Search results for " function"
showing 10 items of 9395 documents
Partition function of the trigonometric SOS model with reflecting end
2010
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Uniform measure density condition and game regularity for tug-of-war games
2018
We show that a uniform measure density condition implies game regularity for all 2 < p < ∞ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for the associated stopping times and density estimates for the sum of independent and identically distributed random vectors. peerReviewed
Empirical investigation of stock price dynamics in an emerging market
1999
Abstract We study the development of an emerging market – the Budapest Stock Exchange – by investigating the time evolution of some statistical properties of heavily traded stocks. Moving quarter by quarter over a period of two and a half years we analyze the scaling properties of the standard deviation of intra-day log-price changes. We observe scaling using both seconds and ticks as units of time. For the investigated stocks a Levy shape is a good approximation to the probability density function of tick-by-tick log-price changes in each quarter: the index of the distribution follows an increasing trend, suggesting it could be used as a measure of market efficiency.
Stock market dynamics and turbulence: parallel analysis of fluctuation phenomena
1997
Abstract We report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state. Specifically, we systematically compare (i) the statistical properties of the S&P 500 cash index recorded during the period January 84–December 89 with (ii) the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the Connecticut Agricultural Research Station. We find non-Gaussian statistics, and intermittency, for both processes (i) and (ii) but the deviation from a Gaussian probability density function are different for stock market dynamics and turbu…
k-Step shape estimators based on spatial signs and ranks
2010
In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in Dümbgen (1998) and Oja and Randles (2004) and further studied for example in Sirkiä et al. (2009). The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the es…
Clustering of spatial point patterns
2006
Spatial point patterns arise as the natural sampling information in many problems. An ophthalmologic problem gave rise to the problem of detecting clusters of point patterns. A set of human corneal endothelium images is given. Each image is described by using a point pattern, the cell centroids. The main problem is to find groups of images corresponding with groups of spatial point patterns. This is interesting from a descriptive point of view and for clinical purposes. A new image can be compared with prototypes of each group and finally evaluated by the physician. Usual descriptors of spatial point patterns such as the empty-space function, the nearest distribution function or Ripley's K-…
Prior-based Bayesian information criterion
2019
We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one ov…
Multitype spatial point patterns with hierarchical interactions.
2001
Multitype spatial point patterns with hierarchical interactions are considered. Here hierarchical interaction means directionality: points on a higher level of hierarchy affect the locations of points on the lower levels, but not vice versa. Such relations are common, for example, in ecological communities. Interacting point patterns are often modeled by Gibbs processes with pairwise interactions. However, these models are inherently symmetric, and the hierarchy can be acknowledged only when interpreting the results. We suggest the following in allowing the inclusion of the hierarchical structure in the model. Instead of regarding the pattern as a realization of a stationary multivariate po…
Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous Diffusion
2017
We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly in $\theta$ and $T$ for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $n^{-1/2}$ for the shape parameter and $n^{-3/2}$ for the periodicity which generalizes known results about LAN when either $\theta$ or $T$ is assumed to be known.
Generalized Symmetry Models for Hypercubic Concordance Tables
2000
Summary Frequency data obtained classifying a sample of 'units' by the same categorical variable repeatedly over 'components', can be arranged in a hypercubic concordance table (h.c.t.). This kind of data naturally arises in a number of different areas such as longitudinal studies, studies using matched and clustered data, item-response analysis, agreement analysis. In spite of the substantial diversity of the mechanisms that can generate them, data arranged in a h.c.t. can all be analyzed via models of symmetry and quasi-symmetry, which exploit the special structure of the h.c.t. The paper extends the definition of such models to any dimension, introducing the class of generalized symmetry…