Showing papers on "Parametric statistics published in 1991"

Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics

Abstract: Continuing the development of the structured singular value approach to robust control design, the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty. The problem is shown to be equivalent to a smooth constrained finite-dimensional optimization problem. In view of the fact that the functional to be maximized may have several local extrema, an upper bound on mu whose computation is numerically tractable is established; this leads to a sufficient condition of robust stability and performance. A historical perspective on the development of the mu theory is included. >

A general parametric approach to the meta-analysis of randomized clinical trials.

Abstract: Meta-analysis provides a systematic and quantitative approach to the summary of results from randomized studies. Whilst many authors have published actual meta-analyses concerning specific therapeutic questions, less has been published about comprehensive methodology. This article presents a general parametric approach, which utilizes efficient score statistics and Fisher's information, and relates this to different methods suggested by previous authors. Normally distributed, binary, ordinal and survival data are considered. Both the fixed effects and random effects model for treatments are described.

Generalized additive models in plant ecology

Abstract: Generalized additive models (GAMs) are a non- parametric extension of generalized linear models (GLMs). They are introduced here as an exploratory tool in the analysis of species distributions with respect to climate. An important result is that the long-debated question of whether a response curve, in one dimension, is actually symmetric and bell- shaped or not, can be tested using GAMs. GAMs and GLMs are discussed and are illustrated by three examples using binary data. A grey-scale plot of one of the fits is constructed to indicate which areas on a map seem climatically suitable for that species. This is useful for species introductions. Further applications are mentioned.

Discrete all-pole modeling

Abstract: A method for parametric modeling and spectral envelopes when only a discrete set of spectral points is given is introduced. This method, called discrete all-pole (DAP) modeling, uses a discrete version of the Itakura-Saito distortion measure as its error criterion. One result is an autocorrelation matching condition that overcomes the limitations of linear prediction and produces better fitting spectral envelopes for spectra that are representable by a relatively small discrete set of values, such as in voiced speech. An iterative algorithm for DAP modeling that is shown to converge to a unique global minimum is presented. Results of applying DAP modeling to real and synthetic speech are also presented. DAP modeling is extended to allow frequency-dependent weighting of the error measure, so that spectral accuracy can be enhanced in certain frequency regions. >

Computational methods for local regression

Abstract: Local regression is a nonparametric method in which the regression surface is estimated by fitting parametric functions locally in the space of the predictors using weighted least squares in a moving fashion similar to the way that a time series is smoothed by moving averages. Three computational methods for local regression are presented. First, fast surface fitting and evaluation is achieved by building ak-d tree in the space of the predictors, evaluating the surface at the corners of the tree, and then interpolating elsewhere by blending functions. Second, surfaces are made conditionally parametric in any proper subset of the predictors by a simple alteration of the weighting scheme. Third degree-of-freedom quantities that would be extremely expensive to compute exactly are approximated, not by numerical methods, but through a statistical model that predicts the quantities from the trace of the hat matrix, which can be computed easily.

Transformations in Density Estimation

Abstract: For the density estimation problem the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations. In this article we propose to transform the data with the intention that a global window width is more appropriate for the density of the transformed data. The density estimate of the original data is the “back-transform” by change of variables of the global window width estimate of the transformed data's density. We explore choosing the transformation from suitable parametric families. Data-based selection rules for the choice of transformations and the window width are discussed. Application to real and simulated data demonstrates the usefulness of our proposals.

On three-dimensional surface reconstruction methods

Abstract: A survey is presented of some of the surface reconstruction methods that can be found in the literature; the focus is on a small, recent, and important subset of the published reconstruction techniques. The techniques are classified based on the surface representation used, implicit versus explicit functions. A study is made of the important aspects of the surface reconstruction techniques. One aspect is the viewpoint invariance of the methods. This is an important property if object recognition is the ultimate objective. The robustness of the various methods is examined. It is determined whether the parameter estimates are biased, and the sensitivity to obscuration is addressed. The latter two aspects are particularly important for fitting functions in the implicit form. A detailed description is given of a parametric reconstruction method for three-dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations. This technique is invariant to rigid motion in dimensional space. >

