Functional summary statistics for point processes on the sphere with an application to determinantal point processes

We study point processes on $\mathbb S^d$, the $d$-dimensional unit sphere $\mathbb S^d$, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case $d=2$. The first part studies reduced Palm distributions and functional summary statistics, including nearest neighbour functions, empty space functions, and Ripley's and inhomogeneous $K$-functions. The second part partly discusses the appealing properties of determinantal point process (DPP) models on the sphere and partly considers the application of functional summary statistics to DPPs. In fact DPPs exhibit repulsiveness, but we also use them together with certain dependent thinnings when constructing point process models on the sphere with aggregation on the large scale and regularity on the small scale. We conclude with a discussion on future work on statistics for spatial point processes on the sphere

CDW-Exciton Condensate Competition and a Condensate Driven Force

We examine the competition between the charge-density wave (CDW) instability and the excitonic condensate (EC) in spatially separated layers of electrons and holes. The CDW and the EC order parameters (OPs), described by two different mechanisms and hence two different transition temperatures $T^{CDW}_c$ and $T^{EC}_c$, are self-consistently coupled by a microscopic mean field theory. We discuss the results in our model specifically focusing on the transition-metal dichalcogenides which are considered as the most typical examples of strongly coupled CDW/EC systems with atomic layer separations where the electronic energy scales are large with the critical temperatures in the range $T^{EC}_c \sim T^{CDW}_c \sim 100-200 K$. An important consequence of this is that the excitonic energy gap, hence the condensed free energy, vary with the layer separation resulting in a new type of force ${\cal F}_{EC}$. We discuss the possibility of this force as the possible driver of the structural lattice deformation observed in some TMDCs with a particular attention on the $1 {\it T}$-$TiSe_2$ below $200 K$.Comment: 8 pages, 5 figure

Has inflation targeting increased predictive power of term structure about future inflation: evidence from an emerging market ?

This paper contributes to the vast literature on the predictive power of term structure about future inflation, by focusing on an emerging market case. The following important result emerged in our paper: Monetary policy change is an important determinant of the relationship between term structure and inflation to the extent that even the existence of the relationship critically depends on the nature of monetary policy regime. In our case, the change in monetary policy is associated with the beginning of the implementation of an inflation targeting (IT) regime. While, before IT regime, the information in term structure does not provide any predictive power for future inflation, this phenomenon seems to be completely reversed after IT. Since the implementation of IT, term structure of interest rates has seemed to gain considerable forecasting power for future inflation.Term Structure of Interest Rate, Structural Break, Inflation, Monetary Policy, Inflation Targeting

The role of Regime Shifts in the Term Structure of Interest Rates: Further evidence from an Emerging Market

In this paper, we investigate the interrelations among Turkish interest rates with different maturities by using a regime switching Vector Error Correction (VECM) model. We find a long run equilibrium relationship among interest rates with various maturities. Furthermore we conclude that term structure dynamics exhibit significant nonlinearity. Forecasting experiment also reveals that the nonlinear term structure models do fare better than other linear specifications. However, we cannot conclude that interest rate adjustments are made in an asymmetric way in the long run equilibrium.Term Structure of Interest Rates, Regime Switching, Forecasting, Foreacast Evaluation, Cointegration

Score, Pseudo-Score and Residual Diagnostics for Spatial Point Process Models

We develop new tools for formal inference and informal model validation in the analysis of spatial point pattern data. The score test is generalized to a "pseudo-score" test derived from Besag's pseudo-likelihood, and to a class of diagnostics based on point process residuals. The results lend theoretical support to the established practice of using functional summary statistics, such as Ripley's $K$-function, when testing for complete spatial randomness; and they provide new tools such as the compensator of the $K$-function for testing other fitted models. The results also support localization methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.Comment: Published in at http://dx.doi.org/10.1214/11-STS367 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org