Sampling Zeros Research Articles

The Research of Digital Algorithm Based on Frequency-Dependent Transmission Lines

The algorithm for obtaining the discrete response of popagation function for frequency dependent parameter line is presented. Consider a minimum sampling period Tsm, that is, the highest frequency fH=1/(2Tsm) in the signal is taken into account. The impedance z(w) and the admittance y(w) are obtained in the frequency range of [0,fH] by employing the Carson’s formula. The propagation function at each frequency point is subsequently obtained, the impulse response in discrete time domain is then obtained using Poision Sum Formula. In order to avoid the long length of impulse reponse under the higher sampling frequency, the poles and zeros of z transform of discrete propagation function are evaluated by the Prony’s method. Subsequently, the coeffcients of the discrete infinite impulse response of propagation function are obtained. Using these coefficients the wave transfer sources can be easily computed by discrete convolution operation. The simulation tests show that the results using the propsed method is accurate, the error is not more than 1% in contrast of the results generated by EMTP. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2491

Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case

Remarkable improvements in the asymptotic properties of discrete system zeros may be achieved by properly adjusted fractional-order hold (FROH) circuit. This paper analyzes asymptotic properties of the limiting zeros, as the sampling periodTtends to zero, of the sampled-data models on the basis of the normal form representation of the continuous-time systems with FROH. Moreover, when the relative degree of the continuous-time system is equal to one or two, an approximate expression of the limiting zeros for the sampled-data system with FROH is also given as power series with respect to a sampling period up to the third-order term. And, further, the corresponding stability conditions of the sampling zeros are discussed for fast sampling rates. The ideas of the paper here provide a more accurate approximation for asymptotic zeros, and certain known achievements on asymptotic behavior of limiting zeros are shown to be particular cases of the results presented.

The Box–Cox Transformation and Non‐Iterative Estimation Methods for Ordinal Log‐Linear Models

SummaryRecently Beh and Farver investigated and evaluated three non‐iterative procedures for estimating the linear‐by‐linear parameter of an ordinal log‐linear model. The study demonstrated that these non‐iterative techniques provide estimates that are, for most types of contingency tables, statistically indistinguishable from estimates from Newton's unidimensional algorithm. Here we show how two of these techniques are related using the Box–Cox transformation. We also show that by using this transformation, accurate non‐iterative estimates are achievable even when a contingency table contains sampling zeros.

Design of Compensators to Relocate Sampling Zeros of Digital Control Systems for DC Motors

This paper presents a design method for a pre-filter for relocating sampling zeros based on the Taylor expansion, which was recently found to be reduced to a simple formula for a relative degree of...

Maximum likelihood estimation in log-linear models

We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and investigate estimability of the natural and mean-value parameters under a nonexistent MLE. Our conditions focus on the role of sampling zeros in the observed table. We situate our results within the framework of extended exponential families, and we exploit the geometric properties of log-linear models. We propose algorithms for extended maximum likelihood estimation that improve and correct the existing algorithms for log-linear model analysis.

Factors Influencing the Mixture Index of Model Fit in Contingency Tables Showing Independence

This study: (a) evaluated several competing techniques for dealing with sampling zeros for the two-point mixture model index, * π , in contingency tables when the independence assumption holds; and (b) investigated the performance of the estimate, * π , in various combinations of conditions, as a function of different sizes of tables, different marginal distributions and different sample sizes. Furthermore, the standard error of π ∗ estimated by use of a method proposed by Rudas, Clogg and Lindsay (1994) and the “true” standard error based on empirical simulations in various scenarios especially when encountering small sample sizes and π ∗ close to 0 were compared. These goals were achieved by Monte Carlo methods that simulate a variety of scenarios and then were applied to two real data examples. BACKGROUND AND DEVELOPMENT Traditional methods for evaluating contingency table models based on chi square statistics or quantities derived from them are not appealing in many applied research settings. According to Rudas (1998), “First, when the model is not true, a comparison of the data to what could only be expected if it were is of very little meaning; second, the actual distribution of the statistic may be very different from the reference distribution if some of the underlying assumptions are violated.” In addition, conventional methods are sensitive to sample size; often a model is rejected when fitted to a large data set even though the model may represent a reasonable summary of the data for practical purposes. In sharp contrast to chi-squared tests of fit methods, which rely heavily on size of the table, sample size and actual true probabilities, the mixture index of fit proposed by Rudas,

Frequency domain accuracy of approximate sampled-data models

AbstractAccurate sampled-data models are required when a digital device interacts with a continuous-time system. Even though exact sampled models can be obtained for linear systems, simple approximate models are sometimes preferred in applications to reduce computational load or to preserve the role of physical parameters. In this paper we quantify the frequency domain relative error of three kinds of approximate sampled models: (i) simple models obtained by derivative approximations, (ii) models obtained including the asymptotic sampling zeros, and (iii) models obtained by a truncated Taylor expansion of the system state equations. In particular, we characterize the bandwidth where each of the proposed models provides the highest accuracy.

