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In this paper we analyze a method for approximating the first-passage time density and the corresponding distribution function for a CIR process. This approximation is obtained by truncating a series expansion involving the generalized Laguerre polynomials and the gamma probability density. The suggested approach involves a number of numerical issues which depend strongly on the coefficient of variation of the first passage time random variable. These issues are examined and solutions are proposed also involving the first passage time distribution function. Numerical results and comparisons with alternative approximation methods show the strengths and weaknesses of the proposed method. A general acceptance-rejection-like procedure, that makes use of the approximation, is presented. It allows the generation of first passage time data, even if its distribution is unknown. • Approximation of the first passage time pdf of a CIR stochastic process through a constant boundary. • Study of the error along with considerations on the choice of the reference pdf parameters. • Sufficient conditions for the non-negativity of the approximant. • Computational improvements: standardization, stopping criteria, iterative procedure. • Acceptance-rejection-like method for the generation of first passage time data. [ABSTRACT FROM AUTHOR]

The Gram–Charlier expansion of a target probability density, f (x) , is an L 2 -convergent series f (x) = ∑ 0 ∞ c n p n (x) f ∗ (x) in terms of a reference density f ∗ (x) and its orthonormal polynomials p n (x). We implement this for the density of a regime-switching Lévy process at a given time horizon T. The main step is the evaluation of moments of all orders of f (x) in terms of model primitives, for which we give a matrix-exponential representation. A number of numerical examples, in part involving pricing of European options, are presented. The traditional choice of f ∗ (x) as normal with the same mean and variance as f (x) only works for the regime-switching Black–Scholes model. Outside the scope of Black–Scholes, f ∗ (x) is typically taken as a normal inverse Gaussian. A similar analysis is given for time-changed Lévy processes modelling stochastic volatility. [ABSTRACT FROM AUTHOR]

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise, in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly, without any transformation (e.g., normalization). We illustrate the method in a number of synthetic and real-world applications, with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded from below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method. [ABSTRACT FROM AUTHOR]

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods. [ABSTRACT FROM AUTHOR]

We analyze the solution to the linear stochastic heat equation driven by a multiparameter Hermite process of order q ≥ 1. This solution is an element of the q th Wiener chaos. We discuss various properties of the solution, such as the necessary and sufficient condition for its existence, self-similarity, α -variation and regularity of its sample paths. We will also focus on the probability distribution of the solution, which is non-Gaussian when q ≥ 2. [ABSTRACT FROM AUTHOR]

We consider a d -parameter Hermite process with Hurst index H = (H 1 ,.. , H d) ∈ 1 2 , 1 d and we study its limit behavior in distribution when the Hurst parameters H i , i = 1 ,.. , d (or a part of them) converge to 1 2 and/or 1. The limit obtained is Gaussian (when at least one parameter tends to 1 2) and non-Gaussian (when at least one-parameter tends to 1 and none converges to 1 2). [ABSTRACT FROM AUTHOR]

As the application of probabilistic models in robotic applications increases, a systematic robot control approach considering the effects of uncertainty becomes indispensable. Inspired by human sensorimotor findings, in this paper, we study the stochastic optimal control problem with high-order cost statistics in order to synthesize uncertainty-dependent actions in robotic scenarios with multiple uncertainty sources. We present locally optimal risk-sensitive and cost-cumulant solutions for settings with nonlinear dynamics, multiple additive uncertainty sources, and nonquadratic costs. The influence of each uncertainty source on the cost can be individually parameterized offering additional flexibility in the control design. We further analyze the case in which the static uncertain parameters are involved. The simulations of several linear and nonlinear settings with nonquadratic costs and an experiment on a real robotic platform validate our approach and illustrate its peculiarities. [ABSTRACT FROM AUTHOR]

In this paper, general quadratic forms of nonstationary,α-mixing time series are considered. Under mixing and moment assumptions, asymptotically normality of these forms are derived. These results do not assume that the variance of the generalized quadratic form has a limit, thus allowing for general types of nonstationarity. However, without well-defined limits, it is not possible to understand the differences in sampling properties of quadratic forms of nonstationary and stationary processes. To understand these differences, the nonstationary process is placed within the locally stationary framework. Under the assumption that the nonstationary process is locally stationary the asymptotic expectation and variance of the weighted sample covariance of the discrete Fourier transforms (an important class of quadratic forms) is derived and shown to be very different to its stationary counterpart. [ABSTRACT FROM PUBLISHER]

