A new local estimation method for single index models for longitudinal data

Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They are very useful for longitudinal data analysis. In this paper, we develop a new efficient estimation procedure for single index models with longitudinal data, based on Cholesky decomposition and local linear smoothing method. Asymptotic normality for the proposed estimators of both the parametric and nonparametric parts will be established. Monte Carlo simulation studies show excellent finite sample performance. Furthermore, we illustrate our methods with a real data example.     

New Results for Computing Blaker’s Exact Confidence Interval for One Parameter Discrete Distributions

The authors state new general results for computing Blaker’s exact confidence interval limits for usual one-parameter discrete distributions. Specific results for implementing an accurate and fast algorithm are made explicit for the binomial, negative binomial, Poisson and hypergeometric model.     

Are Private Schools Better Than Public Schools? Appraisal for Ireland by Methods for Observational Studies

In observational studies the assignment of units to treatments is not under control. Consequently, the estimation and comparison of treatment effects based on the empirical distribution of the responses can be biased since the units exposed to the various treatments could differ in important unknown pretreatment characteristics, which are related to the response. An important example studied in this article is the question of whether private schools offer better quality of education than public schools. In order to address this question we use data collected in the year 2000 by OECD for the Programme for International Student Assessment (PISA). Focusing for illustration on scores in mathematics of 15-years old pupils in Ireland, we find that the raw average score of pupils in private schools is higher than of pupils in public schools. However, application of a newly proposed method for observational studies suggests that the less able pupils tend to enroll in public schools, such that their lower scores is not necessarily an indication of bad quality of the public schools. Indeed, when comparing the average score in the two types of schools after adjusting for the enrollment effects, we find quite surprisingly that public schools perform better on average. This outcome is supported by the methods of instrumental variables and latent variables, commonly used by econometricians for analyzing and evaluating social programs.     

Non‐parametric estimation for time-dependent AUC

The area under the receiver operating characteristic (ROC) curve (AUC) is one of the commonly used measure to evaluate or compare the predictive ability of markers to the disease status. Motivated by an angiographic coronary artery disease (CAD) study, our objective is mainly to evaluate and compare the performance of several baseline plasma levels in the prediction of CAD-related vital status over time. Based on censored survival data, the non-parametric estimators are proposed for the time-dependent AUC. The limiting Gaussian processes of the estimators and the estimated asymptotic variance–covariance functions enable us to further construct confidence bands and develop testing procedures. Applications and finite sample properties of the proposed estimation methods and inference procedures are demonstrated through the CAD-related death data from the British Columbia Vital Statistics Agency and Monte Carlo simulations.     

Pilot–pivotal trials for average bioequivalence

Before carrying out a full scale bioequivalence trial, it is desirable to conduct a pilot trial to decide if a generic drug product shows promise of bioequivalence. The purpose of a pilot trial is to screen test formulations, and hence small sample sizes can be used. Based on the outcome of the pilot trial, one can decide whether or not a full scale pivotal trial should be carried out to assess bioequivalence. This article deals with the design of a pivotal trial, based on the evidence from the pilot trial. A two-stage adaptive procedure is developed in order to determine the sample size and the decision rule for the pivotal trial, for testing average bioequivalence using the two one-sided test (TOST). Numerical implementation of the procedure is discussed in detail, and the required tables are provided. Numerical results indicate that the required sample sizes could be smaller than that recommended by the FDA for a single trial, especially when the pilot study provides strong evidence in favor of bioequivalence.     

Subset selection procedures for ΔP-superior populations

In some ranking and selection problems it is reasonable to consider any population which is inferior but sufficiently close to the best (t-th best) as acceptable. Under this assumption, this paper studies classes of procedures to meet two possible goals. A and B. Goal A is to select a subset which contains only good populations, while Goal B is of a screening nature and requires selection of a subset of size not exceeding m (1 ≤ m ≤ k) and containing at least one good population. In each case results loading to the determination of the sample size required to attain the goals above with prespecified probability are obtained. Properties of the procedures are discussed.     

Robust inference for Birnbaum–Saunders regressions

We propose a robust likelihood approach for the Birnbaum–Saunders regression model under model misspecification, which provides full likelihood inferences about regression parameters without knowing the true random mechanisms underlying the data. Monte Carlo simulation experiments and analysis of real data sets are carried out to illustrate the efficacy of the proposed robust methodology.     

Hypothesis testing for Fisher–Snedecor diffusion

We consider the problem of testing the hypothesis on marginal distribution of ergodic diffusion with Fisher–Snedecor invariant distribution, to be called Fisher–Snedecor diffusion. We propose a GMM approach to testing this statistical hypothesis where the moment condition is based on eigenfunctions of the diffusion infinitesimal generator—Fisher–Snedecor polynomials. Statistical test is observed in two different settings: (1) for known values of parameters of the process; (2) for consistent moment based estimators of parameters. Results are illustrated in a short simulation study.     