A Bayesian Approach for Zero-Inflated Count Regression Models by Using the Reversible Jump Markov Chain Monte Carlo Method and an Application

In this study, estimation of the parameters of the zero-inflated count regression models and computations of posterior model probabilities of the log-linear models defined for each zero-inflated count regression models are investigated from the Bayesian point of view. In addition, determinations of the most suitable log-linear and regression models are investigated. It is known that zero-inflated count regression models cover zero-inflated Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. The classical approach has some problematic points but the Bayesian approach does not have similar flaws. This work points out the reasons for using the Bayesian approach. It also lists advantages and disadvantages of the classical and Bayesian approaches. As an application, a zoological data set, including structural and sampling zeros, is used in the presence of extra zeros. In this work, it is observed that fitting a zero-inflated negative binomial regression model creates no problems at all, even though it is known that fitting a zero-inflated negative binomial regression model is the most problematic procedure in the classical approach. Additionally, it is found that the best fitting model is the log-linear model under the negative binomial regression model, which does not include three-way interactions of factors.

Decomposition and Model Selection for Large Contingency Tables

Large contingency tables summarizing categorical variables arise in many areas. One example is in biology, where large numbers of biomarkers are cross-tabulated according to their discrete expression level. Interactions of the variables are of great interest and are generally studied with log-linear models. The structure of a log-linear model can be visually represented by a graph from which the conditional independence structure can then be easily read off. However, since the number of parameters in a saturated model grows exponentially in the number of variables, this generally comes with a heavy computational burden. Even if we restrict ourselves to models of lower-order interactions or other sparse structures, we are faced with the problem of a large number of cells which play the role of sample size. This is in sharp contrast to high-dimensional regression or classification procedures because, in addition to a high-dimensional parameter, we also have to deal with the analogue of a huge sample size. Furthermore, high-dimensional tables naturally feature a large number of sampling zeros which often leads to the nonexistence of the maximum likelihood estimate. We therefore present a decomposition approach, where we first divide the problem into several lower-dimensional problems and then combine these to form a global solution. Our methodology is computationally feasible for log-linear interaction models with many categorical variables each or some of them having many levels. We demonstrate the proposed method on simulated data and apply it to a bio-medical problem in cancer research.

Speaking Stata: I. J. Good and Quasi-Bayes Smoothing of Categorical Frequencies

I. J. Good (1916–2009) was a prolific scientist who contributed to many fields, mostly from a Bayesian standpoint. This column explains his idea of quasi-Bayes (a.k.a. pseudo-Bayes) estimation or smoothing of categorical frequencies in a contingency table, which is especially useful as a way of dealing with awkward sampling or random zeros. It shows how the method can be implemented, almost calculator-style, using a combination of Stata and Mata. Convenience commands qsbayesi and qsbayes are also introduced.

Stability of Zero Dynamics of Sampled-Data Nonlinear Systems

One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Hence, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed an accurate approximate model which includes extra zero dynamics corresponding to the relative degree of the continuous-time nonlinear system. Such extra zero dynamics are called sampling zero dynamics. A more accurate sampled-data model is, however, required when the relative degree of a continuous-time nonlinear plant is two. The reason is that the closed-loop system becomes unstable when the more accurate sampled-data model has unstable sampling zero dynamics and a controller design method based on cancellation of the zero dynamics is applied. This paper derives the sampling zero dynamics of the more accurate sampled-data model and shows a condition which assures the stability of the sampling zero dynamics of the model. Further, it is shown that this extends a well-known result for the stability condition of linear systems to the nonlinear case.

Three centuries of categorical data analysis: Log-linear models and maximum likelihood estimation

The common view of the history of contingency tables is that it begins in 1900 with the work of Pearson and Yule, but in fact it extends back at least into the 19th century. Moreover, it remains an active area of research today. In this paper we give an overview of this history focussing on the development of log-linear models and their estimation via the method of maximum likelihood. Roy played a crucial role in this development with two papers co-authored with his students, Mitra and Marvin Kastenbaum, at roughly the mid-point temporally in this development. Then we describe a problem that eluded Roy and his students, that of the implications of sampling zeros for the existence of maximum likelihood estimates for log-linear models. Understanding the problem of non-existence is crucial to the analysis of large sparse contingency tables. We introduce some relevant results from the application of algebraic geometry to the study of this statistical problem.

ADAPTIVE CONTROL VIA FINITELY-CONVERGENT ALGORITHMS

A short review of the method of finitely-convergent algorithms in the theory of adaptive systems is presented. The method was proposed in (Yakubovich, V.A., Recurrent Finite-convergent Algorithms to Solve the Systems of Inequalities, Dokl. Akad. Nauk SSSR, 1966, vol. 166, no. 6, pp. 1308–1311. English translation in Soviet Math. Dokl., 1966, vol. 7, pp. 300–304). The method consists of reduction of an adaptive control problem to a countable system of inequalities. A procedure of their solution plays a role of adaptation algorithm. It should converge in a finite time in a closed loop system. The method often allows to obtain suboptimal (in the minimax sense) adaptive control systems.Basic ideas and achievments of the method as well as some recent results are considered. Among them are adaptive control of sampled systems with time delay which is not a multiple of the sampling period. In this relation a problem of limiting zeros of sampled systems with delay arise. It is shown that limiting values of the sampling zeros have the same properties as zeros of Euler polynomials.

