Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

ABC: A Big CAD Model Dataset for Geometric Deep Learning

Abstract: We introduce ABC-Dataset, a collection of one million Computer-Aided Design (CAD) models for research of geometric deep learning methods and applications. Each model is a collection of explicitly parametrized curves and surfaces, providing ground truth for differential quantities, patch segmentation, geometric feature detection, and shape reconstruction. Sampling the parametric descriptions of surfaces and curves allows generating data in different formats and resolutions, enabling fair comparisons for a wide range of geometric learning algorithms. As a use case for our dataset, we perform a large-scale benchmark for estimation of surface normals, comparing existing data driven methods and evaluating their performance against both the ground truth and traditional normal estimation methods.

Statistical matching: theory and practice

Abstract: Preface. 1 The Statistical Matching Problem. 1.1 Introduction. 1.2 The Statistical Framework. 1.3 The Missing Data Mechanism in the Statistical Matching Problem. 1.4 Accuracy of a Statistical Matching Procedure. 1.4.1 Model assumptions. 1.4.2 Accuracy of the estimator. 1.4.3 Representativeness of the synthetic file. 1.4.4 Accuracy of estimators applied on the synthetic data set. 1.5 Outline of the Book. 2 The Conditional Independence Assumption. 2.1 The Macro Approach in a Parametric Setting. 2.1.1 Univariate normal distributions case. 2.1.2 The multinormal case. 2.1.3 The multinomial case. 2.2 The Micro (Predictive) Approach in the Parametric Framework. 2.2.1 Conditional mean matching. 2.2.2 Draws based on conditional predictive distributions. 2.2.3 Representativeness of the predicted files. 2.3 Nonparametric Macro Methods. 2.4 The Nonparametric Micro Approach. 2.4.1 Random hot deck. 2.4.2 Rank hot deck. 2.4.3 Distance hot deck. 2.4.4 The matching noise. 2.5 Mixed Methods. 2.5.1 Continuous variables. 2.5.2 Categorical variables. 2.6 Comparison of Some Statistical Matching Procedures under the CIA. 2.7 The Bayesian Approach. 2.8 Other IdentifiableModels. 2.8.1 The pairwise independence assumption. 2.8.2 Finite mixture models. 3 Auxiliary Information. 3.1 Different Kinds of Auxiliary Information. 3.2 Parametric Macro Methods. 3.2.1 The use of a complete third file. 3.2.2 The use of an incomplete third file. 3.2.3 The use of information on inestimable parameters. 3.2.4 The multinormal case. 3.2.5 Comparison of different regression parameter estimators through simulation. 3.2.6 The multinomial case. 3.3 Parametric Predictive Approaches. 3.4 Nonparametric Macro Methods. 3.5 The Nonparametric Micro Approach with Auxiliary Information. 3.6 Mixed Methods. 3.6.1 Continuous variables. 3.6.2 Comparison between some mixed methods. 3.6.3 Categorical variables. 3.7 Categorical Constrained Techniques. 3.7.1 Auxiliary micro information and categorical constraints. 3.7.2 Auxiliary information in the form of categorical constraints. 3.8 The Bayesian Approach. 4 Uncertainty in Statistical Matching. 4.1 Introduction. 4.2 A Formal Definition of Uncertainty. 4.3 Measures of Uncertainty. 4.3.1 Uncertainty in the normal case. 4.3.2 Uncertainty in the multinomial case. 4.4 Estimation of Uncertainty. 4.4.1 Maximum likelihood estimation of uncertainty in the multinormal case. 4.4.2 Maximum likelihood estimation of uncertainty in the multinomial case. 4.5 Reduction of Uncertainty: Use of Parameter Constraints. 4.5.1 The multinomial case. 4.6 Further Aspects of Maximum Likelihood Estimation of Uncertainty. 4.7 An Example with Real Data. 4.8 Other Approaches to the Assessment of Uncertainty. 4.8.1 The consistent approach. 4.8.2 The multiple imputation approach. 4.8.3 The de Finetti coherence approach. 5 Statistical Matching and Finite Populations. 5.1 Matching Two Archives. 5.1.1 Definition of the CIA. 5.2 Statistical Matching and Sampling from a Finite Population. 5.3 Parametric Methods under the CIA. 5.3.1 The macro approach when the CIA holds. 5.3.2 The predictive approach. 5.4 Parametric Methods when Auxiliary Information is Available. 5.4.1 The macro approach. 5.4.2 The predictive approach. 5.5 File Concatenation. 5.6 Nonparametric Methods. 6 Issues in Preparing for Statistical Matching. 6.1 Reconciliation of Concepts and Definitions of Two Sources. 6.1.1 Reconciliation of biased sources. 6.1.2 Reconciliation of inconsistent definitions. 6.2 How to Choose the Matching Variables. 7 Applications. 7.1 Introduction. 7.2 Case Study: The Social Accounting Matrix. 7.2.1 Harmonization step. 7.2.2 Modelling the social accounting matrix. 7.2.3 Choosing the matching variables. 7.2.4 The SAM under the CIA. 7.2.5 The SAM and auxiliary information. 7.2.6 Assessment of uncertainty for the SAM. A Statistical Methods for Partially Observed Data. A.1 Maximum Likelihood Estimation with Missing Data. A.1.1 Missing data mechanisms. A.1.2 Maximum likelihood and ignorable nonresponse. A.2 Bayesian Inference withMissing Data. B Loglinear Models. B.1 Maximum Likelihood Estimation of the Parameters. C Distance Functions. D Finite Population Sampling. E R Code. E.1 The R Environment. E.2 R Code for Nonparametric Methods. E.3 R Code for Parametric and Mixed Methods. E.4 R Code for the Study of Uncertainty. E.5 Other R Functions. References. Index.

