Showing papers on "Parametric statistics published in 2012"

High dimensional semiparametric gaussian copula graphical models

Abstract: ing the Spearman’s rho and Kendall’s tau. We prove that the nonparanormal skeptic achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation. This result suggests that the nonparanormal graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian. Besides theoretical analysis, we also conduct thorough numerical simulations to compare the graph recovery performance of dierent estimators under both ideal and noisy settings. The proposed methods are then applied on a largescale genomic dataset to illustrate their empirical usefulness. The R package huge implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran.r-project.org/.

Neighborhood Component Feature Selection for High-Dimensional Data

Abstract: Feature selection is of considerable importance in data mining and machine learning, especially for high dimensional data. In this paper, we propose a novel nearest neighbor-based feature weighting algorithm, which learns a feature weighting vector by maximizing the expected leave-one-out classification accuracy with a regularization term. The algorithm makes no parametric assumptions about the distribution of the data and scales naturally to multiclass problems. Experiments conducted on artificial and real data sets demonstrate that the proposed algorithm is largely insensitive to the increase in the number of irrelevant features and performs better than the state-of-the-art methods in most cases.

Accurate detection of outliers and subpopulations with Pmetrics, a nonparametric and parametric pharmacometric modeling and simulation package for R

Abstract: Introduction:Nonparametric population modeling algorithms have a theoretical superiority over parametric methods to detect pharmacokinetic and pharmacodynamic subgroups and outliers within a study population.Methods:The authors created “Pmetrics,” a new Windows and Unix R software package that updat

Face alignment by Explicit Shape Regression

Abstract: We present a very efficient, highly accurate, “Explicit Shape Regression” approach for face alignment. Unlike previous regression-based approaches, we directly learn a vectorial regression function to infer the whole facial shape (a set of facial landmarks) from the image and explicitly minimize the alignment errors over the training data. The inherent shape constraint is naturally encoded into the regressor in a cascaded learning framework and applied from coarse to fine during the test, without using a fixed parametric shape model as in most previous methods. To make the regression more effective and efficient, we design a two-level boosted regression, shape-indexed features and a correlation-based feature selection method. This combination enables us to learn accurate models from large training data in a short time (20 minutes for 2,000 training images), and run regression extremely fast in test (15 ms for a 87 landmarks shape). Experiments on challenging data show that our approach significantly outperforms the state-of-the-art in terms of both accuracy and efficiency.

On Bayesian Upper Confidence Bounds for Bandit Problems

Abstract: Stochastic bandit problems have been analyzed from two different perspectives: a frequentist view, where the parameter is a deterministic unknown quantity, and a Bayesian approach, where the parameter is drawn from a prior distribution. We show in this paper that methods derived from this second perspective prove optimal when evaluated using the frequentist cumulated regret as a measure of performance. We give a general formulation for a class of Bayesian index policies that rely on quantiles of the posterior distribution. For binary bandits, we prove that the corresponding algorithm, termed Bayes-UCB, satisfies finite-time regret bounds that imply its asymptotic optimality. More generally, Bayes-UCB appears as an unifying framework for several variants of the UCB algorithm addressing different bandit problems (parametric multi-armed bandits, Gaussian bandits with unknown mean and variance, linear bandits). But the generality of the Bayesian approach makes it possible to address more challenging models. In particular, we show how to handle linear bandits with sparsity constraints by resorting to Gibbs sampling.

Hypothesis Testing and Power Calculations for Taxonomic-Based Human Microbiome Data

Abstract: This paper presents new biostatistical methods for the analysis of microbiome data based on a fully parametric approach using all the data. The Dirichlet-multinomial distribution allows the analyst to calculate power and sample sizes for experimental design, perform tests of hypotheses (e.g., compare microbiomes across groups), and to estimate parameters describing microbiome properties. The use of a fully parametric model for these data has the benefit over alternative non-parametric approaches such as bootstrapping and permutation testing, in that this model is able to retain more information contained in the data. This paper details the statistical approaches for several tests of hypothesis and power/sample size calculations, and applies them for illustration to taxonomic abundance distribution and rank abundance distribution data using HMP Jumpstart data on 24 subjects for saliva, subgingival, and supragingival samples. Software for running these analyses is available.

