Abstract: 1. Word Frequencies. 2. Non-parametric models. 3. Parametric models. 4. Mixture distributions. 5. The Randomness Assumption. 6. Examples of Applications. A. List of Symbols. B. Solutions of the exercises. C. Software. D. Data sets. Bibliography. Index.

Abstract: Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models, to nonparametric estimation, for which it provides a very powerful tool that allows adaptation under quite general circumstances. Our approach to model selection also provides a natural connection between the parametric and nonparametric points of view and copes naturally with the fact that a model is not necessarily true. The method is based on the penalization of a least squares criterion which can be viewed as a generalization of Mallows’Cp. A large part of our efforts will be put on choosing properly the list of models and the penalty function for various estimation problems like classical variable selection or adaptive estimation for various types of lp-bodies.

Abstract: We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n -1/2 . Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n -1/2 . There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.

Abstract: Modeling and Data Analysis.- Parametric Modeling.- Diagnostic Tools.- Statistical Inference in Parametric Models.- An Introduction to Parametric Inference.- Extreme Value Models.- Generalized Pareto Models.- Advanced Statistical Analysis.- Statistics of Dependent Variables.- Conditional Extremal Analysis.- Statistical Models for Exceedance Processes.- Elements of Multivariate Statistical Analysis.- Basic Multivariate Concepts and Visualization.- Elliptical and Related Distributions.- Multivariate Maxima.- Multivariate Peaks Over Threshold.- Topics in Hydrology and Environmental Sciences.- Flood Frequency Analysis.- Environmental Sciences.- Topics in Finance and Insurance.- Extreme Returns in Asset Prices.- The Impact of Large Claims on Actuarial Decisions.- Topics in Material and Life Sciences.- Material Sciences.- Life Science.

Abstract: Adaptation over different procedures is of practical importance. Different procedures perform well under different conditions. In many practical situations, it is rather hard to assess which conditions are (approximately) satisfied so as to identify the best procedure for the data at hand. Thus automatic adaptation over various scenarios is desirable. A practically feasible method, named adaptive regression by mixing (ARM), is proposed to convexly combine general candidate regression procedures. Under mild conditions, the resulting estimator is theoretically shown to perform optimally in rates of convergence without knowing which of the original procedures work the best. Simulations are conducted in several settings, including comparing a parametric model with nonparametric alternatives, comparing a neural network with a projection pursuit in multidimensional regression, and combining bandwidths in kernel regression. The results clearly support the theoretical property of ARM. The ARM algorithm assigns we...

Abstract: Single-index modeling is widely applied in,for example,econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric models. By such modeling the statistical analysis usually focuses on estimating the index coefficients. The average derivative estimator (ADE) of the index vector is based on the fact that the average gradient of a single index function $f(x^{\top}\beta)$ is proportional to the index vector $\beta$. Unfortunately,a straightforward application of this idea meets the so-called “curse of dimensionality” problem if the dimensionality $d$ of the model is larger than 2. However, prior information about the vector $\beta$ can be used for improving the quality of gradient estimation by extending the weighting kernel in a direction of small directional derivative. The method proposed in this paper consists of such iterative improvements of the original ADE. The whole procedure requires at most 2 $\log n$ iterations and the resulting estimator is $\sqrt{n}$-consistent under relatively mild assumptions on the model independently of the dimensionality $d$.

Abstract: This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt = µ(xt) + et where the functional form of µ(.) is unknown. We propose viewing µ(.) itself as the outcome of a random process. The paper introduces a new stationary random random field m(.) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for µ(.). We view the parameters that characterize the relation between a given realization of m(.) and the particular value of µ(.) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions µ(.). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment tradeoff may explain the previously reported uneven empirical success of the Phillips Curve.