In a fundamental lemma we characterize 'generating functions' of certain functors on the category of algebraic non-commutative probability spaces. Special families of such generating functions correspond to 'unital, associative universal products' on this category, which again define a notion of non-commutative stochastic independence. Using the fundamental lemma, we prove the existence of cumulants and of 'cumulant Lie algebras' for all independences coming from a unital, associative universal product. These include the five independences (tensor, free, Boolean, monotone, anti-monotone) appearing in Muraki's classification, c-free independence of Bożejko and Speicher, the indented product of Hasebe and the bi-free independence of Voiculescu. We show how the non-commutative independence can be reconstructed from its cumulants and cumulant Lie algebras. [ABSTRACT FROM AUTHOR]

We obtain the rate function for the level 2.5 of large deviations for pure jump and diffusion processes. This result is proved by two methods: tilting, for which a tilted process with an appropriate typical behavior is considered, and a spectral method, for which the scaled cumulant generating function is used. We also briefly discuss fluctuation relations, pointing out their connection with large deviations at the level 2.5. [ABSTRACT FROM AUTHOR]

An approach was developed to retrieve the ocean slope bispectrum, which describes the nonlinearity of the slope surface, from ocean sunglint data. The departure from Gaussianity of the ocean slope was described using an N-dimensional slope joint probability density function, which was derived using a perturbative approach. The resulting Edge-worth series had various slope cumulants and cumulant functions as series coefficients, and multidimensional Hermite polynomials as the series basis functions. The slope probability density was used to specify a series of relationships between the slope and glint cumulants and cumulant functions up to third order. These relationships were inverted to retrieve the slope third cumulant function, from which we obtained the slope bispectrum via Fourier transformation. The retrieval method was validated using synthetic 1-D ocean wave slope datasets with controlled phase correlations imposed on a subset of the wave spectrum components. [ABSTRACT FROM PUBLISHER]

Many multivariate statistical distributions have been derived using the well-known product model to stochastically model polSAR data. One important factor in their utilization is the estimation of their texture parameters. Recently, it has been shown that the method of matrix log cumulants (MoMLC) for multilook PolSAR statistical distributions results in estimators with low bias and variance properties. This method is becoming increasingly popular and can be regarded as state of the art. However, some distributions (e.g., G distribution) do not have closed-form MLC expressions, making the application of MoMLC a challenge. It is therefore desirable to have alternative parameter estimation methods. In this paper, we propose a new estimation method based on fractional moments of the multilook polarimetric whitening filter (MPWF). This results in estimators with mean square error that is even lower than the MoMLC-based estimators. In addition, the mathematical expressions of the estimators are computationally less complicated than MoMLC-based estimators. The proposed estimators can be easily derived for all commonly occurring multilook PolSAR distributions but have been only given for G, K, and G0 distributions in this paper. Comparisons are made with other known estimators for these distributions using simulated and real PolSAR data. For real data, formal goodness-of-fit testing, which is based on MLCs, has been used to assess the fitting accuracy of G, K, and G0 models using different estimators. [ABSTRACT FROM PUBLISHER]

We prove a function field version of Chowla's conjecture on the autocorrelation of the Möbius function in the limit of a large finite field. [ABSTRACT FROM PUBLISHER]

A simple model of death, birth and immigration is studied, which is autonomous, by which it is meant that the evolution equation for k -or-less-point functions is closed, for all k 's. The model contains three rate parameters, one of which is absorbed in a de-dimensionalization of time. Hence it is an effectively two-parameter model. The probability-generating function and the generating function for the cumulants are explicitly obtained in terms of these two parameters (the ratios of the death and immigrations rates to the birth rate). It is seen that the generating function for the cumulants is the sum of two terms, a term which is proportional to the immigration rate and independent of the initial conditions, and another term which is independent of the immigration rate and dependent of the initial condition. A similar decomposition happens for the cumulants as well. The one and two point functions are explicitly obtained. A careful investigation of the large time behavior of the system is performed. Also, the entropy of the system and of the environment, and their large-time behavior are investigated. [ABSTRACT FROM AUTHOR]

