Showing papers on "Parametric model published in 1994"

Simulation Procedures and Likelihood Inference for Spatial Point Processes

Abstract: An alternative algorithm to the usual birth-and-death procedure for simulating spatial point processes is introduced. The algorithm is used in a discussion of unconditional versus conditional likelihood inference for parametric models of spatial point processes.

Text-independent speaker identification

Abstract: We describe current approaches to text-independent speaker identification based on probabilistic modeling techniques. The probabilistic approaches have largely supplanted methods based on comparisons of long-term feature averages. The probabilistic approaches have an important and basic dichotomy into nonparametric and parametric probability models. Nonparametric models have the advantage of being potentially more accurate models (though possibly more fragile) while parametric models that offer computational efficiencies and the ability to characterize the effects of the environment by the effects on the parameters. A robust speaker-identification system is presented that was able to deal with various forms of anomalies that are localized in time, such as spurious noise events and crosstalk. It is based on a segmental approach in which normalized segment scores formed the basic input for a variety of robust 43% procedures. Experimental results are presented, illustrating 59% the advantages and disadvantages of the different procedures. 64%. We show the role that cross-validation can play in determining how to weight the different sources of information when combining them into a single score. Finally we explore a Bayesian approach to measuring confidence in the decisions made, which enabled us to reject the consideration of certain tests in order to achieve an improved, predicted performance level on the tests that were retained. >

Robust Bounded-Influence Tests in General Parametric Models

Abstract: We introduce robust tests for testing hypotheses in a general parametric model. These are robust versions of the Wald, scores, and likelihood ratio tests and are based on general M estimators. Their asymptotic properties and influence functions are derived. It is shown that the stability of the level is obtained by bounding the self-standardized sensitivity of the corresponding M estimator. Furthermore, optimally bounded-influence tests are derived for the Wald- and scores-type tests. Applications to real and simulated data sets are given to illustrate the tests' performance.

Integrated models of signal and background with application to speaker identification in noise

Abstract: Discusses the problem of robust parametric model estimation and classification in noisy acoustic environments. Characterization and modeling of the external noise sources in these environments is in itself an important issue in noise compensation. The techniques described provide a mechanism for integrating parametric models of the acoustic background with the signal model so that noise compensation is tightly coupled with signal model training and classification. Prior information about the acoustic background process is provided using a maximum likelihood parameter estimation procedure that integrates an a priori model of the acoustic background with the signal model. An experimental study is presented on the application of this approach to text-independent speaker identification in noisy acoustic environments. Considerable improvement in speaker classification performance was obtained for classifying unlabeled sections of conversational speech utterances from a 16-speaker population under cross-environment training and testing conditions. >

Multichannel ARMA processes

Abstract: Parametric modeling of multichannel time series is accomplished by using higher (than second) order statistics (HOS) of the observed nonGaussian data. Cumulants of vector processes are defined using a Kronecker product formulation, and consistency of their sample estimators is addressed. Identifiability results in connection with the HOS-based parameter estimation of causal and noncausal multivariate ARMA processes are established. Estimates of the parameters of causal ARMA models are obtained as the solution to a set of linear equations, whereas those of noncausal ARMA models are obtained as the solution to a cumulant matching algorithm. Conventional approaches based on second-order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix. HOS-based methods yield solutions that are unique to within post-multiplication by an (extended) permutation matrix; additionally, the multiminimum phase assumption can be relaxed, and the observations may be contaminated with colored Gaussian noise. Frequency-domain methods for nonparametric system identification are discussed briefly. Simulations results validating the multichannel parameter estimation algorithms are provided. >

Testing a Parametric Model against a Semiparametric Alternative

Abstract: This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions The results of Monte Carlo experiments and an application illustrate the usefulness of the new test

Bayesian Nonparametric Estimation for Incomplete Data Via Successive Substitution Sampling

Abstract: In the problem of estimating an unknown distribution function $F$ in the presence of censoring, one can use a nonparametric estimator such as the Kaplan-Meier estimator, or one can consider parametric modeling. There are many situations where physical reasons indicate that a certain parametric model holds approximately. In these cases a nonparametric estimator may be very inefficient relative to a parametric estimator. On the other hand, if the parametric model is only a crude approximation to the actual model, then the parametric estimator may perform poorly relative to the nonparametric estimator, and may even be inconsistent. The Bayesian paradigm provides a reasonable framework for this problem. In a Bayesian approach, one would try to put a prior distribution on $F$ that gives most of its mass to small neighborhoods of the entire parametric family. We show that certain priors based on the Dirichlet process prior can be used to accomplish this. For these priors the posterior distribution of $F$ given the censored data appears to be analytically intractable. We provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm. We also show convergence of the algorithm.