Abstract: In a previous paper, the author presented a new velocity estimation algorithm, using orientation tensors and parametric motion models to provide both fast and accurate results. One of the tradeoffs between accuracy and speed was that no attempts were made to obtain regions of coherent motion when estimating the parametric models. In this paper we show how this can be improved by doing a simultaneous segmentation of the motion field. The resulting algorithm is slower than the previous one, but more accurate. This is shown by evaluation on the well-known Yosemite sequence, where already the previous algorithm showed an accuracy which was substantially better than for earlier published methods. This result has now been improved further.

Abstract: This paper developes statistical models of the size distribution of lightning-caused wildfires in the boreal mixedwood forests of Alberta, Canada, for the intervals 1980––1998 and 1961––1998 Above

Abstract: In this paper, the application of auto-regressive moving average vector models to system identification and damage detection is investigated. These parametric models have already been applied for the analysis of multiple input-output systems under ambient excitation. Their main advantage consists in the capability of extracting modal parameters from the recorded time signals, without the requirement of excitation measurement. The excitation is supposed to be a stationary Gaussian white noise. The method also allows the estimation of modal parameter uncertainties. On the basis of these uncertainties, a statistically based damage detection scheme is performed and it becomes possible to assess whether changes of modal parameters are caused by, e.g. some damage or simply by estimation inaccuracies. The paper reports first an example of identification and damage detection applied to a simulated system under random excitation. The `Steel-Quake' benchmark proposed in the framework of COST Action F3 `Structural Dynamics' is also analysed. This structure was defined by the Joint Research Centre in Ispra (Italy) to test steel building performance during earthquakes. The proposed method gives an excellent identification of frequencies and mode shapes, while damping ratios are estimated with less accuracy.

Abstract: In variational CAD design, parametric models may fail to regenerate raising the question of which parameter values lead to valid models. The problem is easy to state but difficult to solve. Using a simplification, we present an algorithm that computes for parametric models valid parameter ranges within which the model will regenerate. We explain also why the general problem is hard.

Abstract: We consider m distributions in which the first m − 1 are obtained by multiplicative exponential distortions of the mth distribution, which is a reference. The combined data fromm samples, one from each distribution, are used in the semiparametric large-sample problem of estimating each distortion and the reference distribution and testing the hypothesis that the distributions are identical. The approach generalizes the classical normal-based one-way analysis of variance in the sense that it obviates the need for a completely specified parametric model. An advantage is that the probability density of the reference distribution is estimated from the combined data and not only from the mth sample. A power comparison with the t and F tests and with two nonparametric tests, obtained by means of a simulation, points to the merit of the present approach. The method is applied to rain-rate data from meteorological instruments.

Abstract: Nonlinear regression with measurement error is important for estimation from microeconomic data. One approach to identification and estimation is a causal model, in which the unobserved true variable is predicted by observable variables. This paper details the estimation of such a model using simulated moments and a flexible disturbance distribution. An estimator of the asymptotic variance is given for parametric models. Also, a semiparametric consistency result is given. The value of the estimator is demonstrated in a Monte Carlo study and an application to estimating Engel Curves.

Abstract: We present a simple paradigm for fitting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classical MSE algorithms. This is done by considering each point on the model as a possible source for each data point. The paradigm can be used to solve problems which are ill-posed in the classical MSE approach, such as fitting a segment (as opposed to a line). It is shown to be nonbiased and to achieve excellent results for general curves, even in the presence of strong discontinuities. Results are shown for a number of fitting problems, including lines, circles, elliptic arcs, segments, rectangles, and general curves, contaminated by Gaussian and uniform noise.

Abstract: In this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a central role in this matter. We review the literature on extreme value methodology and consider its use in reinsurance. Whereas the models in extreme-value methods are non-parametric or semi-parametric of nature, practitioners often need a fully parametric model for assessing a portfolio risk both in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small sample simulation study is performed to validate the different methods for estimating excess-ofloss reinsurance premiums.

