Range Dependent Data Research Articles

Global Mean Sea Level. Time Trends and Persistence with Long Range Dependent Data

Global mean sea level data are examined in this work by looking at the presence of time trends in the context of long memory or long range dependent processes. By looking at both seasonal signals retained and seasonal signals removed data from 1992 to 2020, the results show that the two series display significant time trend coefficients and high levels of persistence.

Functional central limit theorems for the Nelson–Aalen and Kaplan–Meier estimators for dependent stationary data

We derive process limit distribution results for the Nelson–Aalen estimator of a hazard function and for the Kaplan–Meier estimator of a distribution function, under different dependence assumptions. The data are assumed to be right censored observations of a stationary time series. We treat weakly dependent as well as long range dependent data, and allow for qualitative differences in the dependence for the censoring times versus the time of interest.

Fractional Brownian motion time-changed by gamma and inverse gamma process

Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kind of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures.

Multivariate generalized linear-statistics of short range dependent data

Generalized linear ($GL$-) statistics are defined as functionals of an $U$-quantile process and unify different classes of statistics such as $U$-statistics and $L$-statistics. We derive a central limit theorem for $GL$-statistics of strongly mixing sequences and arbitrary dimension of the underlying kernel. For this purpose we establish a limit theorem for $U$-statistics and an invariance principle for $U$-processes together with a convergence rate for the remaining term of the Bahadur representation. An application is given by the generalized median estimator for the tail-parameter of the Pareto distribution, which is commonly used to model exceedances of high thresholds. We use subsampling to calculate confidence intervals and investigate its behaviour under independence and under strong mixing in simulations.

Iterative Shannon Entropy - a Methodology to Quantify the Information Content of Value Range Dependent Data Distributions. Application to Descriptor and Compound Selectivity Profiling.

We introduce an entropy-based methodology, Iterative Shannon entropy (ISE), to quantify the information contained in molecular descriptors and compound selectivity data sets taking data spread directly into account. The method is applicable to determine the information content of any value range dependent data distribution. An analysis of descriptor information content has been carried out to explore alternative binning schemes for entropy calculation. Using this entropic measure we have profiled 153 compound selectivity data sets for combinations of 68 target proteins belonging to 10 target families. With the ISE measure, we aim to assign high information content to compound data sets that span a wide range of selectivity values and different selectivity relationships and hence correspond to more than one biological phenotype. Target families with high average entropy scores are identified. For members of these families, active compounds display highly differentiated selectivity profiles.

A general asymptotic scheme for inference under order restrictions

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various pointwise limit distributions are obtained, and the rate of convergence depends on the self similarity properties and on the rate of convergence of the processes considered.

Phenomenological and global optimization inversion

This paper discusses geoacoustic inversion results based on benchmark range-dependent data using SAGA, a global inversion package, and using phenomenological inversions. In phenomenological inversions, physical and signal-processing approaches are used to enhance the data to extract specific features. The global optimization approach is carried out on complex-valued vertical array data, transmission loss data, and reverberation data. The importance of checking the solution is emphasized by inspecting the match with the data and the error estimates and by checking the solution using data that has not been used in constructing the solution. The results show that we are able to estimate the geoacoustic parameters and that these parameters could be used to predict the field for different frequencies and/or source-receiver geometry than used in the inversion.

Geoacoustic inversion of range-dependent data with added gaussian noise

A rotated coordinates inversion algorithm is used on subsets of the Inversion Techniques 2001 Geoacoustic Workshop data, to which white Gaussian noise is added. The resulting data sets are equivalent to noisy broad-band signals received on a horizontal line array (HLA) during a single integration time interval. The inversions are performed using a technique called systematic decoupling using rotated coordinates (SDRC), which expands the original idea of rotated coordinates by using multiple sets of rotated coordinates, each corresponding to a different set of bounds, to systematically decouple the unknowns in a series of efficient simulated annealing inversions. The cost function minimized in the inversion is based on the coherent broad-band correlation between data and model cross spectra, which increases the coherence gain of the signal relative to incoherent noise. Using the coherent broad-band cost function with sparse HLA-like data sets, the SDRC inversion method yields good estimates for the sensitive environmental parameters for signal-to-noise ratios as low as -15 dB.

Monotone Regression and Density Function Estimation at a Point of Discontinuity

Pointwise limit distribution results are given for the isotonic regression estimator at a point of discontinuity. The cases treated are independent data, - and f -mixing data and subordinated Gaussian long range dependent data. Pointwise limit results for the nonparametric maximum likelihood estimator of a monotone density are given at a point of discontinuity, for independent data. The limit distributions are non-standard and differ from the ones obtained for differentiable regression and density functions.

A low cost approximation for a controlled load service in a bridged/switched LAN environment

This paper reports the design and the implementation results of a Controlled Load service in a bridged/switched Local Area Network (LAN). In contrast to other approaches, the service was built based on traffic aggregation and simple two level Static Priority scheduling within LAN switches. All complex control functions such as the per-flow packet classification, policing and traffic reshaping are only performed within end-nodes (hosts or routers) of the LAN. Admission Control is used to restrict the access to the new service. Measurement results received in a bridged test network exhibit low average end-to-end delay characteristics and no packet loss despite: 1) the simplicity of the traffic control implemented in our LAN switches, 2) a worst-case network load, and 3) the use of long range dependent data sources within the experiments.

Distribution of Irradiance in Haze and Fog*

Experimental measurements of the transmission properties of New England haze and fog are correlated with a modification of the single scatter theory. The modified single scatter theory is derived and its consequences are compared graphically with measured range dependent data and the angular distribution of scattered flux. The results may be summarized within the limits of 0.04 < σ <16 (km−1) and 0.2 < D < 10 (km) by T=e−σD+0.3σ0.5De−σ0.3D,where T is the transmission function for radiant energy intercepted by a 2π detector, σ the atmospheric attenuation coefficient, and D the range from the isotropic source.