Statistical inference for time-varying ARCH processes

In this paper the class of ARCH$(\infty)$ models is generalized to the nonstationary class of ARCH$(\infty)$ models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation ``locally stationary ARCH$(\infty)$ process.'' The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH$(p)$ processes ($p<\infty$) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.Comment: Published at http://dx.doi.org/10.1214/009053606000000227 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A recursive online algorithm for the estimation of time-varying ARCH parameters

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an estimator of the parameter at time point $t$. The sampling properties of this estimator are studied in a non-stationary context -- in particular, asymptotic normality and an expression for the bias due to non-stationarity are established. By running two recursive online algorithms in parallel with different step sizes and taking a linear combination of the estimators, the rate of convergence can be improved for parameter curves from H\"{o}lder classes of order between 1 and 2.Comment: Published at http://dx.doi.org/10.3150/07-BEJ5009 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The quantile spectral density and comparison based tests for nonlinear time series

In this paper we consider tests for nonlinear time series, which are motivated by the notion of serial dependence. The proposed tests are based on comparisons with the quantile spectral density, which can be considered as a quantile version of the usual spectral density function. The quantile spectral density 'measures' sequential dependence structure of a time series, and is well defined under relatively weak mixing conditions. We propose an estimator for the quantile spectral density and derive its asympototic sampling properties. We use the quantile spectral density to construct a goodness of fit test for time series and explain how this test can also be used for comparing the sequential dependence structure of two time series. The method is illustrated with simulations and some real data examples

Mainstreaming Mentally Retarded Children Through Inclusive Education Under SSA - A Case Study

‘Sarva  Shiksha  Abhiyan’ is a national govt. scheme for primary education. Under this scheme, all physically & mentally challenged students of age gr. 6-14 were brought under inclusive education section.  Access and retention in school was challenge for MR student. Parents were not ready to send them in school as it was meaningless for the children. But, schooling not only retained but developed them optimally through formal education and connected with society. A case study of girl child is presented here

Ocular Manifestations of Blood Dyscrasias

The ocular manifestations of blood dyscrasias are distinctive and are attributed to high vascularity and to the unique anatomy of the eye. They may be the initial finding of the underlying pathology or discovered during the course of the disease. This study is undertaken to describe the incidence and various types of manifestations seen in blood dyscrasias and to assess the diagnostic and prognostic importance as well as the resolution of lesions with treatment. This study was done on 100 patients of various age groups with different types of hematological disorders over a period of two years from Nov 2015 to Aug 2016 in the Department of Ophthalmology, Govt. Stanley Hospital. Of 100 patients, 63 patients had hematological malignancies, Non-Hodgkin Lymphomas being the single largest group, 34 patients with anemia and 3 patients had bleeding disorders.31 patients presented primarily to the ophthalmologist with defective vision as the most common symptom and following evaluation were diagnosed to have blood dyscrasias, thus emphasising the need for thorough ocular screening. 41% patients examined for ocular findings showed retinopathy, most commonly in the form of retinal hemorrhages followed by cotton-wool spots. The lesions show resolution with treatment in 90% of cases in both malignant and non- malignant disorders. Thus ocular manifestations are a frequent occurrence in blood dyscrasias and should be evaluated with a high index of suspicion when found

Structure and Dynamics of Charged Colloidal Disks in Colloid-Polymer Mixtures

Complex fluid mixtures of colloids and polymers are extensively used in several conventional and emerging technological applications. Particles self-assemble under different conditions to form colloidal glasses and gels and it often leads to the development of unusual viscoelastic features. In the case of aspherical particles, shape anisotropy and physical aging effects add to the existing complexities so the implementation of a strategic formulation method to improve performance and stability remains a critical challenge. This thesis presents a comprehensive analysis of particle interactions in mixtures of charged disk-shaped colloids and weakly-adsorbing polymers like poly(ethylene oxide) (PEO). Here, we discuss the behavior of suspensions containing laponite® and PEO of molecular weights (Mw) varying between 4.6 and 300 kg/mol and at concentrations within the dilute through concentrated regimes. Techniques such as rheology, light (DLS) and x-ray scattering (XPCS and USAXS) were used to understand and characterize the effect of chain number and length on the macroscopic behavior, microstructure and dynamics of particles in these colloid-polymer mixtures. Laponite® suspensions gradually transition from a homogeneous fluid to a structurally arrested phase. With the addition of polymers, rheological measurements show that in addition to the typical re-entrant behavior observed in the dilute polymer phase, there is another onset of stabilization close to the semi dilute polymer regime. While DLS and XPCS results show three different regimes in the microstructural dynamics along these transitions, USAXS measurements indicate the presence of only finite sized ellipsoidal structures that are directed by polymer-particle interactions. We believe that the arrested phase is a glassy system as no large scale structure is observed. On the other hand, adding high Mw PEO results in the formation of strong colloidal gels where laponite® particles act as junctions in the colloid-polymer network. Nanometer to micron-sized clusters form with the addition of PEO chains larger than the minimum required for polymer-clay bridging. Increasing the concentration of PEO changes the density of clusters and this directly affects the bulk elasticity of the material. The results thus serve as an excellent benchmark to understand how to effectively formulate an anisotropic colloid-polymer mixture for an application

Novel Regulatory Mechanisms and Functions of MUC4 in Pancreatic Cancer

Mucins are high molecular weight glycoproteins and have critical functions in protecting epithelial cells from a myriad of cellular stress. However, mucins are expressed aberrantly under cancer conditions that allow tumors to progress and metastasize. Among many mucins, Mucin 4 (MUC4) serves as one of the top-differentially expressed proteins in pancreatic cancer (PC), however, the precise mechanism responsible for its aberrant expression is still not clear. The evolving view of cancer as an energetic and growing ecosystem underlines an intricate interplay between cancer and its microenvironment. In spite of being recognized as one of the most critical oncogenic proteins in PC, MUC4 regulation in terms of micro-environmental stress has not been determined. In my dissertation research, I have investigated the role of PC microenvironment in the regulation of MUC4. From my studies, I have demonstrated that MUC4 stability is significantly reduced due to hypoxia-mediated induction of reactive oxygen species (ROS), which promotes autophagy by inhibiting pAkt/mTORC1 pathway. Hypoxia-mediated degradation of MUC4 provides necessary metabolites to ensure the survival of highly stressed PC cells. The longstanding model of cancer development involves that presence of cytokines can trigger chronic inflammation and impact tumor development, including PC. In addition to cytokines, bile acids (BA) facilitated chronic inflammation has shown to induce intestinal metaplasia, but their role in PC is still elusive. Elevated levels of BA (p In addition to the regulation, I have pinpointed the novel functional roles of MUC4 in determining the fate of receptor tyrosine kinases (RTKs) in PC. Multiple studies have associated MUC4 overexpression with increased stability of RTKs for sustained proliferation; however, no studies have so far highlighted the implicated mechanism. I have demonstrated that the presence of MUC4 leads to increased internalization and recycling of EGFR and HER2 to the plasma membrane compared to MUC4 silenced PC cells. Mechanistically, the impact of MUC4 on RTKs trafficking is associated with its ability to regulate the activity of RAB5A, which is known to catalyze the rate-limiting step in receptor internalization. Lastly, I have detected the presence of MUC4 in pancreatic cancer associated stellate cells (PaSC). This was an unexpected finding given that MUC4 is normally expressed in the epithelial cells. These results indicate towards the involvement of MUC4 expression in determining the activation status of PaSC and provide us an additional strong rationale to therapeutically target MUC4. Altogether, in my dissertation research, I have elucidated the novel regulatory mechanisms and functions of MUC4 in PC condition