Abstract: In this paper, neural networks have been proposed as an alternative technique to build software reliability growth models A feedforward neural network was used to predict the number of faults initially resident in a program at the beginning of a test/debug process To evaluate the predictive capability of the developed model, data sets from various projects were used A comparison between regression parametric models and neural network models is provided

Abstract: Models are not perfect; they do not fit the data exactly and they do not allow exact prediction. Given that models are imperfect, we need to assess the uncertainties in the fits of the models and their ability to predict new outcomes. The goals of building models for scientific problems include (1) understanding and developing appropriate relationships between variables, and (2) predicting variables in the future or at locations where data have not been collected. Ecological models range in complexity from those that are relatively simple (e.g., linear regression) to those that are very complex (e.g., ecosystem models, forest-growth models, and nitrogen-cycling models). In a mathematical model, parameters control the relationships between variables in the model. In this framework of parametric modeling, inference is the process whereby we take output (data) and estimate model parameters, whereas deduction is the process whereby we take a parameterized model and obtain output (data) or deduce properties. We often add random components in both inference and deduction to reflect a model’s lack-of-fit and our uncertainty about predicting outcomes. Complex models in ecology have largely been of the deductive type, where the scientist takes some values of parameters (usually obtained from an independent data source or chosen from a reasonable range of values) and then simulates results based on model relationships. These models may be quite realistic, but the manner in which their parameters are obtained for the simulations is questionable.

Abstract: This paper describes the derivation of a consistent and comprehensive set of geometrical constraints for shape definition in CAD. Such a set is needed to enable compatibility in parametric data exchange and to promote both standard capabilities and predictable solutions from constraint solving software kernels. The paper looks at the mathematical basis for constraints present in the literature and elaborates about all types of constraints that can be described by the same mathematical basis. Exhaustive combinations of distance and angle constraints, on one point or all points of curves and surfaces, as well as transformations and mappings that are required in mechanical design are included in the proposed taxonomy and representation. Consistency is promoted by distinguishing necessary constraint types from redundant constraint types. Comprehensiveness is promoted by including all constraint types from the literature that are within the scope and considering combinatorial variations of them.

Abstract: Problems in data analysis often require the unsupervised partitioning of a data set into classes. Several methods exist for such partitioning but many have the weakness of being formulated via strict parametric models (e.g., each class is modeled by a single Gaussian) or being computationally intensive in high-dimensional data spaces. We reconsider the notion of such cluster analysis in information-theoretic terms and show that an efficient partitioning may be given via a minimization of partition entropy. A reversible-jump sampling is introduced to explore the variable-dimension space of partition models.

Abstract: In this paper, a novel approach composed of digital signal-processing techniques and optimization algorithms is developed to design and implement filters at microwave frequencies. The design phase begins with the adoption of digital filter prototypes and the implementation phase is facilitated by using both parametric modeling techniques and optimization algorithms. All the zeros of digital filter prototypes are removed first; the remaining part of the prototypes is then transformed to an autoregressive (AR) process by parametric modeling techniques. The values of characteristic impedances of transmission lines synthesizing the filters are adjusted according to the AR process by optimization algorithms. Both low-pass and bandpass filters are designed and then implemented in the form of a microstrip line, and their frequency responses are measured to validate the novel approach.

Abstract: A method of generating values of a predistortion look up table (106) for linerization of a transmitter. The method includes accumulating (102) a plurality of pairs of values (100) representing input and output values of samples entering one or more non-linear elements of the transmitter, fitting the pairs of values into a parametric model (104) of at least one of the one or more non-linear elements, so as to determine values for parameters of a parametric model, and generating values of a look up table (106) responsive to the fitted parametric model.