A theoretical approach for characterizing the influence of asymmetry of noise distribution on the escape rate of a multistable system is presented. This was carried out via the estimation of an action, which is defined as an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The approach takes into account all cumulants of the noise distribution and demonstrates an excellent agreement with the results of numerical simulations. An approximation of the third-order cumulant was shown to have limitations on the range of dynamic stochastic system parameters. The applicability of the theoretical approaches developed so far is discussed for an adequate characterization of the escape rate measured in experiments. [ABSTRACT FROM AUTHOR]

Individual random trajectories of stochastic processes are often analyzed by using quadratic forms such as time averaged (TA) mean square displacement (MSD) or velocity auto-correlation function (VACF). The appropriate quadratic form is expected to have a narrow probability distribution in order to reduce statistical uncertainty of a single measurement. We consider the problem of finding the optimal quadratic form that minimizes a chosen cumulant moment (e.g., the variance) of the probability distribution, under the constraint of fixed mean value. For discrete noncentered Gaussian processes, we construct the optimal quadratic form by using the spectral representation of cumulant moments. Moreover, we obtain a simple explicit formula for the smallest achievable cumulant moment that may serve as a quality benchmark for other quadratic forms. We illustrate the optimality issues by comparing the optimal variance with the variances of the TA MSD and TA VACF of fractional Brownian motion superimposed with a constant drift and independent Gaussian noise. [ABSTRACT FROM AUTHOR]

We present the results of cumulant analysis for detection of random process using a Schottky diode with δ-doping. The statistical characteristics of the output process of the detector, based on a Schottky diode with δ-doping, are investigated. We discuss noninertial and inertial detection mode. It was shown that at a relatively large dispersion of the input noise a noninertial detection mode occurs. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of entropic value-at-risk (EVaR), a new coherent risk measure that corresponds to the tightest possible upper bound obtained from the Chernoff inequality for the value-at-risk (VaR) as well as the conditional value-at-risk (CVaR). We show that a broad class of stochastic optimization problems that are computationally intractable with the CVaR is efficiently solvable when the EVaR is incorporated. We also prove that if two distributions have the same EVaR at all confidence levels, then they are identical at all points. The dual representation of the EVaR is closely related to the Kullback-Leibler divergence, also known as the relative entropy. Inspired by this dual representation, we define a large class of coherent risk measures, called g-entropic risk measures. The new class includes both the CVaR and the EVaR. [ABSTRACT FROM AUTHOR]

Proliferation of wind generators (WGs) requires a change in distribution system planning techniques as WGs have intermittent and uncertain output. This paper proposes a Cumulant based stochastic optimal reactive power planning method for distribution systems with high penetration of WGs. Uncertainties in the output of WGs and load forecasts are modeled using probability density functions (PDFs). With a stochastic framework, an optimization challenge is formulated to minimize the total costs of new capacitors and the total annual energy loss. The optimization problem is then solved by using the Logarithmic Barrier Interior Point Method (LBIPM). At the optimal solution, LBIPM provides a linear relationship between the cumulants of independent variables (load and wind power) and the cumulants of the dependent system parameters. The Cumulant method offers a generous advantage in speed, while maintaining acceptable accuracy, as compared to the computationally cumbersome traditional Monte Carlo simulation (MCS) method. The method is tested on 7-bus, 33-bus, and 129-bus systems. The results are reported and discussed. The performance and accuracy are assessed by comparing the results with those from MCS method. [ABSTRACT FROM PUBLISHER]

This paper applies a probabilistic power flow (PPF) algorithm to evaluate the influence of photovoltaic (PV) generation uncertainty on transmission system performance. PV generation has the potential to cause a significant impact on power system reliability in the near future. A cumulant-based PPF algorithm suitable for large systems is used to avoid convolution calculations. Correlation among input random variables is considered. Specifically correlation between adjacent PV resources are considered. Three types of approximation expansions based on cumulants, namely the Gram-Charlier expansion, the Edgeworth expansion, and the Cornish-Fisher expansion, are compared, and their properties, advantages, and deficiencies are discussed. Additionally, a novel probabilistic model of PV generation is developed to obtain the probability density function (PDF) of the PV generation production based on the environmental conditions. The proposed approaches with the three expansions are compared with Monte Carlo simulations (MCS) with results for a 2497-bus representation of the Arizona area of the Western Electricity Coordinating Council (WECC) system. [ABSTRACT FROM PUBLISHER]

