Statistical inference for olfactometer data

Summary.  Olfactometer experiments are used to determine the effect of odours on the behaviour of organisms such as insects or nematodes, and typically result in data comprising many groups of small overdispersed counts. We develop a non-homogeneous Markov chain model for data from olfactometer experiments with parasitoid wasps and discuss a relation with the Dirichlet–multinomial distribution. We consider the asymptotic relative efficiencies of three different observation schemes and give an analysis of data intended to shed light on the effect of previous experience of odours in the wasps.     

Approximate self consistency for middle-censored data

Middle censoring refers to data that becomes unobservable if it falls within a random interval. The lifetime distribution of such data is defined via the self-consistency equation. We propose an approximation to this distribution function for which an estimator and its asymptotic properties are very easy to establish.     

Statistical model and inference for pharmacokinetic data

In this paper, we consider a statistical model for the drug concentration–time profiles that are obtained in a pharmacokinetic (PK) study when the drug is orally administered. In the proposed statistical PK model, the subject-specific concentration–time curve is described by the one-compartment PK model with first-order absorption and elimination. Moreover, a multivariate generalized gamma distribution is developed for the joint distribution of the drug concentrations that are repeatedly measured from the same subject. We then construct confidence intervals for the subject–exposure parameters which provide a further insight into the individual exposure of the drug under study. The proposed statistical PK model and the associated inference are then applied to illustrate a real data set. A simulation study is also implemented to investigate the performances of the coverage probability and expected length of the proposed confidence intervals. Finally, we give conclusions and discussions on the application of the proposed procedures.     

The nonparametric maximum likelihood estimator for middle-censored data

In this note, we consider data subjected to middle censoring where the variable of interest becomes unobservable when it falls within an interval of censorship. We demonstrate that the nonparametric maximum likelihood estimator (NPMLE) of distribution function can be obtained by using Turnbull's (1976) EM algorithm or self-consistent estimating equation (Jammalamadaka and Mangalam, 2003) with an initial estimator which puts mass only on the innermost intervals. The consistency of the NPMLE can be established based on the asymptotic properties of self-consistent estimators (SCE) with mixed interval-censored data ( [Yu et al., 2000] and [Yu et al., 2001]).     

Statistical inference in dynamic panel data models

Anderson and his collaborators have made seminal contributions to inference with instrumental variables and to dynamic panel data models. We review these contributions and the extensive economic and statistical literature that these contributions spawned. We describe our recent work in these two areas, presenting new approaches to (a) making valid inferences in the presence of weak instruments and (b) instrument and model selection for dynamic panel data models. Both approaches use empirical likelihood and resampling. For inference in the presence of weak instruments, our approach uses model averaging to achieve asymptotic efficiency with strong instruments but maintain valid inferences with weak instruments. For instrument and model selection, our approach aims at choosing valid instruments that are strong enough to be useful.     

Statistical inference for varying-coefficient partially linear errors-in-variables models with missing data

Abstract

The purpose of this paper is twofold. First, we investigate estimations in varying-coefficient partially linear errors-in-variables models with covariates missing at random. However, the estimators are often biased due to the existence of measurement errors, the bias-corrected profile least-squares estimator and local liner estimators for unknown parametric and coefficient functions are obtained based on inverse probability weighted method. The asymptotic properties of the proposed estimators both for the parameter and nonparametric parts are established. Second, we study asymptotic distributions of an empirical log-likelihood ratio statistic and maximum empirical likelihood estimator for the unknown parameter. Based on this, more accurate confidence regions of the unknown parameter can be constructed. The methods are examined through simulation studies and illustrated by a real data analysis.     

Statistical inference for oscillation processes

ABSTRACT

A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a generalized state space model. Identifiability of the model is proved and a method for statistical inference based on a particle smoother and a nonparametric EM algorithm is developed. In particular, the oscillation pattern and the unobserved phase process are estimated. The proposed algorithms are computationally efficient and their performance is assessed through simulations and an application to human electrocardiogram recordings.     