Parametric Random Vibration

Abstract: PARAMETRIC random vibration is an applied scientific discipline that covers problems from the broad field of applied dynamics, e.g. structural dynamics, aerodynamics, naval architecture etc. The system equations are characterized by random perturbed parameters while, in many practical situations, non-linearities and random forcing terms create additional complications. Various textbooks have appeared covering the field of random vibration of time-invariant systems. This monograph, a state of the art presentation of parametric random vibration, based on an enormous number of published papers and reports, is a great credit to the author. In the first chapter the reader is introduced to the basic definitions of parametric and autoparametric instabilities, chaotic motion, pseudo-random excitation and crypto-deter-ministic systems and a brief review of parametric random vibration is given. In random vibrations, the emphasis is on the response and stability of systems under wide band random parametric excitations. Unfortunately system equations with physical wide band noise excitation are very difficult to handle, therefore physical Gaussian wide band noise is often replaced by idealized white noise, or the wide band noise is generated by a shaping filter driven by white noise. This is usually the point where many engineers get lost. They are referred to books on stochastic processes and stochastic differential equations and are encouraged to go into theories which are embedded in mathematical abstraction. For these engineers the root of all evil (which is at the same time a source of pleasure for many mathematicians) is the unbounded variation of the Brownian motion, which has white noise as its derivative, in a formal sense. For these processes a new stochastic calculus is needed. In Chapters 2-4 the author provides the necessary tools for deriving response statistical functions and techniques for examining stochastic parameter stability, as required in later chapters. The author has chosen an engineering approach without mathematical abstraction, which implies that some important theorems are verified in a heuristic way, while many others are only mentioned. The result is a nice reference frame for readers with a reasonable background in stochastic processes and stochastic differential equations. Readers without this background will certainly get into trouble, for example, when reading the definitions of random variables and random processes. Obviously, the author could not resist the temptation to give some flavour of mathematical abstraction by introducing a random variable as a function of a sample space f~, which is confusing in the context it is used. …

On the relationship between parametric and geometric active contours

Abstract: Geometric active contours have many advantages over parametric active contours, such as computational simplicity and the ability to change the curve topology during deformation. While many of the capabilities of the older parametric active contours have been reproduced in geometric active contours, the relationship between the two has not always been clear. We develop a precise relationship between the two which includes spatially-varying coefficients, both tension and rigidity, and non-conservative external forces. The result is a very general geometric active contour formulation for which the intuitive design principles of parametric active contours can be applied. We demonstrate several novel applications in a series of simulations.

The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing

Abstract: This article shows how to fit a smooth curve (polynomial spline) to pairs of data values (yi, xi ). Prior specification of a parametric functional form for the curve is not required. The resulting curve can be used to describe the pattern of the data, and to predict unknown values of y given x. Both point and interval estimates are produced. The method is easy to use, and the computational requirements are modest, even for large sample sizes. Our method is based on maximum likelihood estimation of a signal-in-noise model of the data. We use the Kalman filter to evaluate the likelihood function and achieve significant computational advantages over previous approaches to this problem.