Fitting Generalized Hyperbolic processes - New insights for generating initial values

The fitting of Lévy processes is an important field of interest in both option pricing and risk management. In literature, a large number of fitting methods requiring adequate initial values at the start of the optimization procedure exists. A so-called simplified method of moments (SMoM) generates by assuming a symmetric distribution these initial values for the Variance Gamma process, whereby the idea behind can be easily transferred to the Normal Inverse Gaussian process. However, the characteristics of the Generalized Hyperbolic process prevent such an easy adaption. Therefore, we provide by applying a Taylor series approximation for the modified Bessel function of the third kind, a Tschirnhaus transformation and a symmetric distribution assumption, a SMOM for the Generalized Hyperbolic distribution. Our simulation study compares the results of our SMoM with the results of the maximum likelihood estimation. The results show that our proposed approach is an appropriate and useful way for estimating Generalized Hyperbolic process parameters and significantly reduces estimation time.     

Optimal designs of multivariate synthetic |S| control chart based on median run length

The multivariate synthetic generalized sample variance |S| (synthetic |S|) chart is a combination of the |S| sub-chart and the conforming run length sub-chart. A procedure for optimal designs of the synthetic |S| chart, based on the median run length (MRL), for both zero and steady-state modes are provided by minimizing the out-of-control MRL. The comparative results show that the synthetic |S| chart performs better than the standard |S| chart for detecting shifts in the covariance matrix of a multivariate normally distributed process, in terms of the MRL. An example is given to illustrate the operation of the synthetic |S| chart.     

Estimation for the parameters of the generalized half-normal distribution

As an applicable and flexible lifetime model, the two-parameter generalized half-normal (GHN) distribution has been received wide attention in the field of reliability analysis and lifetime study. In this paper maximum likelihood estimates of the model parameters are discussed and we also proposed corresponding bias-corrected estimates. Unweighted and weighted least squares estimates for the parameters of the GHN distribution are also presented for comparison purpose. Moreover, the likelihood ratio test is provided as complementary. Simulation study and illustrative examples are provided to compare the performance of the proposed methods.     

Quasi-likelihood Bridge estimators for high-dimensional generalized linear models

In this article, we consider the variable selection and estimation for high-dimensional generalized linear models when the number of parameters diverges with the sample size. We propose a penalized quasi-likelihood function with the bridge penalty. The consistency and the Oracle property of the quasi-likelihood bridge estimators are obtained. Some simulations and a real data analysis are given to illustrate the performance of the proposed method.     

On the analysis of unbalanced two-level supersaturated designs via generalized linear models

Supersaturated designs (SSDs) are factorial designs in which the number of experimental runs is smaller than the number of parameters to be estimated in the model. While most of the literature on SSDs has focused on balanced designs, the construction and analysis of unbalanced designs has not been developed to a great extent. Recent studies discuss the possible advantages of relaxing the balance requirement in construction or data analysis of SSDs, and that unbalanced designs compare favorably to balanced designs for several optimality criteria and for the way in which the data are analyzed. Moreover, the effect analysis framework of unbalanced SSDs until now is restricted to the central assumption that experimental data come from a linear model. In this article, we consider unbalanced SSDs for data analysis under the assumption of generalized linear models (GLMs), revealing that unbalanced SSDs perform well despite the unbalance property. The examination of Type I and Type II error rates through an extensive simulation study indicates that the proposed method works satisfactorily.     

A multiple indicator approach to blockmodeling signed networks

Regardless of whether the focus is on algebraic structures, elaborating role structures or the simple delineation of concrete social structures, generalized blockmodeling faces a pair of vulnerabilities. One is sensitivity to poor quality of the relational data and the other is a risk of over fitting blockmodels to the details of specific networks. Over fitting blockmodels can lead to multiple equally well fitting partitions where choices cannot be made between them on a principled basis. This paper presents a method of tackling these problems by viewing (when possible) observed social relations as multiple indicators of an underlying affect dimension. Quadratic assignment methods using matching coefficients, product moment correlations and Goodman and Kruskal's gamma are used to assess the appropriateness of using the sum of observed relations as input for applying generalized blockmodeling. Data for four groups are used to show the value of this approach within which multiple equally well fitting blockmodels for single relations are replaced by unique (or near-unique) partitions of the summed data. This strategy is located also within a broader problem of blockmodeling three-dimensional networks data and suggestions are made for future work.     

Weighted empirical adaptive variance estimators for correlated data regression

Estimating equations based on marginal generalized linear models are useful for regression modelling of correlated data, but inference and testing require reliable estimates of standard errors. We introduce a class of variance estimators based on the weighted empirical variance of the estimating functions and show that an adaptive choice of weights allows reliable estimation both asymptotically and by simulation in finite samples. Connections with previous bootstrap and jackknife methods are explored. The effect of reliable variance estimation is illustrated in data on health effects of air pollution in King County, Washington.     

Relative efficiency of first difference estimator in panel data regression with serially correlated error components

We consider the pooled cross-sectional and time series regression model when the disturbances follow a serially correlated one-way error components. In this context we discovered that the first difference estimator for the regression coefficients is equivalent to the generalized least squares estimator irrespective of the particular form of the regressor matrix when the disturbances are generated by a first order autoregressive process where the autocorrelation is close to unity.     

Bootstrapping the renewal spacings processes

We define the generalized bootstrapped version of the empirical and quantile renewal spacing processes. We show that the asymptotic theory of the renewal spacings processes holds for the bootstrap version.     

Modelling spatial intensity for replicated inhomogeneous point patterns in brain imaging

Summary.  Pharmacological experiments in brain microscopy study patterns of cellular activ- ation in response to psychotropic drugs for connected neuroanatomic regions. A typical ex- perimental design produces replicated point patterns having highly complex spatial variability. Modelling this variability hierarchically can enhance the inference for comparing treatments. We propose a semiparametric formulation that combines the robustness of a nonparametric kernel method with the efficiency of likelihood-based parameter estimation. In the convenient framework of a generalized linear mixed model, we decompose pattern variation by kriging the intensities of a hierarchically heterogeneous spatial point process. This approximation entails discretizing the inhomogeneous Poisson likelihood by Voronoi tiling of augmented point patterns. The resulting intensity-weighted log-linear model accommodates spatial smoothing through a reduced rank penalized linear spline. To correct for anatomic distortion between subjects, we interpolate point locations via an isomorphic mapping so that smoothing occurs relative to common neuroanatomical atlas co-ordinates. We propose a criterion for choosing the degree and spatial locale of smoothing based on truncating the ordered set of smoothing covariates to minimize residual extra-dispersion. Additional spatial covariates, experimental design factors, hierarchical random effects and intensity functions are readily accommodated in the linear predictor, enabling comprehensive analyses of the salient properties underlying replicated point patterns. We illustrate our method through application to data from a novel study of drug effects on neuronal activation patterns in the brain of rats.