Time-domain tests for Gaussianity and time-reversibility

Abstract: Statistical signal processing algorithms often rely upon Gaussianity and time-reversibility, two important notions related to the probability structure of stationary random signals and their symmetry. Parametric models obtained via second-order statistics (SOS) are appropriate when the available data is Gaussian and time-reversible. On the other hand, evidence of nonlinearity, non-Gaussianity, or time-irreversibility favors the use of higher-order statistics (HOS). In order to validate Gaussianity and time-reversibility, and quantify the tradeoffs between SOS and HOS, consistent, time-domain chi-squared statistical tests are developed. Exact asymptotic distributions are derived to estimate the power of the tests, including a covariance expression for fourth-order sample cumulants. A modification of existing linearity tests in the presence of additive Gaussian noise is discussed briefly. The novel Gaussianity statistic is computationally attractive, leads to a constant-false-alarm-rate test and is well suited for parametric modeling because it employs the minimal HOS lags which uniquely characterize ARMA processes. Simulations include comparisons with an existing frequency-domain approach and an application to real seismic data. Time-reversibility tests are also derived and their performance is analyzed both theoretically and experimentally. >

Robust methods for personal-income distribution models†

Abstract: Statistical problems in modelling personal-income distributions include estimation procedures, testing, and model choice. Typically, the parameters of a given model are estimated by classical procedures such as maximum-likelihood and least-squares estimators. Unfortunately, the classical methods are very sensitive to model deviations such as gross errors in the data, grouping effects, or model misspecifications. These deviations can ruin the values of the estimators and inequality measures and can produce false information about the distribution of the personal income in a country. In this paper we discuss the use of robust techniques for the estimation of income distributions. These methods behave like the classical procedures at the model but are less influenced by model deviations and can be applied to general estimation problems.

Autocorrelation techniques in color flow imaging: signal model and statistical properties of the autocorrelation estimates

Abstract: A review of the scattering theory for moving blood, and a model for the signal in a multigated pulsed wave Doppler system is presented. The model describes the relation between a general time-variable velocity field and the signal correlation in space and time, including the effect of movement of the ultrasonic beam for color flow imaging systems with mechanical scanning. In the case of a constant and rectilinear velocity field, a parametric model for the autocorrelation function is deduced. General formulas for a full second order characterization of the set of autocorrelation estimates, with arbitrary lags in the spatial and temporal directions, are developed. The formulas are applied to the parametric model, and numerical results for the estimator variance are presented. A qualitative evaluation of the theoretical results has been performed by offline-processing of 2-D Doppler signals from a color flow imaging scanner. The benefit of spatial and temporal averaging is demonstrated by using different averaging filters to the same set of recorded data. >

A parametric model for cluster correlated categorical data.

Abstract: SUMMARY A fully parametric copula model for symmetric dependent clustered categorical data is discussed. The model accommodates any marginal regression models of interest and admits a broad range of within-cluster association. The form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes. The model contains an association parameter that is estimated from the data to give a measure of the strength of the within-cluster association and also a test of independence. Two examples are given to illustrate the methods.

On the Dynamic Properties of Asymmetric Models of Real GNP

Abstract: There is now a substantial body of evidence that suggests business cycles are asymmetric. However, the evidence has been accumulated using a wide array of statistical techniques and, consequently, is based on various definitions of asymmetry. This paper examines several parametric models that have been used to study asymmetries in real GNP. Although these models capture asymmetries in very different ways, their dynamic properties are remarkably similar.

