Profile likelihood-based confidence interval for the dispersion parameter in count data

The importance of the dispersion parameter in counts occurring in toxicology, biology, clinical medicine, epidemiology, and other similar studies is well known. A couple of procedures for the construction of confidence intervals (CIs) of the dispersion parameter have been investigated, but little attention has been paid to the accuracy of its CIs. In this paper, we introduce the profile likelihood (PL) approach and the hybrid profile variance (HPV) approach for constructing the CIs of the dispersion parameter for counts based on the negative binomial model. The non-parametric bootstrap (NPB) approach based on the maximum likelihood (ML) estimates of the dispersion parameter is also considered. We then compare our proposed approaches with an asymptotic approach based on the ML and the restricted ML (REML) estimates of the dispersion parameter as well as the parametric bootstrap (PB) approach based on the ML estimates of the dispersion parameter. As assessed by Monte Carlo simulations, the PL approach has the best small-sample performance, followed by the REML, HPV, NPB, and PB approaches. Three examples to biological count data are presented.     

Designing flavors for mass consumption

Abstract

In the increasingly competitive market for processed foods after the Second World War, flavor assumed new importance in product design and development as companies struggled to gain advantage and entice repeat buyers. This paper examines the flavor profile, a novel sensory evaluation method developed by chemists at Arthur D. Little, Inc. (ADL), the storied Cambridge, MA consulting firm. Introduced in 1949, the flavor profile claimed to offer a reliable way of measuring and describing the subjective sensory qualities of products. Drawing extensively on archival material, I document the circumstances surrounding the development of the flavor profile at ADL, examine its uses, and consider the conditions that led to its widespread adoption by the food industry. By considering the flavor profile as both a scientific instrument for flavor measurement, and a practical tool for flavor design and development, I hope to illuminate a dark corner in the history of food industrialization: the values, ideologies, and contingencies that shaped how foods were made to taste in the postwar period.     

A new approach to estimating shelf‐life

The current approach to the estimation of shelf‐life and the determination of the label shelf‐life as detailed in the International Conference on Harmonisation guidelines to industry is presented. The shortcomings of the status quo are explained and a possible solution is offered, which gives rise to a new definition of shelf‐life. Several methods for calculating a label shelf‐life are presented and investigated using a simulation study. Recommendations to adopt the new definition and to increase sample sizes are made. Copyright © 2004 John Wiley & Sons, Ltd.     

An explanation of generalized profile likelihoods

Let X, T, Y be random vectors such that the distribution of Y conditional on covariates partitioned into the vectors X = x and T = t is given by f(y; x, ), where = (, (t)). Here is a parameter vector and (t) is a smooth, real–valued function of t. The joint distribution of X and T is assumed to be independent of and . This semiparametric model is called conditionally parametric because the conditional distribution f(y; x, ) of Y given X = x, T = t is parameterized by a finite dimensional parameter = (, (t)). Severini and Wong (1992. Annals of Statistics 20: 1768–1802) show how to estimate and (·) using generalized profile likelihoods, and they also provide a review of the literature on generalized profile likelihoods. Under specified regularity conditions, they derive an asymptotically efficient estimator of and a uniformly consistent estimator of (·). The purpose of this paper is to provide a short tutorial for this method of estimation under a likelihood–based model, reviewing results from Stein (1956. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley, pp. 187–196), Severini (1987. Ph.D Thesis, The University of Chicago, Department of Statistics, Chicago, Illinois), and Severini and Wong (op. cit.).     

The Enhanced Double Digest Problem for DNA Physical Mapping

The double digest problem is a common NP-hard approach to constructing physical maps of DNA sequences. This paper presents a new approach called the enhanced double digest problem. Although this new problem is also NP-hard, it can be solved in linear time in certain theoretically interesting cases.     

Likelihood-Based Inference for the Shape Parameter of a Two Parameter Weibull Distribution

Based on a Type 2 censored sample, we use the likelihood-based approach to draw likelihood inference on the shape parameter gamma of a two-parameter Weibull distribution. In particular, we derive the profile, conditional and marginal likelihoods of gamma. Numerical results along with some concluding remarks regarding the use of likelihood-based methods for inference are provided.     

欧姆形对称型双螺杆的参数化建模与数值模态分析

针对已有螺杆型线方程参数化建模过程复杂、时间长的问题。根据型线的设计原则与要求,利用坐标系转换,构 建了一种易于参数化建模且密封性、啮合性好的欧姆(Q)形对称型端面型线方程,方程的滚圆相对于节圆的公转角￡,根 据螺杆传动几何关系推导并界定范围;以Visual Basic程序设计语言为开发工具,三维软件SolidWorks为二次开发平台, 实现了螺旋套的参数化实体建模;建立了螺杆的固有特性分析模型,用ANSYS软件对螺杆的轴承处进行了刚性与弹性 约束下的模态分析,并考虑了不同的弹性单元刚度对固有频率的影响。结果表明：弹性约束下螺杆的固有频率明显降 低,2种约束下的振型一致,弹性单元的刚度对弹性约束下的固有频率没有影响。文中研究为双螺杆泵型线改进设计及 螺杆模态分析提供理论依据,大大提高设计效率     

Profile Hellinger distance estimation

The successful application of the Hellinger distance approach to fully parametric models is well known. The corresponding optimal estimators, known as minimum Hellinger distance (MHD) estimators, are efficient and have excellent robustness properties [Beran R. Minimum Hellinger distance estimators for parametric models. Ann Statist. 1977;5:445–463]. This combination of efficiency and robustness makes MHD estimators appealing in practice. However, their application to semiparametric statistical models, which have a nuisance parameter (typically of infinite dimension), has not been fully studied. In this paper, we investigate a methodology to extend the MHD approach to general semiparametric models. We introduce the profile Hellinger distance and use it to construct a minimum profile Hellinger distance estimator of the finite-dimensional parameter of interest. This approach is analogous in some sense to the profile likelihood approach. We investigate the asymptotic properties such as the asymptotic normality, efficiency, and adaptivity of the proposed estimator. We also investigate its robustness properties. We present its small-sample properties using a Monte Carlo study.     

Maximum likelihood estimators for ARMA and ARFIMA models: a Monte Carlo study

We analyze by simulation the properties of two time domain and two frequency domain estimators for low-order autoregressive fractionally integrated moving-average Gaussian models, ARFIMA (p,d,q). The estimators considered are the exact maximum likelihood for demeaned data (EML) the associated modified profile likelihood (MPL) and the Whittle estimator with (WLT) and without tapered data (WL). Length of the series is 100. The estimators are compared in terms of pile-up effect, mean square error, bias, and empirical confidence level. The tapered version of the Whittle likelihood turns out to be a reliable estimator for ARMA and ARFIMA models. Its small losses in performance in case of ‘well-behaved’ models are compensated sufficiently in more ‘difficult’ models. The modified profile likelihood is an alternative to the WLT but is computationally more demanding. It is either equivalent to the EML or more favorable than the EML. For fractionally integrated models, particularly, it dominates clearly the EML. The WL has serious deficiencies for large ranges of parameters, and so cannot be recommended in general. The EML, on the other hand, should only be used with care for fractionally integrated models due to its potential large negative bias of the fractional integration parameter. In general, one should proceed with caution for ARMA(1,1) models with almost canceling roots, and, in particular, in case of the EML and the MPL for inference in the vicinity of a moving-average root of +1.