In this paper, we consider incorporating the runs rules into the cumulative quantity control (CQC) chart for monitoring time-between-events data. We propose a simple and effective procedure to design a CQC chart coupled with runs rules that can yield average run length (ARL)-unbiased performance and meet the required in-control ARL. The proposed design involves determining a relation between the upper side and lower side false alarm probabilities. A Markov chain approach is used to evaluate the ARL performance of various control schemes studied in this paper. An extensive numerical comparison shows that the proposed design approach can result in a significant reduction in ARL for detecting increases in the occurrence rate of the event in comparison with the basic CQC charts. [ABSTRACT FROM AUTHOR]

Abstract: The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gaussian and the Levy regimes has been investigated. [Copyright &y& Elsevier]

Non-Gaussian processes may require not only the information provided by first two moments, but also that given by the higher-order statistics, in particular, by the third- and fourth-order moments or cumulants. This paper addresses a fourth-order cumulant estimation problem for real discrete-time random non-i.i.d. signal, that can be approximated as an MA stochastic process. An unbiased estimator is proposed, studied and compared to two other frequently used estimators of the fourth-order cumulant (natural estimator and fourth k-statistics). Statistical comparative studies are undertaken from both bias and MSE points of view, for different distribution laws and MA filters. Algorithms, aiming to reduce computational complexity of the proposed estimator, as well as that of the fourth k-statistics bias, are also provided. [ABSTRACT FROM PUBLISHER]

Spatially distributed and varying natural phenomena encountered in geoscience and engineering problem solving are typically incompatible with Gaussian models, exhibiting nonlinear spatial patterns and complex, multiple-point connectivity of extreme values. Stochastic simulation of such phenomena is historically founded on second-order spatial statistical approaches, which are limited in their capacity to model complex spatial uncertainty. The newer multiple-point (MP) simulation framework addresses past limits by establishing the concept of a training image, and, arguably, has its own drawbacks. An alternative to current MP approaches is founded upon new high-order measures of spatial complexity, termed “high-order spatial cumulants.” These are combinations of moments of statistical parameters that characterize non-Gaussian random fields and can describe complex spatial information. Stochastic simulation of complex spatial processes is developed based on high-order spatial cumulants in the high-dimensional space of Legendre polynomials. Starting with discrete Legendre polynomials, a set of discrete orthogonal cumulants is introduced as a tool to characterize spatial shapes. Weighted orthonormal Legendre polynomials define the so-called Legendre cumulants that are high-order conditional spatial cumulants inferred from training images and are combined with available sparse data sets. Advantages of the high-order sequential simulation approach developed herein include the absence of any distribution-related assumptions and pre- or post-processing steps. The method is shown to generate realizations of complex spatial patterns, reproduce bimodal data distributions, data variograms, and high-order spatial cumulants of the data. In addition, it is shown that the available hard data dominate the simulation process and have a definitive effect on the simulated realizations, whereas the training images are only used to fill in high-order relations that cannot be inferred from data. Compared to the MP framework, the proposed approach is data-driven and consistently reconstructs the lower-order spatial complexity in the data used, in addition to high order. [ABSTRACT FROM AUTHOR]

In this paper, a consistent efficient estimator of the fourth-order cumulant for real discrete-time random i.i.d. (at least up to order 8) zero-mean signal is proposed, in both, batch and adaptive versions. In batch version, the proposed estimator is not only consistent, but also unbiased and efficient. The systematical theoretical and experimental studies with comparisons between the proposed estimator and three other estimators of the fourth-order cumulant (the natural or the traditional one, the trivial unbiased estimator for the known power case and the fourth k-statistics), are undertaken, for both, normal and uniform processes. Then, the adaptive versions of the estimators (all, except the fourth k-statistics), are given and studied in detail. The convergence in mean and the convergence in mean square analyses are performed for them, first theoretically, then empirically. Finally, the whole set of analyses carried out for both batch and adaptive versions shows that from many points of view the proposed estimator is interesting for use in versatile signal processing applications, especially in real-time and short-term ones. [ABSTRACT FROM AUTHOR]

The econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities. We here study this local-constancy approximation as a general approach to estimation in such data. We show that the technique yields asymptotic properties (consistency, normality) that are correct subject to an ex post adjustment involving asymptotic likelihood ratios. These adjustments are derived and documented. Several examples of estimation are provided: powers of volatility, leverage effect, and integrated betas. The first order approximations based on local constancy can be over the period of one observation or over blocks of successive observations. It has the advantage of gaining in transparency in defining and analyzing estimators. The theory relies heavily on the interplay between stable convergence and measure change, and on asymptotic expansions for martingales. [ABSTRACT FROM AUTHOR]

A method, which we believe is simpler and more transparent than the one due to McCullagh (1984) , is described for obtaining the cumulants of a scalar multivariate stochastic Taylor expansion. Its generalisation is also suggested. An important feature, previously not reported, is that the expansion of every cumulant of order≥ 2 is made up of separate subseries. In order to handle certain frequently occurring sums over permutations of members of compound index sets, we introduce a new notation where is a positive integer. [ABSTRACT FROM AUTHOR]

Abstract  Three-dimensional vorticity in the wake of an inclined stationary circular cylinder was measured simultaneously using a multi-hot wire vorticity probe over a streamwise range of x/d = 10–40. The study aimed to examine the dependence of the wake characteristics on cylinder inclination angle α (=0°–45°). The validity of the independence principle (IP) for vortex shedding was also examined. It was found that the spanwise mean velocity $$ \overline{W} , $$ which represents the three-dimensionality of the wake flow, increases monotonically with α. The root-mean-square (rms) values of the streamwise (u) and spanwise (w) velocities and the three vorticity components decrease significantly with the increase of α, whereas the transverse velocity (v) does not follow the same trend. The vortex shedding frequency decreases with the increase of α. The Strouhal number (St N), obtained by using the velocity component normal to the cylinder axis, remains approximately a constant within the experimental uncertainty (±8%) when α is smaller than about 40°. The autocorrelation coefficients ρ u and ρ v of the u and v velocity signals show apparent periodicity for all inclination angles. With increasing α, ρ u and ρ v decrease and approach zero quickly. In contrast, the autocorrelation coefficient ρ w of w increases with α in the near wake, implying an enhanced three-dimensionality of the wake. [ABSTRACT FROM AUTHOR]

This letter introduces a novel method of sequence construction having a zero-correlation zone. The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed zero-correlation zone sequence set can be generated from an arbitrary perfect ternary sequence, the length of which is the product of a pair of odd integers ((2κ + 1)(2n + 1) for κ ≥ 1 and n ≥ 0). The width of the zero-correlation zone of the proposed sequence set can be longer than the length of the perfect sequence that is used for constructing the proposed sequence set. The proposed sequence construction can generate an optimal zero-correlation zone sequence set that satisfies the theoretical bound of the sequence member size for the zero-correlation zone and the sequence period. [ABSTRACT FROM AUTHOR]

In the literature, many constructions of zero correlation zone (ZCZ) sequences have been reported. While most of them are suboptimal with respect to the known upper bound, some constructed by Matsufuji et al. and Torii et al. respectively, are almost optimal (or even optimal). In this paper, we propose a systematic construction of almost optimal ZCZ sequence sets which generalizes the aforementioned constructions so that more flexible relationships between the set size and the sequence length are allowed. In particular, the obtained almost optimal ZCZ sequence sets of size in and length inn are new for 1 < gcd (m, n) < min (m, n). In addition, their alphabets can be binary or nonbinary since our construction is only based on interleaving perfect sequences according to a certain orthogonal matrix. [ABSTRACT FROM AUTHOR]

A direction of arrival (DOA) estimation algorithm in the presence of an unknown mutual coupling is presented for a uniform circular array. This algorithm is based on the fourth-order cumulants, and the DOA of signal sources can be accurately estimated without the need of any calibration source since the coupling is blindly compensated by the inherent mechanism of the proposed method. Because of the use of higher-order statistics, the number of sources that can be coped with may be larger than the number of sensors in the array, and the algorithm is insensitive to Gaussian noise. Comparing with existing calibration methods which use iterative approaches, this algorithm is computationally less expensive since it uses only a one-dimensional search. Validation and performance are illustrated by simulations. [ABSTRACT FROM AUTHOR]

