Showing papers on "Parametric model published in 2002"

Statistical Models and Methods for Lifetime Data

Abstract: Basic Concepts and Models. Observation Schemes, Censoring and Likelihood. Some Nonparametric and Graphical Procedures. Inference Procedures for Parametric Models. Inference procedures for Log-Location-Scale Distributions. Parametric Regression Models. Semiparametric Multiplicative Hazards Regression Models. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models. Multiple Modes of Failure. Goodness of Fit Tests. Beyond Univariate Survival Analysis. Appendix A. Glossary of Notation and Abbreviations. Appendix B. Asymptotic Variance Formulas, Gamma Functions and Order Statistics. Appendix C. Large Sample Theory for Likelihood and Estimating Function Methods. Appendix D. Computational Methods and Simulation. Appendix E. Inference in Location-Scale Parameter Models. Appendix F. Martingales and Counting Processes. Appendix G. Data Sets. References.

Dynamic conditional correlation - a simple class of multivariate garch models

Abstract: Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations and provide sensible empirical results.

Semiparametric Smooth Coefficient Models

Abstract: In this article, we propose a semiparametric smooth coefficient model as a useful yet flexible specification for studying a general regression relationship with varying coefficients. The article proposes a local least squares method with a kernel weight function to estimate the smooth coefficient function. The consistency of the estimator and its asymptotic normality are established. A simple statistic for testing a parametric model versus the semiparametric smooth coefficient model is proposed. An empirical application of the proposed method is presented with an estimation of the production function of the nonmetal mineral industry in China. The empirical findings show that the intermediate production and management expense has played a vital role and is an unbalanced determinant of the labor and capital elasticities of output in production.

Bayesian Treed Models

Abstract: When simple parametric models such as linear regression fail to adequately approximate a relationship across an entire set of data, an alternative may be to consider a partition of the data, and then use a separate simple model within each subset of the partition. Such an alternative is provided by a treed model which uses a binary tree to identify such a partition. However, treed models go further than conventional trees (e.g. CART, C4.5) by fitting models rather than a simple mean or proportion within each subset. In this paper, we propose a Bayesian approach for finding and fitting parametric treed models, in particular focusing on Bayesian treed regression. The potential of this approach is illustrated by a cross-validation comparison of predictive performance with neural nets, MARS, and conventional trees on simulated and real data sets.

Comparing curves using additive models

Abstract: Advances in technology make available thousands of measurements in industrial processes that enable reconstruction of the entire profile of the operation over time and space. The complicated forms of many of these signatures do not fit parametric models..

Elements of computational statistics

Abstract: Preliminaries * Monte Carlo Methods for Inference * Randomization and Data Partitioning * Bootstrap Methods * Tools for Identification of Structure in Data * Estimation of Functions * Graphical Methods in Computational Statistics * Estimation of Probability Density Functions Using Parametric Models * Nonparametric Estimation of Probability Density Functions * Structure in Data * Statistical Models of Dependencies * Appendices

Automatic spectral analysis with time series models

Abstract: The increased computational speed and developments in the robustness of algorithms have created the possibility to identify automatically a well-fitting time series model for stochastic data. It is possible to compute more than 500 models and to select only one, which certainly is one of the better models, if not the very best. That model characterizes the spectral density of the data. Time series models are excellent for random data if the model type and the model order are known. For unknown data characteristics, a large number of candidate models have to be computed. This necessarily includes too low or too high model orders and models of the wrong types, thus requiring robust estimation methods. The computer selects a model order for each of the three model types. From those three, the model type with the smallest expectation of the prediction error is selected. That unique selected model includes precisely the statistically significant details that are present in the data.

Gaussian processes:iterative sparse approximations

Abstract: In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

Comparing proportional hazards and accelerated failure time models for survival analysis

Abstract: This paper describes a method proposed for a censored linear regression model that can be used in the context of survival analysis. The method has the important characteristic of allowing estimation and inference without knowing the distribution of the duration variable. Moreover, it does not need the assumption of proportional hazards. Therefore, it can be an interesting alternative to the Cox proportional hazards models when this assumption does not hold. In addition, implementation and interpretation of the results is simple. In order to analyse the performance of this methodology, we apply it to two real examples and we carry out a simulation study. We present its results together with those obtained with the traditional Cox model and AFT parametric models. The new proposal seems to lead to more precise results.

