Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information

Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.     

Optimal estimation of reactivity ratios for acrylamide/acrylic acid copolymerization

Reactivity ratios for the important acrylamide (AAm)/acrylic acid (AAc) copolymerization system exhibit considerable scatter in previously published literature, and therefore, there is a need for more definitive values for these reactivity ratios. An appropriate methodology, based on the error‐in‐variables‐model (EVM) framework along with a direct numerical integration procedure, is applied in order to determine reliable reactivity ratios. The reliability of the results is confirmed with extensive and independent replication. Furthermore, via an EVM‐based criterion for the design of experiments using mechanistic models, optimal feed compositions are calculated, and from these optimal reactivity ratios are estimated for the first time (r_AAm = 1.33 and r_AAc = 0.23) based on information from the full conversion range. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4819–4827     

Local Sensitivity Analysis in Estimation Problems

This article deals with the problem of local sensitivity analysis, that is, how sensitive are the results of a statistical analysis to changes in the data? A general methodology of sensitivity analysis is applied to some statistical problems. The proposed methods are applicable to any statistical problem that can be expressed as an optimization problem or that involves solving a system of equations. As some particular examples, the methodology is applied to the maximum likelihood method, the standard and constrained methods of moments and the standard and constrained probability weighted moments methods. Unlike the standard method of moments, the constrained method of moments ensures that the obtained estimates are always consistent with the data. Closed analytical formulas for the calculation of these local sensitivities are derived. The obtained sensitivities include: (a) the objective function sensitivities to data points and (b) the sensitivities of the estimated parameters to data points. The derived formulas for the sensitivities are based on recent results in the area of mathematical programming. Several examples of parameter estimation problems are used to illustrate the methodology.     

Gibbs Sampling with Diffuse Proper Priors: A Valid Approach to Data-Driven Inference?

Abstract

This article demonstrates by example that the use of the Gibbs sampler with diffuse proper priors can lead to inaccurate posterior estimates. Our results show that such inaccuracies are not merely limited to small sample settings.     

Profitability in the car industry: New measures for estimating targets and target directions

In this paper we study the profitability of car manufacturers in relation to industry-wide profitability targets such as industry averages. Specifically we are interested in whether firms adjust their profitability in the direction of these targets, whether it is possible to detect any such change, and, if so, what the precise nature is of these changes.     

Large sample prediction intervals for future geometric mean a comparative study

This paper provides simulation comparisons among the performance of 11 possible prediction intervals for the geometric.mean of a Pareto distribution with parameters (αB, ). Six different procedures were used to obtain these intervals , namely; true inter -val , pivotal interval , maximum likelihood estimation interval, centrallimit teorem interval, variance stabilizing interval and a mixture of the above intervals . Some of these intervals are valid if the observed sample size m,are large , others are valid if both, n and the future sample size m, are large. Some of these intervals require a knowledge of α or B, while others do not. The simulation validation and efficiency study shows that intervals depending on the MLE's are the best. The second best intervalsare those obtained through pivotal methods or variance stabilization transformation. The third group of intervals is that which depends on the central limit theorem when λ is known. There are two intervals which proved to be unacceptable under any criterion.     

Precise Radiometry: Some Recent Aspects of Fruitful Interaction with Atomic Physics

Modern radiometric analytics demands a complex consideration of nuclear and electron shell processes, if more pretentious aims are envisaged. As an example the small variation of decay rates of radionuclides presents possibilities for information on chemical situations of decaying atoms. In principle this phenomenon is well known since many years, but now the situation is such that, e.g. in ^99mTc internal conversion, a full agreement of the difficult experiments and the respective theory was established. The secondary emission of X-rays as a consequence of high excitation of electron shells in combination with nuclear transitions supplies another example for a methodical progress of radiometry. Investigations on ⁵¹Cr as an electron capture nuclide have shown that chemically induced variations of the K_α to K_β X-ray intensity ratio is at least qualitatively understood.     

Signal modeling using the gradient search

This letter presents a new method for continuous signal modeling. Firstly, the continuous signal can be represented as a function of the trigonometric functional extension (Fourier series). Fourier series of the signal are parameterized by the fundamental frequency and unknown parameters. Then, the gradient-based iterative identification algorithm is derived, for estimating parameters of the signal model with known and unknown frequencies, separately. Finally, the simulation results indicate that the proposed algorithm is effective.