Browsing by Author "Kedem, Benjamin"
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Item Asymptotic Normality of the Contraction Mapping Estimator for Frequency Estimation(1992) Li, Ta-Hsin; Kedem, Benjamin; Yakowitz, S.; ISRThis paper investigates the asymptotic distribution of the recently-proposed contraction mapping (CM) method for frequency estimation. Given a finite sample composed of a sinusoidal signal in additive noise, the CM method applies to the data a parametric filter that matches its parameter with the first-order autocorrelation of the filtered noise. The CM estimator is defined as the fixed-point of the parametrized first-order sample autocorrelation of the filtered data. In this paper, it is proved that under appropriate conditions, the CM estimator is asymptotically normal with a variance inversely related to the signal-to-noise ratio. A useful example of the AR(2) filter is discussed in detail to illustrate the performance of the CM method.Item Bayesian Prediction of Transformed Gaussian Random Fields(1996) Oliveira, V. De; Kedem, Benjamin; Short, D.; ISRThe purpose of this work is to extend the methodology presented in Handock and Stein (1993) for prediction in Gaussian random fields to the case of transformed Gaussian random fields when the transformation is only known to belong to a parametric family. As the optimal predictor, the median of the Bayesian predictive distribution is used since the mean of this distribution does not exist for many commonly used nonlinear transformations. Monte Carlo integration is used for the approximation of the predictive density function, which is easy to implement in this framework. An application to spatial prediction of weekly rainfall amounts in Darwin Australia is presented.Item Estimation of Multiple Sinusoids by Parametric Filtering(1992) Li, Ta-Hsin; Kedem, Benjamin; ISRThe problem of estimating the frequencies of multiple sinusoids from noisy observations is addressed in this paper. A parametric filtering approach, called the PF method, is proposed that leads to a consistent estimator of the AR representation of the sinusoidal signal, given the number of sinusoids. It is accomplished by using an iterative procedure to a fixed-point of the parametrized least squares estimator (from the filtered data) that comprises a contraction mapping in the vicinity of the true AR parameter. Employing appropriate filters, this method is able to achieve the accuracy of the nonlinear least squares estimator, with much less computational complexity and initialization requirement. It can also be implemented adaptively (recursively) in order to track time-varying frequencies. In this way, the PF method provides a flexible and efficient procedure of frequency estimation. An example of the AR filter is investigated in detail to illustrate the performance of the PF method.Item Exceedances and Moments in Data Containing Zeros(1996) Fokianos, Konstantinos; Kedem, Benjamin; Short, D.A.; ISRRain rate-the speed of rain in mm/hr-assumes zero values when it is not raining, and positive values on a continuum otherwise. For large areas, empirical evidence points to a high correlation between the instantaneous area average rain rate and the instantaneous fractional area where rain rate exceeds a fixed positive threshold. An explanation is provided by appealing to the man value theorem for integrals, in conjunction with the mixed nature of the probability distribution of rain rate. Using a multinomial logits model, the fractional area also is shown useful as a time dependent covariate in categorical prediction of the area average.Item Minimum Chi-Square vs Least Squares in Grouped Data(1997) Kedem, Benjamin; Wu, Y.; ISREstimation of parameters from grouped data is considered using a least squares estimator popular in sceintific applications. The method minimizes the square distance between the empirical and hypothesized cumulative distribution functions, and is reminiscent of a discrete version of the Cramer-von Mises statistic. The resulting least squares estimator, is related to the minimum chi-square estimator, and likewise is asymptotically normal. The two methods are compared briefly for categorized mixed lognormal data with a jump at zero.Item Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State(MDPI, 2021-05-27) Zhang, Xuze; Pyne, Saumyadipta; Kedem, BenjaminIn disease modeling, a key statistical problem is the estimation of lower and upper tail probabilities of health events from given data sets of small size and limited range. Assuming such constraints, we describe a computational framework for the systematic fusion of observations from multiple sources to compute tail probabilities that could not be obtained otherwise due to a lack of lower or upper tail data. The estimation of multivariate lower and upper tail probabilities from a given small reference data set that lacks complete information about such tail data is addressed in terms of pertussis case count data. Fusion of data from multiple sources in conjunction with the density ratio model is used to give probability estimates that are non-obtainable from the empirical distribution. Based on a density ratio model with variable tilts, we first present a univariate fit and, subsequently, improve it with a multivariate extension. In the multivariate analysis, we selected the best model in terms of the Akaike Information Criterion (AIC). Regional prediction, in Washington state, of the number of pertussis cases is approached by providing joint probabilities