Inference Under Convex Cone Alternatives for Correlated Data

In this research, inferential theory for hypothesis testing under general convex cone alternatives for correlated data is developed. While there exists extensive theory for hypothesis testing under smooth cone alternatives with independent observations, extension to correlated data under general convex cone alternatives remains an open problem. This long-pending problem is addressed by (1) establishing that a "generalized quasi-score" statistic is asymptotically equivalent to the squared length of the projection of the standard Gaussian vector onto the convex cone and (2) showing that the asymptotic null distribution of the test statistic is a weighted chi-squared distribution, where the weights are "mixed volumes" of the convex cone and its polar cone. Explicit expressions for these weights are derived using the volume-of-tube formula around a convex manifold in the unit sphere. Furthermore, an asymptotic lower bound is constructed for the power of the generalized quasi-score test under a sequence of local alternatives in the convex cone. Applications to testing under order restricted alternatives for correlated data are illustrated.Comment: 31 page

On large-sample estimation and testing via quadratic inference functions for correlated data

Hansen (1982) proposed a class of "generalized method of moments" (GMMs) for estimating a vector of regression parameters from a set of score functions. Hansen established that, under certain regularity conditions, the estimator based on the GMMs is consistent, asymptotically normal and asymptotically efficient. In the generalized estimating equation framework, extending the principle of the GMMs to implicitly estimate the underlying correlation structure leads to a "quadratic inference function" (QIF) for the analysis of correlated data. The main objectives of this research are to (1) formulate an appropriate estimated covariance matrix for the set of extended score functions defining the inference functions; (2) develop a unified large-sample theoretical framework for the QIF; (3) derive a generalization of the QIF test statistic for a general linear hypothesis problem involving correlated data while establishing the asymptotic distribution of the test statistic under the null and local alternative hypotheses; (4) propose an iteratively reweighted generalized least squares algorithm for inference in the QIF framework; and (5) investigate the effect of basis matrices, defining the set of extended score functions, on the size and power of the QIF test through Monte Carlo simulated experiments.Comment: 32 pages, 2 figure

Impacts of Climate Change on a Spatially Distributed Water Balance in the Gaza Strip, Palestine

As Mediterranean coastal area, the Gaza Strip is likely to be at high risk for water scarcity due to climate change, thus hydrological studies are necessary. This study aims to investigate the impacts of climate change on water balance elements of the Gaza Strip and generate future projections. The Water Balance computer model (WetSPASS) integrated with the GIS was used for simulating the hydrological cycle for the Gaza Strip coastal aquifer in this study. The mean annual simulated evapotranspiration were 157.34 mm/year, 156.46 mm/year, 151.85 mm/year and 131.44 mm/year for baseline, year 2020, year 2050 and year 2080 respectively. While  34.88 mm /year, 32.35 mm /year, 26.73 mm /year and 18.71 mm /year were the mean annual  simulated surface runoff for baseline, year 2020, year 2050 and year 2080 respectively. The  mean annual simulated groundwater recharge were 125.33 mm/year, 105.07 mm/year, 64.44 mm/year and 20.14 mm/year for baseline, year 2020, year 2050 and year 2080 respectively. The mean simulated interception values were 8.31 mm/year, 7.71 mm/year, 6.41 mm/year and 4.56 mm/year for baseline, 2020, 2050 and 2080 respectively. The main conclusion from projected water balance elements is that Gaza Strip will be in a condition of severe water scarcity risk. Keywords: water balance, climate change, WetSPASS, Gaza Stri

Modelling Potential Impacts of Climate Change on Groundwater of the Gaza Coastal Aquifer from Ensemble of Global Climate Model Projections

The Gaza Strip is subjected to considerable impacts of climate change that may adversely affect the groundwater resource. A decrease in annual precipitation as well as an increase in temperatures are projected from an ensemble of global climate models. In this study, the impact of climate change on groundwater resources in Gaza coastal aquifer was evaluated. Regional groundwater flow simulations were made by means of a three-dimensional numerical model. The model was calibrated by adjusting model input parameters until a best fit was achieved between simulated and observed water levels. Simulated groundwater levels compared favorably with observed mean groundwater levels measured in observation wells. SEAWAT groundwater transient model with simulated climate change data input without any adaption pumping scenario was developed in order to determine the impacts of climate change on groundwater of the Gaza coastal aquifer. An effective management scenario was developed and examined by the same groundwater transient model. The scenario was generated to adapt with climate change conditions by developing new water resources and managing pumping rates. The results indicated that lack of water is expected to be a problem in the future. Also, the generated and examined solution scenario is a strategic solution for about a thirty year period. Keywords: Gaza Strip, climate change, groundwater, management, modeling, seawater intrusio

Projection of Future Climate by Multi-Model Median Approach under GIS Environment along the Gaza Strip, Palestine

Climate changes over the Gaza strip area as a semi-arid area is a major factor that affects the developing strategic plans for water sector. This study aims to determine the future climate changes over Gaza strip. Fossil energy intensive (A1F1) with high sensitivity is the emission scenario that was used for the prediction process. The median assembly approach was used to get the representative results from multi General Circulation Model (GCM) outputs. The predicted mean annual temperatures for years 2020, 2050 and 2080 were 20.66 oC, 22.48 oC and 25.08 oC respectively, While 0.85 oC, 2.67 oC and 5.28 oC were the mean annual changes from baseline period for years 2020, 2050 and 2080 respectively.  The predicted mean annual precipitation for years 2020, 2050 and 2080 were 294.68 mm/year, 243.70 mm/year and 170.82 mm/year respectively, Hence -7.48, -23.98 and -46.37 mm/year were the predicted mean annual precipitation changes from baseline period for years 2020, 2050 and 2080 respectively. The mean annual sea level rise for baseline period was 1.097 cm, in the other hand 9.04 cm, 28.84 cm and 59.85 cm were the predicted mean sea level rise values for years 2020, 2050 and 2080 respectively. Keywords: Climate Change, Gaza Strip, Climate projection, GCM, Emission scenario

Evidence of anomalous dispersion of the generalized sound velocity in glasses

The dynamic structure factor, S(Q,w), of vitreous silica, has been measured by inelastic X-ray scattering in the exchanged wavevector (Q) region Q=4-16.5 nm-1 and up to energies hw=115 meV in the Stokes side. The unprecedented statistical accuracy in such an extended energy range allows to accurately determine the longitudinal current spectra, and the energies of the vibrational excitations. The simultaneous observation of two excitations in the acoustic region, and the persistence of propagating sound waves up to Q values comparable with the (pseudo-)Brillouin zone edge, allow to observe a positive dispersion in the generalized sound velocity that, around Q=5 nm-1, varies from 6500 to 9000 m/s: this phenomenon was never experimentally observed in a glass.Comment: 5 pages, 3 figures. To appear in Phys. Rev.