Model Checks for Generalized Linear Models

Abstract: In this paper we propose and study non-parametric tests for the validity of (composite) Generalized Linear Models with a given parametric link structure, which are based on certain empirical processes marked by the residuals. When properly transformed to their innovation part the resulting test statistics are distribution-free. The method perfectly adapts to a situation, when also the input vector follows a dimension reducing model.

Inference for multi-state models from interval-censored data.

Abstract: Clinical statuses of subjects are often observed at a finite number of visits. This leads to interval-censored observations of times of transition from one state to another. The likelihood can still easily be written in terms of both transition probabilities and transition intensities. In homogeneous Markov models, transition probabilities can be expressed simply in terms of transition intensities, but this is not the case in more general multi-state models. In addition, inference in homogeneous Markov models is easy because these are parametric models. Non-parametric approaches to non-homogeneous Markov models may follow two paths: one is the completely non-parametric approach and can be seen as a generalisation of the Turnbull approach; the other implies a restriction to smooth intensities models. In particular, the penalized likelihood method has been applied to this problem. This paper gives a review of these topics.

Time domain phase noise correction for OFDM signals

Abstract: We introduce an algorithm for compensating for carrier phase noise in an OFDM communication system. Through the creation of a linearized parametric model for phase noise, we generate a least squares (LS) estimate of the transmitted symbol. Using digitized DVB-T RF signals created in a laboratory and a DVB-T compliant receiver model, simulation results are presented to evaluate the effectiveness of the algorithm in practical environments.

Non-parametric optimal design in dose finding studies

Abstract: We describe a non-parametric optimal design as a theoretical gold standard for dose finding studies. Its purpose is analogous to the Cramer-Rao bound for unbiased estimators, i.e. it provides a bound beyond which improvements are not generally possible. The bound applies to the class of non-parametric designs where the data are not assumed to be generated by any known parametric model. Whenever parametric assumptions really hold it may be possible to do better than the optimal non-parametric design. The goal is to be able to compare any potential dose finding scheme with the optimal non-parametric benchmark. This paper makes precise what is meant by optimal in this context and also why the procedure is described as non-parametric.

Spline Adaptation in Extended Linear Models (with comments and a rejoinder by the authors

Abstract: In many statistical applications, nonparametric modeling can provide insights into the features of a dataset that are not obtainable by other means. One successful approach involves the use of (univariate or multivariate) spline spaces. As a class, these methods have inherited much from classical tools for parametric modeling. For example, stepwise variable selection with spline basis terms is a simple scheme for locating knots (breakpoints) in regions where the data exhibit strong, local features. Similarly, candidate knot configurations (generated by this or some other search technique), are routinely evaluated with traditional selection criteria like AIC or BIC. In short, strategies typically applied in parametric model selection have proved useful in constructing flexible, low-dimensional models for nonparametric problems. Until recently, greedy, stepwise procedures were most frequently suggested in the literature. Research into Bayesian variable selection, however, has given rise to a number of new spline-based methods that primarily rely on some form of Markov chain Monte Carlo to identify promising knot locations. In this paper, we consider various alternatives to greedy, deterministic schemes, and present a Bayesian framework for studying adaptation in the context of an extended linear model (ELM). Our major test cases are Logspline density estimation and (bivariate) Triogram regression models. We selected these because they illustrate a number of computational and methodological issues concerning model adaptation that arise in ELMs.

Optimization of electromagnetic phased-arrays for hyperthermia via magnetic resonance temperature estimation

Abstract: A technique for the optimization of electromagnetic annular phased arrays (APAs) for therapeutic hyperthermia has been developed and implemented. The controllable inputs are the amplitudes and phases of the driving signals of each element of the array. Magnetic resonance imaging (MRI) is used to estimate noninvasively the temperature distribution based on the temperature dependence of the proton resonance frequency (PRF). A parametric model of the dynamics that couple the control inputs to the resultant temperature elevations is developed based on physical considerations. The unknown parameters of this model are estimated during a pretreatment identification phase and can be continuously updated as new measurement data become available. Based on the parametric model, a controller automatically chooses optimal phases and amplitudes of the driving signals of the APA. An advantage of this approach to optimizing the APA is that no a priori information is required, eliminating the need for patient-specific computational modeling and optimization. Additionally, this approach represents a first step toward employing temperature feedback to make the optimization of the APA robust with respect to modeling errors and physiological changes. The ability of the controller to choose therapeutically beneficial driving amplitudes and phases is demonstrated via simulation. Experimental results are presented which demonstrate the ability of the controller to choose optimal phases for the APA using only information from magnetic resonance thermometry (MRT).