A Progressive Failure Model for Composite Laminates Containing Openings

Abstract: A progressive failure model is developed for laminated composites containing stress concentrations subjected to in-plane loading. The fundamental approach is to model a damaged lamina using a damaged ply constitutive relation in a simplified manner. The environmental effects including the thermal residual stresses and hygroscopic stresses arc taken into consideration. Parametric studies show that load increment only has little effect on the ultimate strength. When the number of elements for the finite element mesh increases to a certain value, the predicted ultimate strength approaches a stable value. The predictions for the ultimate strength, stress-strain behavior and the damage progression agree reasonably well with the experimental result.

Nonparametric and Semiparametric Methods in Econometrics and Statistics

Abstract: This collection of papers delivered at the Fifth International Symposium in Economic Theory and Econometrics in 1988 is devoted to the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data. Particularly in highly non-linear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require string parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations are investigated and developed in these essays by renowned econometricians.

Optical parametric oscillator frequency tuning and control

Abstract: The frequency-tuning and -control properties of monolithic doubly resonant optical parametric oscillators are analyzed for stable single-mode pump radiation. Single-axial-mode operation is observed on the idler and the signal for both pulsed and continuous pumping. Projections are made for tuning-parameter tolerances that are required for maintenance of stable single-frequency oscillation. Continuous frequency tuning is possible through the simultaneous adjustment of two or three parameters; thus the synthesis of specific frequencies within the broad tuning range of the doubly resonant optical parametric oscillator is permitted.

Parametric characterization of general partially coherent beams propagating through ABCD optical systems

Abstract: Within the formalism of the Wigner distribution function, a new parameter is proposed, which characterizes arbitrary tridimensional partially coherent beams and is invariant through ABCD optical systems. The relationship between such a parameter and the bidimensional concept of beam quality is analyzed. An absolute lower bound that the new parameter can reach is also shown.

Unified Theory on Power Laws for Flow Resistance

Abstract: Two general power formulas, one for hydraulically smooth flows and the other for fully rough flows, are derived in a rational way from the widely accepted logarithmic formulas for the velocity profile and the Darcy-Weisbach friction factor A regression analysis based on the method of least squares is used to determine the valid range of the local velocity (or normal distance from the wall) in the power formula Some older empirical formulas, such as Lacey’s, Manning’s, Blasius’, and Hazen-Williams’, and their valid ranges, are actually explained analytically by the results Incomplete self-similarity of the power law, in which the exponent and the associated coefficient vary with the similarity parameters, such as the Reynolds number and the relative roughness, is elucidated through the parametric representations of the power formulas and their counterparts based on the logarithmic law This paper examines the concept and rationale behind the power formulation of uniform turbulent shear flows, thereby addressing some critical issues in the modeling of flow resistance based on the power law

mu analysis with real parametric uncertainty

Abstract: The authors give a broad overview, from a LFT (linear fractional transformation)/ mu perspective, of some of the theoretical and practical issues associated with robustness in the presence of real parametric uncertainty, with a focus on computation. Recent results on the properties of mu in the mixed case are reviewed, including issues of NP completeness, continuity, computation of bounds, the equivalence of mu and its bounds, and some direct comparisons with Kharitonov-type analysis methods. In addition, some advances in the computational aspects of the problem, including a branch-and-bound algorithm, are briefly presented together with the mixed mu problem may have inherently combinatoric worst-case behavior, practical algorithms with modes computational requirements can be developed for problems of medium size ( >

A method of non‐parametric back‐projection and its application to aids data

Abstract: The method of back-projection has been used to estimate the unobserved past incidence of infection with the human immunodeficiency virus (HIV) and to obtain projections of future AIDS incidence. Here a new approach to back-projection, which avoids parametric assumptions about the form of the HIV infection intensity, is described. This approach gives the data greater opportunity to determine the shape of the estimated intensity function. The method is based on a modification of an EM algorithm for maximum likelihood estimation that incorporates smoothing of the estimated parameters. It is easy to implement on a computer because the computations are based on explicit formulae. The method is illustrated with applications to AIDS data from Australia, U.S.A. and Japanese haemophiliacs.