Abstract: Doukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313–342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results. Furthermore, we consider several classes of processes and show that they fulfill appropriate weak dependence conditions. We also sketch applications of our inequalities in probability and statistics. [Copyright &y& Elsevier]

Abstract: Pulse-echo measurements in ultrasonic non-destructive evaluation (NDE) are masked by the characteristics of the measuring instruments, the propagation paths taken by the ultrasonic pulses, and are considered to be corrupted by additive noise. It is assumed that the measured pulse echo is obtained by linearly convolving the defect impulse response (IR) with the measurement system response. Deconvolution operation, therefore, seeks to undo the effect of this convolution and extract the IR which is essential for defect identification. Autocorrelation (or power spectrum) deconvolution techniques are limited to the identification of minimum-phase systems. In this work, we show that higher-order cepstra can be used to deconvolve the IR of the flaw from ultrasonic echo measurements (synthetic as well as real). We also demonstrate that a deconvolution based on the use of the bi-cepstrum gives lower identification error variance when compared with the results of Wiener filtering deconvolution, specially at low signal-to-noise ratios (SNR). [Copyright &y& Elsevier]

Abstract: This discussion presents a new perspective of subspace independent component analysis (ICA). The notion of a function of cumulants (kurtosis) is generalized to vector kurtosis. This vector kurtosis is utilized in the subspace ICA algorithm to estimate subspace independent components. One of the main advantages of the presented approach is its computational simplicity. The experiments have shown promising results in estimating subspace independent components. [Copyright &y& Elsevier]

In this letter, two direction-of-arrival (DOA) estimation are proposed: one is a new fourth-order cumulant-based technique, and the other is a joint second- and fourth-order cumulant technique. Using the full set of cumulants for DOA estimation is computationally expensive; conversely, using a downsized quadricovariance matrix leads to poor DOA estimates. This letter proposes the choice of efficient quadricovariance matrices to he used in the fourth-order estimator. Then, together with these matrices, a joint second- and fourth-order DOA estimator is derived. Both algorithms perform reasonably better than existing fourth-order and second-order algorithms in a spatially correlated Gaussian noise environment. [ABSTRACT FROM AUTHOR]

We describe a connection between discrete birth process and a certain family of multivariate interpolation polynomials. This enables us to compute all asymptotic moments of the birth process, generalizing previously known results for the mean and variance. [ABSTRACT FROM AUTHOR]

We present theoretical tools from statistical physics for the calculation of non-Gaussian moments. In particular, we focus on the variational approximation and the cumulant expansion. These methods enable approximate but explicit moment calculations with non-Gaussian probability density functions (pdfs). Their use is illustrated by calculating the variance and the excess kurtosis for a univariate non-Gaussian pdf. We comment on the potential application of these methods in estimating the parameters of the recently proposed Spartan spatial random fields. [ABSTRACT FROM AUTHOR]

This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properties regarding saddle node bifurcations to create a linear mapping relationship between random bus loading variables and all other system variables. The proposed methodology is tested using a sample system based on the IEEE 30-bus system using random active and reactive bus loading. Monte Carlo simulations consisting of 10000 samples are used as a reference solution for evaluation of the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

The effects of moderate levels of serial correlation on one-sided and ordinary cross-validation in the context of local linear and kernel smoothing is investigated. It is shown both theoretically and by simulation that one-sided cross-validation is much less adversely affected by correlation than is ordinary cross-validation. The former method is a reliable means of window width selection in the presence of moderate levels of serial correlation, while the latter is not. It is also shown that ordinary cross-validation is less robust to correlation when applied to Gasser–Müller kernel estimators than to local linear ones. [Copyright &y& Elsevier]

Maximum likelihood and the method of moments have been popular methods of estimation for analyzing repeated measurements with autocorrelation. They are used for normal and non-normal data respectively. An alternative is the quasi-least squares method of estimation. This method, based on the principle of generalized least squares, does not make any distributional assumptions and differs from the two popular methods in estimating the autocorrelation. In this paper we study large sample properties of the three methods of estimation for unbalanced data. Using asymptotic relative efficiency criterion, for normally distributed measurements we show that the quasi-least squares estimates are better than the moment estimates and are good competitors to the maximum likelihood [ABSTRACT FROM AUTHOR]