The study of long-term HIV dynamics using semi-parametric non-linear mixed-effects models

Abstract: Modelling HIV dynamics has played an important role in understanding the pathogenesis of HIV infection in the past several years. Non-linear parametric models, derived from the mechanisms of HIV infection and drug action, have been used to fit short-term clinical data from AIDS clinical trials. However, it is found that the parametric models may not be adequate to fit long-term HIV dynamic data. To preserve the meaningful interpretation of the short-term HIV dynamic models as well as to characterize the long-term dynamics, we introduce a class of semi-parametric non-linear mixed-effects (NLME) models. The models are non-linear in population characteristics (fixed effects) and individual variations (random effects), both of which are modelled semi-parametrically. A basis-based approach is proposed to fit the models, which transforms a general semi-parametric NLME model into a set of standard parametric NLME models, indexed by the bases used. The bases that we employ are natural cubic splines for easy implementation. The resulting standard NLME models are low-dimensional and easy to solve. Statistical inferences that include testing parametric against semi-parametric mixed-effects are investigated. Innovative bootstrap procedures are developed for simulating the empirical distributions of the test statistics. Small-scale simulation and bootstrap studies show that our bootstrap procedures work well. The proposed approach and procedures are applied to long-term HIV dynamic data from an AIDS clinical study.

Tests For Constancy Of Model Parameters Over Time

Abstract: Suppose that a sequence of data points follows a distribution of a certain parametric form, but that one or more of the underlying parameters may change over time. This paper addresses various natural questions in such a framework. We construct canonical monitoring processes which under the hypothesis of no change converge in distribution to independent Brownian bridges, and use these to construct natural goodness-of-fit statistics. Weighted versions of these are also studied, and optimal weight functions are derived to give maximum local power against alternatives of interest. We also discuss how our results can be used to pinpoint where and what type of changes have occurred, in the event that initial screening tests indicate that such exist. Our unified large-sample methodology is quite general and applies to all regular parametric models, including regression, Markov chain and time series situations.

Random rates in anisotropic regression

Abstract: In the context of minimax theory, we propose a new kind of risk, normalized by a random variable, measurable with respect to the data. We present a notion of optimality and a method to construct optimal procedures accordingly. We apply this general setup to the problem of selecting significant variables in Gaussian white noise. In particular, we show that our method essentially improves the accuracy of estimation, in the sense of giving explicit improved confidence sets in L2-norm. Links to adaptive estimation are discussed. 1. Introduction. Searching for significant variables is certainly one of the oldest and most popular problems in statistics. One of the simplest models where the issue of selecting significant variables was first stated mathematically is linear regression. A vast literature has been devoted to this topic since and different approaches have been proposed over the last forty years, both for estimation and for hypothesis testing. Among many authors, we refer to Akaike [1], Breiman and Freedman [3], Chernoff [5], Csiszar and Korner [6], Dychakov [10], Patel [42], Renyi [46], Freidlina [13], Meshalkin [35], Malyutov and Tsitovich [34], Schwarz [47] and Stone [48]. In classical parametric regression, if we consider a linear model, we first have to measure the possible gain of “searching for a limited number of significant variables.” If the model comes from a specific field of application, then only an adequate description together with its solution is relevant. However, from a mathematical point of view, a theory of selecting significant variables does not lead—at least asymptotically—to a substantial improvement of the accuracy of estimation: in a regular parametric model, the classical √ n rate of convergence is not affected by the number of significant variables. (However, even in this setup, let us emphasize that “asymptotically” has to be understood as “up to a constant” and that the correct choice of significant variables may possibly improve this constant.) If instead of a linear model we consider a nonparametric regression model, the search for significant variables becomes crucial for estimating the regression function: the rate of convergence explicitly depends on the set of significant variables. Let us develop this statement with the following example of multivariate regression: suppose we observe Z (n) = (Xi ,Y i ,i = 1 ,... , n)in the model

