Strong optimality of the normalized ML models as universal codesand information in data

We show that the normalized maximum-likelihood (NML) distribution as a universal code for a parametric class of models is closest to the negative logarithm of the maximized likelihood in the mean code length distance, where the mean is taken with respect to the worst case model inside or outside the parametric class. We strengthen this result by showing that, when the data generating models are restricted to be the most “benevolent” ones in that they incorporate all the constraints in the data and no more, the bound cannot be beaten in essence by any code except when the mean is taken with respect to the data generating models in a set of vanishing size. These results allow us to decompose the code of the data into two parts, the first having all the useful information in the data that can be extracted with the family in question and the rest which has none, and we obtain a measure for the (useful) information in data     

Average type-II censoring times for the 2-parameter Weibulldistribution

The average experiment-time under a type-ll censoring plan, when the lifetime follows a 2-parameter Weibull distribution, is expressed here in computable form. The formulae can be used to compute ratios of average experiment times under type-II censoring and complete sampling plans. The ratios provide information on how much experiment time can be saved by using a type-II censoring plan instead of a complete sampling plan. These measures can help reliability analysts choose a suitable combination of censoring number and initial sample size. Tables of average experiment times and ratios are provided. Applications of the tables, confidence intervals for the ratio, and computational issues are discussed     

Solving the cardiac bidomain equations for discontinuous conductivities

Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities.     

Robust parameter-estimation using the bootstrap method for the2-parameter Weibull distribution

This paper proposes bootstrap robust estimation methods for the Weibull parameters; it applies bootstrap estimators of order statistics to the parametric estimation procedure. Estimates of the Weibull parameters are equivalent to the estimates using the extreme value distribution. Therefore, the bootstrap estimators of order statistics for the parameters of the extreme value distribution are examined. Accuracy and robustness for outliers are examined by Monte Carlo experiments which indicate adequate efficiency of the proposed reliability estimators for data with some outliers     

Homogeneity tests for scale parameters of 2-parameter exponentialpopulations under time censoring

Comparing two or more scale parameters of exponential distributions is often important in life-testing problems. This paper considers tests for the equality of several exponential scale parameters in presence of unspecified location parameters based on time-censored data. Using a conditional approach, various test statistics are derived. The Monte Carlo studies were carried out for comparing the powers of these statistics with the power of the usual likelihood ratio statistic. The power of the usual likelihood ratio test was better than those of the other tests for various combinations of mean number of failures     

用于最大似然2-DOA估计的裂变粒子群算法

最大似然2-DOA估计是一种抗干扰能力强、精确度高的测向算法。对其目标函数求解时容易收敛到局部最优解,最终影响最大似然2-DOA估计的性能。考虑到粒子群（PSO）算法具有全局化寻优能力及计算量巨大的特点,本文提出了一种裂变粒子群(FPSO)算法,在保证全局化寻优能力的同时大大降低计算量。但当2-DOA估计环境恶劣时FPSO算法仍然需要较大的迭代次数才能达到一定的2-DOA估计精度。为了进一步降低计算量,提出了改进的FPSO算法。其采用AP算法初始化全局最优粒子,精确了初始化精度从而降低精确2-DOA估计所需的迭代次数。仿真证明,FPSO算法和改进的FPSO算法能够分别在AWGN信道和短波信道下以较低的计算量实现精确的2-DOA估计,其均方根误差逼近其CRB。      

Estimation in the 2-parameter exponential distribution with priorinformation

This paper proposes a class of estimators for the scale parameter and for the mean of a 2-parameter exponential distribution, which is important in life testing and reliability theory, given a prior estimate of the scale parameter. The class of estimators for the scale parameter is motivated by the work of Jani (1991). These estimators have smaller mean square error than the classical estimators for all values of the location parameter, and for values of the scale parameter in a neighborhood of the prior estimate. Numerical computations indicate that certain of these estimators substantially improve the classical estimators for values of the scale parameter near the prior estimate, especially for small sample sizes     

Analysis of subspace fitting and ML techniques for parameterestimation from sensor array data

It is shown that the multidimensional signal subspace method, termed weighted subspace fitting (WSF), is asymptotically efficient. This results in a novel, compact matrix expression for the Cramer-Rao bound (CRB) on the estimation error variance. The asymptotic analysis of the maximum likelihood (ML) and WSF methods is extended to deterministic emitter signals. The asymptotic properties of the estimates for this case are shown to be identical to the Gaussian emitter signal case, i.e. independent of the actual signal waveforms. Conclusions concerning the modeling aspect of the sensor array problem are drawn     

FDTD Maxwell's equations models for nonlinear electrodynamics andoptics

This paper summarizes algorithms which extend the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics. The use of the FDTD in this field is novel. Previous modeling approaches were aimed at modeling optical-wave propagation in electrically long structures such as fibers and directional couplers, wherein the primary flow of energy is along a single principal direction. However, the FDTD is aimed at modeling compact structures having energy flow in arbitrary directions. Relative to previous methods, the FDTD achieves robustness by directly solving, for fundamental quantities, the optical E and H fields in space and time rather than performing asymptotic analyses or assuming paraxial propagation and nonphysical envelope functions. As a result, it is almost completely general. It permits accurate modeling of a broad variety of dispersive and nonlinear media used in emerging technologies such as micron-sized lasers and optical switches     

Moment estimators for the 3-parameter Weibull distribution

Weibull moments are defined generally and then calculated for the 3-parameter Weibull distribution with non-negative location parameter. Sample estimates for these moments are given and used to estimate the parameters. The results of a simulation investigation of the properties of the parameter estimates are discussed briefly. A simple method of deciding whether the location parameter can be considered zero is described     

Comparisons of Point Estimation Methods in the 2-parameter Weibull Distribution

The following 3 estimation methods in a Weibull distribution are well-known; Maximum Likelihood Estimation (MLE), Coefficient of Variation (CV), and Weibull Probability Paper (WPP). By simulation we conclude that the WPP method is best.     