Reflexive graphs and parametric polymorphism

Abstract: The pioneering work on relational parametricity for the second order lambda calculus was done by Reynolds (1983) under the assumption of the existence of set-based models, and subsequently reformulated by him, in conjunction with his student Ma, using the technology of PL-categories. The aim of this paper is to use the different technology of internal category theory to re-examine Ma and Reynolds' definitions. Apart from clarifying some of their constructions, this view enables us to prove that if we start with a non-parametric model which is left exact and which satisfies a completeness condition corresponding to Ma and Reynolds "suitability for polymorphism", then we can recover a parametric model with the same category of closed types. This implies, for example, that any suitably complete model (such as the PER model) has a parametric counterpart. >

Handling covariates in population pharmacokinetics

Abstract: Population models were developed to analyze processes, described by parametric models, from measurements obtained in a sample of individuals. In order to analyze the sources of interindividual variability, covariates may be incorporated in the population analysis. The exploratory analyses and the two-stage approaches which use standard non-linear regression techniques are simple tools to select meaningful covariates. The global population approaches may be divided into two classes within which the covariates are handled differently: the parametric and the non-parametric methods. The power as well as the limitations of each approach regarding handling of covariates are illustrated and compared using the same data set which concerns the pharmacokinetics of gentamicin in neonates. With parametric approaches a second-stage model between structural parameters and covariates has to be defined. In the non-parametric method the joint distribution of parameters and covariates is estimated without parametric assumptions; however, it is assumed that covariates are observed with some error and parameters involved in functional relationships are not estimated. The important results concerning gentamicin in neonates were found by the two methods.

Estimation of linear parametric models of nonGaussian discrete random fields with application to texture synthesis

Abstract: A general (possibly asymmetric noncausal and/or nonminimum phase) 2D autoregressive moving average random field model driven by an independent and identically distributed 2D nonGaussian sequence is considered. The model is restricted to be invertible, i.e., system zeros are not allowed to lie on the unit bicircle. Three performance criteria are investigated for parameter estimation of the system parameters given only the output measurements (image pixels). The proposed criteria are functions of the higher order cumulant statistics of an inverse filter output. One of these criteria is novel and the others have been considered in past only for moving average inverses and without any analysis of their consistency. In the paper strong consistency of the proposed methods under the assumption that the system order is known is proved. The convergence of the proposed parameter estimators under overparametrization is also analyzed. Experimental results involving synthesized as well as real life textures are presented to illustrate the performance of two of the considered approaches. Experimental results of synthesis of 128/spl times/128 textures visually resembling several real life textures in the Brodatz album (and other sources) are presented. >

Minimum complexity regression estimation with weakly dependent observations

Abstract: The minimum complexity regression estimation framework, due to Barron, is a general data-driven methodology for estimating a regression function from a given list of parametric models using independent and identically distributed (i.i.d.) observations. We extend Barron's regression estimation framework to m-dependent observations and to strongly mixing observations. In particular, we propose abstract minimum complexity regression estimators for dependent observations, which may be adapted to a particular list of parametric models, and establish upper bounds on the statistical risks of the proposed estimators in terms of certain deterministic indices of resolvability. Assuming that the regression function satisfies a certain Fourier-transform-type representation, we examine minimum complexity regression estimators adapted to a list of parametric models based on neural networks and, by using the upper bounds for the abstract estimators, we establish rates of convergence for the statistical risks of these estimators. Also, as a key tool, we extend the classical Bernstein inequality from i.i.d. random variables to m -dependent processes and to strongly mixing processes.

Count Data Models: Econometric Theory and an Application to Labor Mobility

Abstract: This text presents statistical methods for the analysis of events. The primary focus is on single equation cross-section models. It addresses both the methodology and the practice of the subject and provides both a synthesis of a diverse body of literature and a contribution to the progress of the methodology, establishing several new results and introducing new models. Starting from the standard Poisson regression model as a benchmark, the causes, symptoms and consequences of misspecification are worked out. Both parametric and semi-parametric alternatives are discussed. While semi-parametric models allow for robust interference, parametric models can identify features of the underlying data generation process.

Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically

Abstract: We introduce a new kernel smoother for nonparametric regression that uses prior information on regression shape in the form of a parametric model In effect, we nonparametrically encompass the parametric model We derive pointwise and uniform consistency and the asymptotic distribution of our procedure It has superior performance to the usual kernel estimators at or near the parametric model It is particularly well motivated for binary data using the probit or logit parametric model as a base We include an application to the Horowitz (1993) transport choice dataset

Estimating multiple independent motions in segmented images using parametric models with local deformations

Abstract: This paper presents a new model for optical flow based on the motion of planar regions plus local deformations. The approach exploits brightness information to organize and constrain the interpretation of the motion by using segmented regions of piecewise smooth brightness to hypothesize planar regions in the scene. Parametric flow models are fitted to these regions an a two step process which first computes a coarse fit and then refines it using a generalization of the standard area-based regression approaches. Since the assumption of planarity is likely to be violated, we allow local deformations from the planar assumption. This parametric+deformation model exploits the strong constraints of parametric approaches while retaining the adaptive nature of regularization approaches. >

The identification of nonlinear discrete-time fading-memory systems using neural network models

Abstract: A fading-memory system is a system that tends to forget its input asymptotically over time. It has been shown that discrete-time fading-memory systems can be uniformly approximated arbitrarily closely over a set of bounded input sequences simply by uniformly approximating sufficiently closely either the external or internal representation of the system. In other words, the problem of uniformly approximating a fading-memory system reduces to the problem of uniformly approximating continuous real-valued functions on compact sets. The perceptron is a parametric model that realizes a set of continuous real-valued functions that is uniformly dense in the set of all continuous real-valued functions. Using the perceptron to uniformly approximate the external and internal representations of a discrete-time fading-memory system results, respectively, in simple finite-memory and infinite-memory parametric system models. Algorithms for estimating the model parameters that yield a best approximation to a given fading-memory system are discussed. An application to nonlinear noise cancellation in telephone systems is presented. >

Context-dependent markov model structured by locus equations : applications to phonetic classification

Abstract: In this paper, a quantitative and parametric model is presented that incorporates the role of context‐dependent formant transitions in phonetic decoding of speech. The idea is to use the locus equations established from speech science to constrain the model parameters so that the number of parameters for the context‐dependent model reduces to the same order as that for the context‐independent model. In contrast to the knowledge‐based, largely qualitative approaches employing also the formant transition information, our approach allows the parameters of the phonetic classifier, including the locus‐equation slopes and intercepts, in conjunction with the hidden Markov model parameters, to be subject to mathematical optimization via an effective and efficient training procedure developed in this study. Detailed analysis of the results obtained from automatic training shows that the estimates of the locus‐equation slopes and intercepts are consistent with those manually derived and reported in the speech scien...

Statistical analysis of a spatial birth-and-death process model with a view to modelling linear dune fields

Abstract: Statistical inference for parametric models of spatial birth-and-death processes is discussed in detail. In particular, a flexible and statistically tractable parametric class of such processes, defined on the real line, is presented and analysed by likelihood and partial likelihood methods. The suggested methods are illustrated by applying them to two sets of data given in the form of aerial photographs from the Kalahari Desert.

Parametric modeling of spaceborne SAR image geometry. Application: SEASAT/SPOT image registration

Abstract: A parametric modeling of the image geometry of spaceborne synthethic-aperture radar (SAR) sensor is presented. The model parameters are orbital parameters, sensor parameters and SAR processing parameters. This modeling allows geometric processing (points location, geocoding, registration), the accuracy of which is dependent only on parameter measurement errors. In addition, error models enable one to refine the parameters through Bayesian estimation by using control points (ground control points when a map is available, homologous points in the case of image registration). SEASAT/SPOT image registration is presented as an application. The relief effect is discussed and is decorrelated from the parameter error effect. The resulting pixel registration error is less than 10 metres if the relief effect is compensated for

Zernike moment-based feature detectors

Abstract: A novel model-based unified approach is proposed for generating a set of image feature maps (or primal sketches). For each type of feature, a parametric model is developed to characterize the local intensity function in an image. Projections of intensity profile onto a set of orthogonal Zernike moment-generating polynomials are used to estimate model-parameters and in turn generate the desired feature map. A small set of moment-based detectors is identified that can extract various kinds of primal sketches from intensity as well as range images. One main advantage of using parametric model-based techniques is that it is possible to extract complete information (i.e., model parameters) about the underlying image feature, which is desirable in many high-level vision tasks. Experimental results are included to demonstrate the effectiveness of the proposed feature detectors. >