Abstract: International standards for wind turbine certification depend on finding long-term fatigue load distributions that are conservative with respect to the state of knowledge for a given system Statistical models of loads for fatigue application are described and demonstrated using flap and edge blade-bending data from a commercial turbine in complex terrain Distributions of rainflow-counted range data for each ten-minute segment are characterized by parameters related to their first three statistical moments (mean, coefficient of variation, and skewness) Quadratic Weibull distribution functions based on these three moments are shown to match the measured load distributions if the non-damaging low-amplitude ranges are first eliminated The moments are mapped to the wind conditions with a two-dimensional regression over ten-minute average wind speed and turbulence intensity With this mapping, the short-term distribution of ranges is known for any combination of average wind speed and turbulence intensity The longterm distribution of ranges is determined by integrating over the annual distribution of input conditions First, we study long-term loads derived by integration over wind speed distribution alone, using standard-specified turbulence levels Next, we perform this integration over both wind speed and turbulence distribution for the example site Results are compared between standarddriven and site-driven load estimates Finally, using statistics based on the regression of the statistical moments over the input conditions, the uncertainty (due to the limited data set) in the long-term load distribution is represented by 95% confidence bounds on predicted loads

Abstract: Weighted versions of the likelihood ratio, Wald, score and disparity tests are proposed for parametric inference. If the parametric model is correct, the weighted likelihood tests are asymptotically equivalent to the corresponding likeli- hood based tests, while the disparity test has asymptotically the same distribution as that of p=1 λiZ 2 i ,w hereZi are standard normal random variables and λi are eigenvalues of an appropriate matrix. The tests have high level and power break- down points and they perform well in finite samples. A simulation study and a data example illustrate the performance of the tests in the presence of symmetric and asymmetric contamination.

Abstract: Addresses the problem of regulating the dynamic model of a nonholonomic underactuated autonomous underwater vehicle (AUV) to a point with a desired orientation. A time-invariant discontinuous controller is proposed that yields convergence of the trajectories of the closed-loop system in the presence of parametric modeling uncertainty. Controller design relies on a non-smooth coordinate transformation in the original state space followed by the derivation of a Lyapunov-based, adaptive, smooth control law in the new coordinates. Convergence of the regulation system is analyzed and simulation results are presented.

Abstract: This paper presents a new practical autopilot design approach to acceleration control for tail-controlled skid-to-turn (STT) missiles. The approach is novel in that the proposed parametric affine missile model adopts acceleration as the controlled output and considers the couplings between the forces as well as the moments and control fin deflections. The aerodynamic coefficients in the proposed model are expressed in a closed form with parameters that can be fitted over the whole operating range. The parameters are fitted from aerodynamic coefficient lookup tables by the proposed function approximation technique, which is based on the combination of local parametric models through curve fitting using the corresponding influence functions. In addition, a feedback linearizing controller is designed by using the proposed parametric affine missile model. Stability analysis for the overall closed-loop system is provided, considering the uncertainties arising from approximation errors. The validity of the proposed modeling and control approach is demonstrated through simulations for an STT missile.

Abstract: This paper presents a parametric modeling approach to the design of ship hull forms that allows creation and variation of ship hulls to be completed quickly and efficiently The paper introduced a design-oriented parametric definition language featuring high-level descriptions of hull characteristics well-known in naval architecture A modeling system is presented that produces a complete mathematical description of the hull via geometric optimization, enabling effective shape variations by keeping selected parameters constant while adjusting others automatically All curves and surfaces yield excellent fairness The paper presents examples that illustrate parametric shape and variation The parametric modeling approach provides the ideal basis to hydrodynamic optimization and one week ship design

Abstract: The model-based effort described here is focused on predictive diagnostics for primary and secondary batteries. However, this novel approach can also be applied to other electrochemical energy sources such as fuel cells. This method is based on accurate parametric modeling of the transport mechanisms within the battery. This system knowledge was used for the careful development of electrochemical and thermal models. These models have been used to extract new features to be used in conjunction with several traditional measured parameters to assess the condition of the battery. The resulting output and any usable information available about the battery is then evaluated using hybrid automated reasoning schemes consisting of neural network and decision theoretic methods. The focus of this paper is on the model identification and data fusion of the monitored and virtual sensor data. The methodology and analysis presented is applicable to mechanical systems where multiple sensor types are used for diagnostic assessment.