Journal of Iranian Statistical Society
Volume:11 Issue: 2, 2012

In this paper، multivariate skew-normal distribution is em- ployed for analyzing an outcome based dropout model for repeated mea- surements with non-random dropout in skew regression data sets. A probit regression is considered as the conditional probability of an ob- servation to be missing given outcomes. A simulation study of using the proposed methodology and comparing it with a semi-parametric method، GEE، is provided. The standardized bias is used for compari- son of different approaches. Furthermore، for investigation of efficiency of the methodology two applications are analyzed where observed infor- mation matrix is used to find the variances of the parameter estimates. In one of the applications a sensitivity analysis is also performed to in- vestigate the change on the response model’s parameter estimates due to perturbation of drop-out model’s parameter of interest.

The image recognotion and the classification of objects according to the images are more in focus of interests، especially in medicine. A mathematical procedure allows us، not only to evaluate the amount of data per se، but also ensures that each image is pro- cessed similarly. Here in this study، we propose the power of shape analysis، in conjunction with neural networks for reducing white noise instead of searching an optimal metric، to support the user in his eval- uation of MRI of renal tumors. Therapy of renal tumors in childhood bases on therapy optimizing SIOP (Society of Pediatric Oncology and Hematology) -study protocols in Europe. The most frequent tumor is the nephroblastoma. Other tumor entities in the retroperitoneum are clear cell sarcoma، renal cell carcinoma and extrarenal tumors، espe- cially neuroblastoma. Radiological diagnosis is produced with the helpof cross sectional imaging methods (computertomography CT or Mag- netic Resonance Images MRI). Our research is the first mathematical approach on MRI of retroperitoneal tumors (n=108). We use MRI in 3 planes and evaluate their potential to differentiate other types of tumor by Statistical Shape Analysis. Statistical shape Analysis is a methology for analyzing shapes in the presence of randomness. It allows to study two- or more dimensional objects، summarized according to key points called landmarks، with a possible correction of size and position of the object. To get the shape of an object without information about posi- tion and size، centralisation and standardisation procedures are used in some metric space. This approach provides an objective methodology for classification whereas even today in many applications the decision for classifying according to the appearance seems at most intuitive. We determine the key points or three dimensional landmarks of retroperitoneal tumors in childhood by using the edges of the platonic body (C60) and test the difference between the groups (nephroblastoma versus non-nephroblastoma).

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The distribution of the positive definite quadratic forms involved in the representations is approximated by means of gamma-type distributions. We are also considering general ratios of quadratic forms، as well as ratios whose denominator involves an idempotent matrix and ratios for which the quadratic form in the denominator is positive definite. Additionally، an approximation to the density of ratios of quadratic expressions in singular normal vectors is being proposed. The results are applied to the Durbin-Watson statistic and Burg’s estimator، both of which are expressible as ratios of quadratic forms.

The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper، we introduce an modification of the INAR (1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structural mathematical properties of the process comparing with classical INAR (1). Also، the superiority of the model in contrast with the INAR (1) is shown by some real time series.

In this paper، we introduce a goodness of fit test for expo- nentiality based on Lin-Wong divergence measure. In order to estimate the divergence، we use a method similar to Vasicek’s method for estimat- ing the Shannon entropy. The critical values and the powers of the test are computed by Monte Carlo simulation. It is shown that the proposed test are competitive with other tests of exponentiality based on entropy.

A case of the matrix Kummer relation of Herz (1955) based on the Pearson VII type matrix model is derived in this paper. As a con- sequence، the polynomial Pearson VII configuration density is obtained and this sets the corresponding exact inference as a solvable aspect in shape theory. An application in postcode recognition، including a nu- merical comparison between the exact polynomial and the truncated configuration density، is given at the end of the paper.