Discrete Roesser state models from 2D frequency data

Multidimensional Systems and Signal Processing - We identify a general, i.e. not necessarily denominator-separable Roesser model from 2D discrete vector-geometric trajectories generated by a...     

Estimators of 2-parameter Weibull distributions from incompletedata with residual lifetimes

It is common for residual lifetimes to be either discarded or treated as if they were right-censored data estimating two-parameter Weibull distributions. The exact maximum likelihood (ML) estimators for dealing with sampled data with residual lifetimes are formulated. Monte Carlo simulation is used to compare the performance of ML estimators for various approaches to the treatment of residual data. Two types of LS (least squares) estimators are also evaluated: LSMR (LS median rank) estimators and LSNPML (LS nonparametric ML) estimators. For ML estimators, the exact method performs better than the approximate ones. Of the two types of LS estimators, the better one is sensitive to the true value of the shape parameter. The exact ML estimation procedure is therefore preferred over the LS procedures even though the former is not always better     

Quasi-interpolating spline models for hexagonally-sampled data.

The reconstruction of a continuous-domain representation from sampled data is an essential element of many image processing tasks, in particular, image resampling. Until today, most image data have been available on Cartesian lattices, despite the many theoretical advantages of hexagonal sampling. In this paper, we propose new reconstruction methods for hexagonally sampled data that use the intrinsically 2-D nature of the lattice, and that at the same time remain practical and efficient. To that aim, we deploy box-spline and hex-spline models, which are notably well adapted to hexagonal lattices. We also rely on the quasi-interpolation paradigm to design compelling prefilters; that is, the optimal filter for a prescribed design is found using recent results from approximation theory. The feasibility and efficiency of the proposed methods are illustrated and compared for a hexagonal to Cartesian grid conversion problem.     

Solving two-spiral problem through input data encoding

The authors show that the two-spiral problem can be easily solved using a standard back propagation neural network by properly encoding the raw input data. The authors also examine and compare several data encoding schemes for use in neural networks to improve the training efficiency and generalisation property     

Sphere-constrained ML detection for frequency-selective channels

The maximum-likelihood (ML) sequence detection problem for channels with memory is investigated. The Viterbi algorithm (VA) provides an exact solution. Its computational complexity is linear in the length of the transmitted sequence, but exponential in the channel memory length. On the other hand, the sphere decoding (SD) algorithm also solves the ML detection problem exactly, and has expected complexity which is a low-degree polynomial (often cubic) in the length of the transmitted sequence over a wide range of signal-to-noise ratios. We combine the sphere-constrained search strategy of SD with the dynamic programming principles of the VA. The resulting algorithm has the worst-case complexity determined by the VA, but often significantly lower expected complexity.     

Parameter estimation for the 3-parameter Gamma distribution usingthe continuation method

This paper shows a maximum-likelihood (ML) parameter estimation algorithm for the 3-parameter Gamma distribution. The algorithm, a combination of the continuation method and the extended Gamma distribution model, can find the local ML estimates of the parameters without a careful selection of the starting point in the iterative process. This algorithm is more efficient than previous algorithms, and can find the multiple local ML estimates     

Solving some overflow traffic models with changed serving intensities

This paper investigates specific systems with overflow traffic. A primary group with two Poisson traffics is considered whereupon the rejected calls from one traffic are directed to the alternative group with changed serving intensities. The generating function technique is used for analytical solving the model with secondary and ternary groups and the model that separately treated the channels in alternative groups. The obtained analytical solutions essentially reduce the constraints concerning the equation system size, convergence, and calculation time, which arise when numerically solving the steady-state system equations. For the case with single channels in the ternary group, explicit solutions for traffic parameters are obtained. Also, comparison with the model that has a unique serving intensity of overflow traffic is made.     

Parsimonious correlated nonstationary models for real baseband UWB data

Few ultrawide-band (UWB) models directly fit original baseband UWB data to simultaneously account for their correlation structure, non-Gaussianity, and nonstationarity. The difficulty arises from the fact that no relevant result is available, even in multivariate statistical analysis. It also arises from the attempt to pursue the details of the mechanism that is imagined to be responsible for the generation of UWB data. The consequence is the modeling complexity, which makes it difficult to handle the received signal correlation on the basis of a single realization. Accordingly, various partial characterization is used in the literature instead by virtue of second-order statistics (such as power delay profile), nonparametric characteristics (such as zero-crossing rate), or their combination. In this paper, we take a different philosophy, which believes that the information in the received UWB data itself, as long as fully exploited, plus some simple physical intuition should suffice for the model identification and its parameter estimation. A received UWB signal is decomposed into three factor processes and each is parsimoniously parameterized. The application of the new model to data regeneration and receiver design is illustrated by using the real UWB data acquired by Intel and the TimeDomain Corporation.