Modelling Variability in the Branching Structure of Strawberry Inflorescences

The branching structure of inflorescences of the cultivated strawberry ( Fragaria × ananassa Duch.) is very variable. This paper demonstrates that some aspects of this variability are well described by a simple stochastic model of branching that has two adjustable parameters. The model is shown to provide a good fit to data from a set of almost 700 inflorescences of the cultivar Elsanta, collected over two successive years. For one parameter the maximum likelihood estimator is a moment estimator which is fully efficient even if the detailed branching structure of the inflorescences is not recorded. This parameter provides a convenient summary of branching vigour. The maximum likelihood estimator of the second parameter must be determined iteratively and can be quite inefficient unless the full branching structure is recorded. The model demonstrates that branching structure is affected by the order in which inflorescences emerge on the plant.     

Simplified Estimating Functions for Diffusion Models with a High-dimensional Parameter

We consider estimating functions for discretely observed diffusion processes of the following type: for one part of the parameter of interest we propose to use a simple and explicit estimating function of the type studied by Kessler (2000); for the remaining part of the parameter we use a martingale estimating function. Such an approach is particularly useful in practical applications when the parameter is high-dimensional. It is also often necessary to supplement a simple estimating function by another type of estimating function because only the part of the parameter on which the invariant measure depends can be estimated by a simple estimating function. Under regularity conditions the resulting estimators are consistent and asymptotically normal. Several examples are considered in order to demonstrate the idea of the estimating procedure. The method is applied to two data sets comprising wind velocities and stock prices. In one example we also propose a general method for constructing diffusion models with a prescribed marginal distribution which have a flexible dependence structure.     

The role of tobacco taxes in starting and quitting smoking: Duration analysis of British data

The annual 5% increase in tobacco taxes in real terms proposed in the recent White Paper on smoking has reaffirmed the commitment of successive UK Governments to above-inflation increases in tobacco taxation to encourage people to stop smoking. This paper presents evidence on the determinants of starting and quitting smoking by using data from the British Health and Lifestyle Survey and is the first to identify tax elasticities for starting and quitting smoking using British data. Self-reported individual smoking histories are coupled with a long time series for the tax rate on cigarettes to construct a longitudinal data set. Estimates are obtained for the effect of above-inflation tax rises on the age of starting smoking and the number of years of smoking. The estimates of the tax elasticity of the age of starting smoking are 0.16 for men and 0.08 for women. The estimates of the tax elasticity of quitting are −0.60 for men and −0.46 for women. These are robust to different specifications.     

Parameter Estimation Through Weighted Least-Squares Rank Regression with Specific Reference to the Weibull and Gumbel Distributions

Probability plots are often used to estimate the parameters of distributions. Using large sample properties of the empirical distribution function and order statistics, weights to stabilize the variance in order to perform weighted least squares regression are derived. Weighted least squares regression is then applied to the estimation of the parameters of the Weibull, and the Gumbel distribution. The weights are independent of the parameters of the distributions considered. Monte Carlo simulation shows that the weighted least-squares estimators outperform the usual least-squares estimators totally, especially in small samples.     

An Approximate Bayesian Marginal Likelihood Approach for Estimating Finite Mixtures

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This article gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior model, a computationally efficient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a finite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data examples show that this novel stochastic approximation and simulated annealing procedure compares favorably with existing methods.     

Basu's Lemma and Goodness-of-Fit Tests

In this paper we develop a technique that is useful in goodness of fit problems with nuisance location and scale parameters. Using Basu's lemma, we transform the sample so that it is independent of the nuisance parameters. The technique will be illustrated by several examples, a discussion of the efficiency of the proposed procedure, and some concluding remarks will given.     

A review of classic non-asymptotic methods for comparing two proportions by means of independent sampLES

The 2 × 2 tables used to present the data in an experiment for comparing two proportions by means of two observations of two independent binomial distributions may appear simple but are not. The debate about the best method to use is unending, and has divided statisticians into practically irreconcilable groups. In this article, all the available non-asymptotic tests are reviewed (except the Bayesian methodology). The author states which is the optimal (for each group), referring to the tables and programs that exist for them, and contrast the arguments used by supporters of each of the options. They also sort the tangle of solutions into "families", based on the methodology used and/or prior assumptions, and point out the most frequent methodological mistakes committed when comparing the different families.     

Asymptotically Optimal Nonparametric Empirical Bayes Via Predictive Recursion

An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This article presents a general notion of empirical Bayes asymptotic optimality, and it is shown that PR-based procedures satisfy this property under certain conditions. As an application, the problem of in-season prediction of baseball batting averages is considered. There the PR-based empirical Bayes rule performs well in terms of prediction error and ability to capture the distribution of the latent features.