Bayesian Estimation and Statistical Analysis of Risk Measurements

The Bayesian model are established for the VaR and related risk measurements. The relationship between VaR and other risk measurements including expect shortfall, tail condition expectation and conditional value at risk are discussed. Furthermore, the Bayesian estimates and Bayesian predictors of these risk measurement are derived. Thirdly, the consistency and asymptotic normality in the exponential risk model are proved. Finally, the numerical simulation method is used to verify the convergence rate under different sample sizes.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.     

Data-Adaptive Estimation of Time-Varying Spectral Densities

This article introduces a data-adaptive nonparametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The performance of these nonparametric estimators, however, depends crucially on the smoothing bandwidths that need to be specified in both time and frequency direction. As an alternative and extension to traditional bandwidth selection methods, we propose an iterative algorithm for constructing localized smoothing kernels data-adaptively. The main idea, inspired by the concept of propagation-separation, is to determine for a point in the time-frequency plane the largest local vicinity over which smoothing is justified by the data. By shaping the smoothing kernels nonparametrically, our method not only avoids the problem of bandwidth selection in the strict sense but also becomes more flexible. It not only adapts to changing curvature in smoothly varying spectra but also adjusts for structural breaks in the time-varying spectrum. Supplementary materials, including the R package tvspecAdapt containing an implementation of the routine, are available online.     

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     

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.