Analysis of middle-censored data with exponential lifetime distributions

Recently Jammalamadaka and Mangalam [2003. Non-parametric estimation for middle censored data. J. Nonparametric Statist. 15, 253–265] introduced a general censoring scheme called the “middle-censoring” scheme in non-parametric set up. In this paper we consider this middle-censoring scheme when the lifetime distribution of the items is exponentially distributed and the censoring mechanism is independent and non-informative. In this set up, we derive the maximum likelihood estimator and study its consistency and asymptotic normality properties. We also derive the Bayes estimate of the exponential parameter under a gamma prior. Since a theoretical construction of the credible interval becomes quite difficult, we propose and implement Gibbs sampling technique to construct the credible intervals. Monte Carlo simulations are performed to evaluate the small sample behavior of the techniques proposed. A real data set is analyzed to illustrate the practical application of the proposed methods.     

Statistical inference for queueing models

The paper briefly describes methods and results in the statistical analysis of queueing systems     

Statistical inference on censored data for targeted clinical trials under enrichment design

For the traditional clinical trials, inclusion and exclusion criteria are usually based on some clinical endpoints; the genetic or genomic variability of the trial participants are not totally utilized in the criteria. After completion of the human genome project, the disease targets at the molecular level can be identified and can be utilized for the treatment of diseases. However, the accuracy of diagnostic devices for identification of such molecular targets is usually not perfect. Some of the patients enrolled in targeted clinical trials with a positive result for the molecular target might not have the specific molecular targets. As a result, the treatment effect may be underestimated in the patient population truly with the molecular target. To resolve this issue, under the exponential distribution, we develop inferential procedures for the treatment effects of the targeted drug based on the censored endpoints in the patients truly with the molecular targets. Under an enrichment design, we propose using the expectation–maximization algorithm in conjunction with the bootstrap technique to incorporate the inaccuracy of the diagnostic device for detection of the molecular targets on the inference of the treatment effects. A simulation study was conducted to empirically investigate the performance of the proposed methods. Simulation results demonstrate that under the exponential distribution, the proposed estimator is nearly unbiased with adequate precision, and the confidence interval can provide adequate coverage probability. In addition, the proposed testing procedure can adequately control the size with sufficient power. On the other hand, when the proportional hazard assumption is violated, additional simulation studies show that the type I error rate is not controlled at the nominal level and is an increasing function of the positive predictive value. A numerical example illustrates the proposed procedures. Copyright © 2013 John Wiley & Sons, Ltd.     

Statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data

In this article, the statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data is discussed. The estimation of the parameters for Gompertz distribution is obtained using maximum likelihood method (MLE) and Bayesian method under three different loss functions. We also proved the existence and uniqueness of the MLE. The one-sample Bayesian prediction intervals are obtained. The work is done for different values of the parameters. We apply the Monto Carlo simulation to compare the proposed methods, also an example is discussed to construct the Prediction intervals.     

Statistical inference for multiple change-point models

In this article, we propose a new technique for constructing confidence intervals for the mean of a noisy sequence with multiple change-points. We use the weighted bootstrap to generalize the bootstrap aggregating or bagging estimator. A standard deviation formula for the bagging estimator is introduced, based on which smoothed confidence intervals are constructed. To further improve the performance of the smoothed interval for weak signals, we suggest a strategy of adaptively choosing between the percentile intervals and the smoothed intervals. A new intensity plot is proposed to visualize the pattern of the change-points. We also propose a new change-point estimator based on the intensity plot, which has superior performance in comparison with the state-of-the-art segmentation methods. The finite sample performance of the confidence intervals and the change-point estimator are evaluated through Monte Carlo studies and illustrated with a real data example.     