LOCATING THE STRUCTURAL ZEROS FOR INTERNAL ANCHOR TESTS: INCLUDING THE CASE OF ROUNDED FORMULA SCORES

There are test-equating situations in which it may be appropriate to fit a loglinear or other type of probability model to the joint distribution of a total score on a test and a score on part of that test. For anchor test designs, this situation arises for internal anchor tests, which are embedded within the total test. Similarly, a part-whole relationship arises between two scores when a few test items are dropped from a test and a single group design is used to equate the scores of the full test to the part that remains after those items are deleted. In these part-whole situations, the resulting bivariate frequency distribution will exhibit structural zeros due to the fact that some scores on the total test are impossible for specific values on the partial test. Without knowing where the structural zeros are, it is impossible to distinguish them from zero frequencies that are simply due to size of the sample (i.e., sampling zeros). When probability models are estimated for these joint distributions, it is usual to require the models to assign positive probability to the sampling zeros but to avoid assigning positive probability to the structural zeros. To do this, it is important to be able to locate where the structural zeros are in the bivariate distribution. When the scores on the tests are consecutive integers, it is easy to determine the location of the structural zeros. This report gives a solution to the problem of locating the structural zeros that arise for a class of bivariate distributions that includes both number-right scores and formula scores that have been rounded to integer values. The result for rounded formula scores is a simple alteration of the case where all the scores are consecutive integers.

Influence Measures in Contingency Tables With Application in Sampling Zeros

Based on the local influence approach with an appropriate perturbation scheme, measures are developed to assess the influence of an individual cell in contingency tables. The authors demonstrate that the developed measures are particularly suitable for sensitivity analysis in tables with sampling zeros. The independence model and the log-linear model, together with numerical examples, are presented for illustration.

Sampling zeros and the Euler-Frobenius polynomials

We show that the zeros of sampled-data systems resulting from rapid sampling of continuous-time systems preceded by a zero-order hold (ZOH) are the roots of the Euler-Frobenius polynomials. Using known properties of these polynomials, we prove two conjectures of Hagiwara et al. (1993), the first of which concerns the simplicity, negative realness, and interlacing properties of the sampling zeros of ZOH- and first-order hold (FOH-) sampled systems. To prove the second conjecture, we show that in the fast sampling limit, and as the continuous-time relative degree increases, the largest sampling zero for FOH-sampled systems approaches 1/e, where e is the base of the natural logarithm.

Using covariates in loglinear models with sampling zeros; A cautionary note

When analyzing loglinear models, most computer packages will first construct the contingency table and subsequently fit the required loglinear model. Some computer packages allow the incorporation of covariates, such as age and/or income, into the loglinear model. In the SPSS modules LOGLINEAR and GENLOG this option is implemented by calculating for each pattern of the classifying variables the mean value(s) of the covariate(s), while this covariate vector is subsequently added to the design matrix describing the loglinear model. In this article it is shown that the use of covariates in the case of contingency tables containing sampling zeros will lead to incorrect results for the SPSS modules LOGLINEAR and GENLOG. Parameter estimates, deviances and the number of degrees of freedom may be highly incorrect. This is illustrated in the case of the loglinear uniform association model, using an example from a handbook on categorical data analysis. A second, more complex example is discussed where, as a result of this incorrect handling of covariates, wrong results have been published in the literature. It is concluded that (conditional) multinomial logit models should be used. While SPSS currently does not include such models, it is demonstrated how to obtain correct results for the case that covariates are functions of the classifying variables.

Zeros of discretized continuous systems expressed in the Euler operator-an asymptotic analysis

The structure of the zeros of SISO continuous-time systems, which are discretized via a zero-order hold and expressed in the Euler operator, is studied. In particular, it is shown that when state-space descriptions of linear SISO continuous-time systems with relative degree /spl ges/2 are discretized, then the zero dynamics of the resulting discrete system is singularly perturbed and shows a separation of time scale. The part of the zero dynamics associated with the fast time scale is shown to correspond to the zeros introduced by the sampling process (sampling zeros). An asymptotic formula for this part of the zero dynamics is given, and implications of the result to control design based on pole zero cancellation is discussed. >

Digital model-reference flight control of aircraft with unstable sampling zeros

Digital model-reference flight control of aircraft with unstable sampling zeros

On Analysis of Two-Way Contingency Tables with some Sampling Zero Cell Counts — Application to Human Reproduction Wastage according to Age —

A systematic procedure is described for the analysis of I x J cross-classifications with some nonstructural zeros. This includes (1) use of pseudo-Bayes estimators to remove zeros (2) fitting the smoothed array to all possible configurations of the log-linear models (3) fitting the data to the quasi -independence model after omitting counts of some anomalous cells — on the basis of standardized residuals to detect the cause of deviation from the null independence model. As a guide, a risk function value is computed for each array of smoothed pseudo-Bayesian estimates.Real-life data (based on a sampling survey conducted on the population of female nurses in Kuwait) is used for illustration.