using fused data from several relatively small samples following the selected density ratio model. The model is validated by a graphical goodness-of-fit plot comparing the estimated reference distribution obtained from the fused data with that of the empirical distribution obtained from the reference sample only.Item On Autocovariance Estimation for Discrete Spectrum Stationary Time Series(1993) Houdre, Christian; Kedem, Benjamin; ISRWe provide a necessary and sufficient condition for the almost sure convergence and the strong consistency of the sample autocovariance of a discrete spectrum weakly stationary process. This also clarifies the estimation of the autocovariance function of a mixed spectrum weakly stationary processes.Item On Combining Instruments(1996) Fokianos, Konstantinos; Kedem, Benjamin; Qin, J.; Haferman, Jeffrey L.; Short, D.A.; ISRSuppose two instruments Io and I1 measure the same quantity with the same resolution, where it is know Io is more reliable. The second, I1 , is assumed a distortion of Io in some sense. A method is outlined whereby: 1. The information from both Io , I1 is combined to increase the reliability of Io . 2.. The distortion is qualified. An example is given in terms of ship borne precipitation radar and a space borne radiometer both measuring rain rate.Item On the Contraction Mapping Method for Frequency Detection(1992) Kedem, Benjamin; Yakowitz, S.; ISRThe contraction mapping method for frequency estimation in the presence of noise, identifies the cosine of the frequency to be detected as a fixed point of a certain correlation mapping. At its hear, the method provides a plan for automatic self tuning of parametric filters. A variant of the method, called the HK algorithm, produces recursive zero-crossing rates (normalized HOC sequences) that converge to the frequency of interest. A statistical explanation for the contraction mapping method as epitomized by the HK algorithm is provided when the HOC sequences are produced by bandpass filters. The outright consistency of the zero-crossing rate is not required. Examples show that the method performs quite remarkably.Item Partial Likelihood Analysis of Categorical Time Series Models(1995) Fakianos, Konstantinos; Kedem, Benjamin; Short, David A.; ISRPartial likelihood analysis of two generalized logistic regression models for nominal and ordinal categorical time series is presented, taking into account stochastic time-dependent covariates. Under some conditions on the covariates, the resulting estimators are consistent and asymptotically normal. The analysis is applied to rainfall data where the goodness of fit is judged by a certain chi square statistic.Item Power Considerations in Acoustic Emission(1995) Barnett, John T.; Clough, Roger B.; Kedem, Benjamin; ISRIn stochastic acoustic emission, both theory and experiments suggest that the power of the acoustic emission signal is proportional to the source energy. Hence, inference about the power is equivalent to inference about the source energy except for a constant multiple. In this regard, the connection between peaks exceeding a fixed level and the power in random acoustic emission waves is explored when the source energy is an impulse of short duration. Under certain conditions, the peak distribution is sensitive to power changes, determines it and is determined by it. The maximum likelihood estimator of the power from a random sample of peaks- the peak estimator - is more efficient than the maximum likelihood estimator - average sum of squares - from a random sample of the same size of signal values. When evaluated from nonrandom samples, indications are that the peak estimator may still have a relatively small mean square error. A real data example indicates that the left-truncated Rayleigh probability distribution may serve as an adequate model for high peaks.Item Prediction and Classification of Non-stationary Categorical Time Series(1996) Fokianos, Konstantinos; Kedem, Benjamin; ISRPartial Likelihood analysis of a general regression model for the analysis of non-stationary categorical time series is presented, taking into account stochastic time dependent covariates. The model links the probabilities of each category to a covariate process through a vector of time invariant parameters. Under mild regularity conditions, we establish good asymptotic properties of the estimator by appealing to martingale theory. Certain diagnostic tools are presented for checking the adequacy of the fit.Item Recursive Estimation for Time Series Following Generalized Linear Models(1996) Fokianos, Konstantinos; Kedem, Benjamin; ISRA recursive estimation method for time series models following generalized linear models is studied in two ways. The estimation procedure, suitably modified, gives rise to a stochastic approximation scheme. We use the modified estimation procedure to illustrate a connection between control theory and generalized linear models by employing a logistic regression model.Item Strong Consistency of the Contraction Mapping Method for Frequency Estimation(1992) Li, Ta-Hsin; Kedem, Benjamin; ISRConsider the super position of a sinusoid plus noise. By the application of certain parametric filter, the first-order autocorrelation becomes a contraction mapping. The sample estimator of the first-order autocorrelation is also a contraction whose fixed point converges almost surely to the cosine of the frequency to be detected. The theory is illustrated by two specific examples corresponding to two different parametric filters,