Statistical inference for the size-biased Weibull distribution

In this paper, statistical inferences for the size-biased Weibull distribution in two different cases are drawn. In the first case where the size r of the bias is considered known, it is proven that the maximum-likelihood estimators (MLEs) always exist. In the second case where the size r is considered as an unknown parameter, the estimating equations for the MLEs are presented and the Fisher information matrix is found. The estimation with the method of moments can be utilized in the case the MLEs do not exist. The advantage of treating r as an unknown parameter is that it allows us to perform tests concerning the existence of size-bias in the sample. Finally a program in Mathematica is written which provides all the statistical results from the procedures developed in this paper.     

Statistical inference for a single-index varying-coefficient model

We investigate the estimators of parameters of interest for a single-index varying-coefficient model. To estimate the unknown parameter efficiently, we first estimate the nonparametric component using local linear smoothing, then construct an estimator of parametric component by using estimating equations. Our estimator for the parametric component is asymptotically efficient, and the estimator of nonparametric component has asymptotic normality and optimal uniform convergence rate. Our results provide ways to construct confidence regions for the involved unknown parameters. The finite-sample behavior of the new estimators is evaluated through simulation studies, and applications to two real data are illustrated.     

Statistical inference for the quintile share ratio

In recent years, the Quintile Share Ratio (or QSR) has become a very popular measure of inequality. In 2001, the European Council decided that income inequality in European Union member states should be described using two indicators: the Gini Index and the QSR. The QSR is generally defined as the ratio of the total income earned by the richest 20% of the population relative to that earned by the poorest 20%. Thus, it can be expressed using quantile shares, where a quantile share is the share of total income earned by all of the units up to a given quantile. The aim of this paper is to propose an improved methodology for the estimation and variance estimation of the QSR in a complex sampling design framework. Because the QSR is a non-linear function of interest, the estimation of its sampling variance requires advanced methodology. Moreover, a non-trivial obstacle in the estimation of quantile shares in finite populations is the non-unique definition of a quantile. Thus, two different conceptions of the quantile share are presented in the paper, leading us to two different estimators of the QSR. Regarding variance estimation, [Osier, 2006] and [Osier, 2009] proposed a variance estimator based on linearization techniques. However, his method involves Gaussian kernel smoothing of cumulative distribution functions. Our approach, also based on linearization, shows that no smoothing is needed. The construction of confidence intervals is discussed and a proposition is made to account for the skewness of the sampling distribution of the QSR. Finally, simulation studies are run to assess the relevance of our theoretical results.     

Statistical inference for reciprocal gamma diffusion process

We consider the problem of parameter estimation for an ergodic diffusion with reciprocal gamma invariant distribution. Spectral decomposition of the transition density of such a Markov process is presented in terms of a finite number of discrete eigenfunctions (Bessel polynomials) and eigenfunctions related to a continuous part of the spectrum of the negative infinitesimal generator of reciprocal gamma diffusion. Consistency and asymptotical normality of proposed estimators are presented. Based on the Stein equation for reciprocal gamma diffusion and Bessel polynomials, the hypothesis testing procedure is considered.     

Statistical inference for Sobol pick-freeze Monte Carlo method

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs. We study asymptotic and non-asymptotic properties of two estimators of Sobol indices. These properties are applied to significance tests and estimation by confidence intervals.     

Statistical inference for heteroscedastic semi-varying coefficient EV models

This paper proposes an estimation procedure for a class of semi-varying coefficient regression models when the covariates of the linear part are subject to measurement errors. Initial estimates for the regression and varying coefficients are first constructed by the profile least-squares procedure without input from heteroscedasticity, a bias-corrected kernel estimate for the variance function then is proposed, which in turn is used to define re-weighted bias-corrected estimates of the regression and varying coefficients. Large sample properties of the proposed estimates are thoroughly investigated. The finite-sample performance of the proposed estimates is assessed by an extensive simulation study and an application to the Boston housing data set. The simulation results show that the re-weighted bias-corrected estimates outperform the initial estimates and the naive estimates.