We calculate the first four cumulants of the integrated current of the one-dimensional symmetric simple exclusion process of N sites with open boundary conditions. For large system size N, the generating function of the integrated current depends on the densities ρa and ρb of the two reservoirs and on the fugacity z, the parameter conjugated to the integrated current, through a single parameter. Based on our expressions for these first four cumulants, we make a conjecture which leads to a prediction for all the higher cumulants. In the case ρa=1 and ρb=0, our conjecture gives the same universal distribution as the one obtained by Lee, Levitov, and Yakovets for one-dimensional quantum conductors in the metallic regime. [ABSTRACT FROM AUTHOR]

Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a physically compelling interpretation of representing the highest precision with which the first cumulant of the random variable, i.e., its mean, can he estimated from its statistical realizations. We construct a complete hierarchy of information measures that determine the best precision with which all of the cumulants of a random variable--and thus its complete probability distribution--can be estimated from its statistical realizations. Several properties of these information measures and their generating functions are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a method of harmonics extraction from Higher Order Statistics (HOS) is developed for texture decomposition. We show that the diagonal slice of the fourth-order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies. We propose to use this fourth-order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted. Hence, a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a Wold-like decomposition procedure. The simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods. [ABSTRACT FROM AUTHOR]

We continue the investigation of noncommutative cumulants. In this paper various characterizations of generalized Gaussian random variables are proved. [ABSTRACT FROM AUTHOR]

In this paper, the spectral density estimation of a nonstationary class of stochastic processes is investigated. Although these processes are not stationary with respect to the additive binary operation, i.e., in the classical weak sense, they are stationary with respect to the multiplicative binary operation. These processes exist naturally as continuous-time processes. In order to answer many questions in practical situations using these processes, we develop a random sampling method for estimating their spectral densities by using a discrete-time process. Some simulation results are given. [Copyright &y& Elsevier]

The moment closure method was recently shown in Na˚sell (Theor. Popul. Biol. 63 (2) (2003a) 159) to give asymptotic approximations of the first few cumulants for the stochastic logistic model. A slight extension of the method is introduced. It is shown to be robust with regard to the specific distributional assumption that is used to achieve moment closure. The phenomenon of spurious solutions is shown to be related to the domain of attraction of the non-spurious critical point. [Copyright &y& Elsevier]

Extensions of nondirectional spatial autocorrelation techniques to two dimensions have existed for many years, but the results are difficult to compare to the traditional nondirectional techniques and often lack ease of interpretability. This paper reviews the traditional one- and two-dimensional spatial autocorrelation methods and proposes a new directional method which is both easier to compare to nondirectional methods and easier to interpret than previous directional methods. [ABSTRACT FROM AUTHOR]

We express the logarithm of the thermal density matrix ρ[sub H,β](X,X')≡〈X [sub e][sup -βH]X'), where H = H[sub 0] + V, as a cumulant expansion in powers of the perturbation V, by associating with {H[sub 0], X), '〉] I a stochastic process. If the ground state of Ho is isolated, this stochastic process is of finite memory; it then follows from the properties of cumulants that the above expansion of 1n ρ is nonsecular as β→∝ (all its terms ββ), and is thus usable down to zero temperature, unlike the direct expansion of ρ in powers of V, whose nth term ∼β[sup n]. To determine explicitly the low- temperature behavior, we apply an analysis familiar in the theory of relaxation, and obtain the form In ρ[sub H,β](X,X') = h (X,X',β]) + a(X) + a(X')[sup †] - bβ, where a,b,h are cumulant expansions in powers of V; a(X), b are independent of β; and h (X,X',β)→0 as β→∞. Comparing with ρ→〈Xψ[sub 0]〉e[sup - βE[sub 0] 〈ψ[sub 0]X' β→ ∞, where ψ[sub 0] and E[sub 0] are the ground state and energy of H, we deduce E[sub 0] = b, ln〈Xψ[sub 0]) = a(X), i.e., the Rayleigh-Schrödinger perturbation series for E[sub 0] and ln〈X ψ[sub 0]〉 (with 〈ψ[sub 0]ψ[sub 0]〉 = 1) emerge as cumulant expansions. In the case ora many-body system, the properties of cumulants immediately imply linked cluster theorems for 1n ρ, as well as for E[sub 0] and ln〈X ψ[sub 0]〉. [ABSTRACT FROM AUTHOR]