Additive–multiplicative rates model for recurrent events

Recurrent events are frequently encountered in biomedical studies. Evaluating the covariates effects on the marginal recurrent event rate is of practical interest. There are mainly two types of rate models for the recurrent event data: the multiplicative rates model and the additive rates model. We consider a more flexible additive–multiplicative rates model for analysis of recurrent event data, wherein some covariate effects are additive while others are multiplicative. We formulate estimating equations for estimating the regression parameters. The estimators for these regression parameters are shown to be consistent and asymptotically normally distributed under appropriate regularity conditions. Moreover, the estimator of the baseline mean function is proposed and its large sample properties are investigated. We also conduct simulation studies to evaluate the finite sample behavior of the proposed estimators. A medical study of patients with cystic fibrosis suffered from recurrent pulmonary exacerbations is provided for illustration of the proposed method.     

Optimal row–column design for three treatments

The A-optimality problem is solved for three treatments in a row–column layout. Depending on the numbers of rows and columns, the requirements for optimality can be decidedly counterintuitive: replication numbers need not be as equal as possible, and trace of the information matrix need not be maximal. General rules for comparing 3×3$3\times 3$ information matrices for their A-behavior are also developed, and the A-optimality problem is also solved for three treatments in simple block designs.     

Sup–Hellinger consistency for local density regression

Abstract

This article studies the consistency of a local density regression model under a supremum Hellinger distance. Such model applies a piecewise structure where a mixture of Dirichlet process model (MDP) is assigned as the fixed density on each piece. The piecewise construction is a straightforward way to establish sup–Hellinger consistency in a regression settings. A specific piecewise density example is presented in a simulation study.     

Simultaneous estimation of λs for poisson distributions

Consider the problem of simultaneously estimating an integral power of the parameters of POISSOK populations using independent samples. Let the loss be the sum of quadratic losses for the components. An estimator which is better than the unbiased esti¬mator is obtained     

Robust inference for the stress–strength reliability

We address the problem of robust inference about the stress–strength reliability parameter R = P(X < Y), where X and Y are taken to be independent random variables. Indeed, although classical likelihood based procedures for inference on R are available, it is well-known that they can be badly affected by mild departures from model assumptions, regarding both stress and strength data. The proposed robust method relies on the theory of bounded influence M-estimators. We obtain large-sample test statistics with the standard asymptotic distribution by means of delta-method asymptotics. The finite sample behavior of these tests is investigated by some numerical studies, when both X and Y are independent exponential or normal random variables. An illustrative application in a regression setting is also discussed.     

A new approach for disclosure control in the IAB establishment panel—multiple imputation for a better data access

For micro-datasets considered for release as scientific or public use files, statistical agencies have to face the dilemma of guaranteeing the confidentiality of survey respondents on the one hand and offering sufficiently detailed data on the other hand. For that reason, a variety of methods to guarantee disclosure control is discussed in the literature. In this paper, we present an application of Rubin’s (J. Off. Stat. 9, 462–468, 1993) idea to generate synthetic datasets from existing confidential survey data for public release.We use a set of variables from the 1997 wave of the German IAB Establishment Panel and evaluate the quality of the approach by comparing results from an analysis by Zwick (Ger. Econ. Rev. 6(2), 155–184, 2005) with the original data with the results we achieve for the same analysis run on the dataset after the imputation procedure. The comparison shows that valid inferences can be obtained using the synthetic datasets in this context, while confidentiality is guaranteed for the survey participants.     

Prediction Techniques for Box–Cox Regression Models

This article reviews several techniques useful for forming point and interval predictions in regression models with Box-Cox transformed variables. The techniques reviewed—plug-in, mean squared error analysis, predictive likelihood, and stochastic simulation—take account of nonnormality and parameter uncertainty in varying degrees. A Monte Carlo study examining their small-sample accuracy indicates that uncertainty about the Box–Cox transformation parameter may be relatively unimportant. For certain parameters, deterministic point predictions are biased, and plug-in prediction intervals are also biased. Stochastic simulation, as usually carried out, leads to badly biased predictions. A modification of the usual approach renders stochastic simulation predictions largely unbiased.     

Efficient likelihood-free Bayesian Computation for?household epidemics

Considerable progress has been made in applying Markov chain Monte Carlo (MCMC) methods to the analysis of epidemic data. However, this likelihood based method can be inefficient due to the limited data available concerning an epidemic outbreak. This paper considers an alternative approach to studying epidemic data using Approximate Bayesian Computation (ABC) methodology. ABC is a simulation-based technique for obtaining an approximate sample from the posterior distribution of the parameters of the model and in an epidemic context is very easy to implement. A new approach to ABC is introduced which generates a set of values from the (approximate) posterior distribution of the parameters during each simulation rather than a single value. This is based upon coupling simulations with different sets of parameters and we call the resulting algorithm coupled ABC. The new methodology is used to analyse final size data for epidemics amongst communities partitioned into households. It is shown that for the epidemic data sets coupled ABC is more efficient than ABC and MCMC-ABC.