Variable Resolution Dynamic Programming: Efficiently Learning Action Maps in Multivariate Real-valued State-spaces

Abstract: An effective method to create an autonomous reactive controller is to learn a model of the environment and then use dynamic programming to derive a policy to maximize long term reward. Neither learning environmental models nor dynamic programming require parametric assumptions about the world, and so learning can proceed with no danger of becoming “stuck― by a mismatch between the parametric assumptions and reality. The paper discusses how such an approach can be realized in real valued multivariate state spaces in which straightforward discretization falls prey to the curse of dimensionality.

Sensitivity Analysis for Mean-Variance Portfolio Problems

Abstract: This paper shows how to perform sensitivity analysis for Mean-Variance MV portfolio problems using a general form of parametric quadratic programming. The analysis allows an investor to examine how parametric changes in either the means or the right-hand side of the constraints affect the composition, mean, and variance of the optimal portfolio. The optimal portfolio and associated multipliers are piecewise linear functions of the changes in either the means or the right-hand side of the constraints. The parametric parts of the solution show the rates of substitution of securities in the optimal portfolio, while the parametric parts of the multipliers show the rates at which constraints are either tightening or loosening. Furthermore, the parametric parts of the solution and multipliers change in different intervals when constraints become active or inactive. The optimal MV paths for sensitivity analyses are piecewise parabolic, as in traditional MV analysis. However, the optimal paths may contain negatively sloping segments and are characterized by types of kinks, i.e., points of nondifferentiability, not found in MV analysis.

Effect of operating conditions on the characteristics of pressure fluctuations in a bubble column

Abstract: The effects of operating parameters on the basic statistical characteristics of pressure fluctuations were studied for different measurement configurations in a bubble column of diameter 0.292 m. Different sources of the pressure signal were identified using cross-spectral analysis. A simple parametric method was proposed for on-line flow pattern identification based on the optimal order of the autoregressive model.

Bootstrap statistics for paleomagnetic data

Abstract: The power and utility of paleomagnetic analyses stem largely from the ability to quantify such parameters as the degree of rotation of a rock body, or the orientation of an anisotropy axis. Until recently, estimates for uncertainty in these paleomagnetically determined parameters derived from assumptions concerning the underlying parametric distribution functions of the data. In many geologically important situations, the commonly used parametric distribution functions fail to model the data adequately and the uncertainty estimates so obtained are unreliable. Such essentials as the test for common mean require data sets consistent with a spherically symmetric underlying distribution; their application in inappropriate circumstances can result in flawed interpretations. Moreover, the almost universally used approximation for a cone of 95% confidence for the mean of a sample drawn from a Fisher distribution is quite biased even for moderate dispersions (K = 25). The availablity of inexpensive, powerful computers makes possible the empirical estimation of confidence regions by means of data resampling techniques such as the bootstrap. These resampling schemes replace analytical solutions with repeated simple calculations. We describe a bootstrap approach for the calculation of uncertainties for means or principal directions of paleomagnetic data. The method is tested on means of simulated Fisher distributions with known parameters and is found to be reliable for data sets with more than about 25 elements. Because a Fisher distribution is not assumed, the approach is applicable to a wide range of paleomagnetic data and can be used equally well on directions or associated virtual poles. We also illustrate bootstrap techniques for the discrimination of directions and for the fold test which enable the use of these powerful tests on the wider range of data sets commonly obtained in paleomagnetic investigations.

Semiparametric estimation of monotone and concace utility functions for polychotomous choice models

Abstract: This paper introduces a semiparametric estimation method for Polychotomous Choice models. The method does not require a parametric structure for the systematic subutility of observable exogenous variables. The distribution of the random terms is assumed to be known up to a finite-dimensional parameter vector. In contrast, previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified. The systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory. The estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent. A computational technique to calculate the estimators is developed. Copyright 1991 by The Econometric Society.