Estimation of the transfer function of a subscriber loop by means of a one-port scattering parameter measurement at the central office

Abstract: In order to qualify a subscriber loop for xDSL transmission, the channel capacity has to be estimated, which depends on the transfer function of the network. A method is provided to estimate the transfer function of the subscriber loop only measuring the one-port scattering parameter at the central office. We consider three types of networks according to their topology: a single line, a homogeneous network with a bridged tap, and a cascade of two line sections. For each type of network a parametric model is derived of its one-port scattering parameter and transfer function based on the physical line model VUB0. The model for the scattering parameter is used to identify the network based on the corresponding measurements by means of a maximum-likelihood estimator. The estimated parameters are substituted in the transfer function model, which is needed for the capacity estimation. The proposed models and estimators are validated by measurements and simulations. For the measurements, which were performed with a network analyzer, three types of twisted-pair cables were used: British Telecom (BT), Deutsch Telekom (FT), and Belgacom.

Effect of Turbulence Variation on Extreme Loads Prediction for Wind Turbines

Abstract: The effect of varying turbulence levels on long-term loads extrapolation techniques was examined using a joint probability density function of both mean wind speed and turbulence level for loads calculations. The turbulence level has a dramatic effect on the statistics of moment maxima extracted from aeroelastic simulations. Maxima from simulations at lower turbulence levels are more deterministic and become dominated by the stochastic component as turbulence level increases. Short-term probability distributions were calculated using four different moment-based fitting methods. Several hundred of these distributions were used to calculate a long-term probability function. From the long-term probability, 1- and 50-year extreme loads were estimated. As an alternative, using a normal distribution of turbulence level produced a long-term load comparable to that of a log-normal distribution and may be more straightforward to implement. A parametric model of the moments was also used to estimate the extreme loads. The parametric model predicted nearly identical loads to the empirical model and required less data. An input extrapolation technique was also examined. Extrapolating the turbulence level prior to input into the aeroelastic code simplifies the loads extrapolation procedure but, in this case, produces loads lower than the empirical model and may be non-conservative in general.Copyright © 2002 by ASME

A flexible additive multiplicative hazard model

Abstract: We present a new additive-multiplicative hazard model which consists of two components. The first component contains additive covariate effects through an additive Aalen model while the second component contains multiplicative covariate effects through a Cox regression model. The Aalen model allows for time-varying covariate effects, while the Cox model allows only a common time-dependence through the baseline. Approximate maximum likelihood estimators are derived by solving the simultaneous score equations for the nonparametric and parametric components of the model. The suggested estimators are provided with large-sample properties and are shown to be efficient. The efficient estimators depend, however, on some estimated weights. We therefore also consider unweighted estimators and describe their large-sample properties. We finally extend the model to allow for time-varying covariate effects in the multiplicative part of the model as well.

Prediction of wind power using time-varying coefficient-functions

Abstract: A method for adaptive and recursive estimation in a class of non-linear autore- gressive models with external input is proposed. The model class considered is conditionally parametric ARX-models (CPARX-models), which is conventional ARX-models in which the parameters are replaced by smooth, but otherwise unknown, functions of a low-dimensional input process. These coefficient-functions are estimated adaptively and recursively without specifying a global parametric form, i.e. the method allows for on-line tracking of the coefficient-functions. The usefulness of the method is illustrated using prediction of power production from wind farms as an example. A CPARX model for predicting the power pro- duction is suggested and the coefficient-functions are estimated using the proposed method. The new models are evaluated for five wind farms in Denmark as well as one wind farm in Spain. It is shown that the predictions based on conditional parametric models are superior to the predictions obtained by previously identified parametric models.

Parametric control charts

Abstract: Standard control charts are based on the assumption that the observations are normally distributed. In practice, normality often fails and consequently the false alarm rate is seriously in error. Application of a nonparametric approach is only possible with many Phase I observations. Since nowadays such very large sample sizes are usually not available, there is need for an intermediate approach by considering a larger parametric model containing the normal family as a submodel. In this paper control limits are presented in such larger parametric models, with emphasis on the so called normal power family. Correction terms are derived, taking into account that the parameters are estimated. Simulation results show that the control limits are accurate, not only in the considered parametric family, but also for common distributions outside the parametric family, thus covering a broad class of distributions.