatisfactory parameter estimates are sometimes obtained, e.g. S(I) estimates virtually zero or unrealistically high and affected by very large uncertainty, making the practical use of MM difficult. The first result of this paper concerns the mathematical demonstration that these estimation difficulties are inherent to MM structure which can expose S(I) estimation to the risk of numerical non-identifiability. The second result is based on simulation studies and shows that Bayesian parameter estimation techniques are less sensitive, in terms of both accuracy and precision, than the Fisherian ones with respect to these difficulties. In conclusion, Bayesian parameter estimation can successfully deal with difficulties of MM identification inherently due to its structure.     

Shrinkage Pre-Test Estimator of the Intercept Parameter for a Regression Model with Multivariate Student-t Errors

In the presence of an uncertain prior information about the value of the slope parameter, the estimation of the intercept parameter of a simple regression model with a multivariate Student-t error distribution is investigated. The unrestricted, restricted and shrinkage preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiences are analyzed. A maximin criterion is established, and graphs are constructed for an arbitrary number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance level is also discussed.     

Evaluating the mean frequency of responding cells in limiting dilution assays

Summary The validity of limiting dilution assays can be compromised or negated by the use of statistical methodology which does not consider all issues surrounding the biological process. This study critically evaluates statistical methods for estimating the mean frequency of responding cells in multiple sample limiting dilution assays. We show that methods that pool limiting dilution assay data, or samples, are unable to estimate the variance appropriately. In addition, we use Monte Carlo simulations to evaluate an unweighted mean of the maximum likelihood estimator, an unweighted mean based on the jackknife estimator, and a log transform of the maximum likelihood estimator. For small culture replicate size, the log transform outperforms both unweighted mean procedures. For moderate culture replicate size, the unweighted mean based on the jackknife produces the most acceptable results. This study also addresses the important issue of experimental design in multiple sample limiting dilution assays. In particular, we demonstrate that optimization of multiple sample limiting dilution assays is achieved by increasing the number of biological samples at the expense of repeat cultures.     

Testing the Equality of the Intra‐Subject Treatment Covariance Matrices in a Crossover Study

In a 2 × 2 crossover bioavailability study, the sets of estimates of the pharmacokinetic parameters quite often have a symmetric covariance structure between the two treatments. For testing the equality of the intra‐subject covariance matrices for the two treatments in such studies, we suggest in this paper some statistical tests. When the response vectors are bivariate, we propose an exact test. Since the statistical procedures depend on the assumption of a symmetric covariance structure between the two treatments, we put forth some statistical tests for this assumption. We then apply the discussed tests to real data from a crossover bioavailability trial.