Adaptive Stabilization of Nonlinear-systems

Abstract: An overview of the various parametric approaches which can be adopted to solve the problem of adaptive stabilization of nonlinear systems is presented. The Lyapunov design and two estimation designs —equation error filtering and regressor filtering— are revisited. This allows us to unify and generalize most of the available results on the topic and to propose a classification depending on the required extra assumptions — matching conditions or growth conditions.

Optimal morphological pattern restoration from noisy binary images

Abstract: A theoretical analysis of morphological filters for the optimal restoration of noisy binary images is presented. The problem is formulated in a general form, and an optimal solution is obtained by using fundamental tools from mathematical morphology and decision theory. Consideration is given to the set-difference distance function as a measure of comparison between images. This function is used to introduce the mean-difference function as a quantitative measure of the degree of geometrical and topological distortion introduced by morphological filtering. It is proved that the class of alternating sequential filters is a set of parametric, smoothing morphological filters that best preserve the crucial structure of input images in the least-mean-difference sense. >

On robust stability of interval control systems

Abstract: The authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty. The basic system considered is that of the classical Lur'e problem of nonlinear control theory. A robust version of the Lur'e problem consisting of a family of linear time-invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector-bounded nonlinear gains is presently treated. By using the Kharitonov theorem to develop some extremal results on positive realness of interval transfer functions (i.e. a family of rational transfer functions with bounded independent coefficient perturbations), the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed. These calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations. >

A class modelling technique based on potential functions

Abstract: A probabilistic and distribution-free class-modelling technique is developed from potential function discriminant analysis. In the multidimensional space of variables the class boundary is built either by the sample percentile of the probability density estimated by means of potential functions, or by the estimate of the ‘equivalent’ determinant of the variance–covariance matrix. The equivalent determinant is that of a hypothetical multivariate normal distribution whose mean probability density was obtained by potential functions. The bases of this modelling rule are evaluated by means of Monte Carlo experiments. The results on four datasets are used to measure the performances of this method, which equal and sometimes exceed the performances of parametric class-modelling methods based on linear and quadratic discriminant analysis which were used for comparison.

Terminal sliding modes: a new approach to nonlinear control synthesis

Abstract: Many robotic systems would, in the future, be required to operate in environments that are highly unstructured (with varying dynamical properties) and active (possessing means of self-actuation). Many issues pertinent to the stabilization of contact interactions with unpredictable environments remain unresolved, especially in dealing with large magnitude and high frequency parametric uncertainties. The authors propose a new approach to nonlinear control synthesis, based upon a new class of sliding modes, denoted terminal sliders. Terminal controllers that enforce finite convergence to equilibrium are synthesized for an example nonlinear system (with and without parametric uncertainties). Improved performance is demonstrated through the elimination of high frequency control switching employed previously for robustness to parametric uncertainties. The dependence of terminal slider stability upon the rate of change of uncertainties over the sliding surface (rather than the magnitude of the uncertainty itself) results in improved control robustness. Improved reliability is demonstrated through the elimination of interpolation region. Improved (guaranteed) precision is argued for through an analysis of steady state behavior. >

Stability and sensitivity-analysis for stochastic programming

Abstract: Stability and sensitivity studies for stochastic programs have been motivated by the problem of incomplete information about the true probability measure through which the stochastic program is formulated and in connection with the development and evaluation of algorithms. The first part of this survey paper briefly introduces and compares different approaches and points out the contemporary efforts to remove and weaken assumptions that are not realistic (e.g., strict complementarity conditions). The second part surveys recent results on qualitative and quantitative stability with respect to the underlying probability measure and describes the ways and means of statistical sensitivity analysis based on Gâteaux derivatives. The last section comments on parallel statistical sensitivity results obtained in the parametric case, i.e., for probability measures belonging to a parametric family indexed by a finite dimensional vector parameter.

Experimental-evidence of suppression of chaos by resonant parametric perturbations

Abstract: Experimental results are reported concerning the possibility of reducing and even suppressing chaoticity in a bistable magnetoelastic beam system by means of parametric periodic perturbations. The experimental parameters are chosen such that a strange attractor is observed. Then a parametric perturbation is added. When its frequency approaches some resonant value, laminar phases are observed of increasing duration up to complete regularization of the motion at exact resonance.