Stochastic Non-Smooth Envelopment of Data: Semi-Parametric Frontier Estimation Subject to Shape Constraints

Abstract: The field of productive efficiency analysis is currently divided between two main paradigms: the deterministic, nonparametric Data Envelopment Analysis (DEA) and the parametric Stochastic Frontier Analysis (SFA). This paper examines an encompassing semiparametric frontier model that combines the DEA-type nonparametric frontier, which satisfies monotonicity and concavity, with the SFA-style stochastic homoskedastic composite error term. To estimate this model, a new two-stage method is proposed, referred to as Stochastic Non-smooth Envelopment of Data (StoNED). The first stage of the StoNED method applies convex nonparametric least squares (CNLS) to estimate the shape of the frontier without any assumptions about its functional form or smoothness. In the second stage, the conditional expectations of inefficiency are estimated based on the CNLS residuals, using the method of moments or pseudolikelihood techniques. Although in a cross-sectional setting distinguishing inefficiency from noise in general requires distributional assumptions, we also show how these can be relaxed in our approach if panel data are available. Performance of the StoNED method is examined using Monte Carlo simulations.

Two-Point Boundary Value Problems: Lower and Upper Solutions

Abstract: Preface. Introduction - The History. Chapter 1 - The Periodic Problem. Chapter 2 - The Separated BVP. Chapter 3 - Relation with Degree Theory. Chapter 4 - Variational Methods. Chapter 5 - Monotone Iterative Methods. Chapter 6 - Parametric Multiplicity Problems. Chapter 7 - Resonance and Nonresonance. Chapter 8 - Positive Solutions. Chapter 9 - Problem with Singular Forces. Chapter 10 - Singular Perturbations. Chapter 11 - Bibliographical Notes. Appendix. Bibliography. Index

Robust Control: The Parameter Space Approach

Abstract: * Parametric Plants and Controllers: A Crane Example * Boundary Crossing and Parameter Space Approach * Eigenvalue Specifications * Boundary Mapping in Parameter Space * Frequency Domain Analysis and Design * Case Studies in Car Steering * Case Studies in Flight Control * Robustness Analysis by Value Sets * Values Sets for Non-linear Co-efficient Functions * The Stability Radius * Robustness of Sampled-Data Control Systems A Polynominals and Polynominals Equations, Resultant Method B Introduction to PARADISE Bibliography

Very‐short‐term probabilistic forecasting of wind power with generalized logit–normal distributions

Abstract: Summary. Very-short-term probabilistic forecasts, which are essential for an optimal management of wind generation, ought to account for the non-linear and double-bounded nature of that stochastic process. They take here the form of discrete–continuous mixtures of generalized logit–normal distributions and probability masses at the bounds. Both auto-regressive and conditional parametric auto-regressive models are considered for the dynamics of their location and scale parameters. Estimation is performed in a recursive least squares framework with exponential forgetting. The superiority of this proposal over classical assumptions about the shape of predictive densities, e.g. normal and beta, is demonstrated on the basis of 10-min-ahead point and probabilistic forecasting at the Horns Rev wind farm in Denmark.

Robust Nonfragile $H_\infty$ Filtering of Fuzzy Systems With Linear Fractional Parametric Uncertainties

Abstract: This paper is concerned with the H∞ filtering problem for continuous-time Takagi-Sugeno (T-S) fuzzy systems. Different from existing results for fuzzy H∞ filtering, the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties. Attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed H∞ performance, where the filter to be designed is assumed to have gain variations. By a descriptor representation approach, two sufficient conditions for the H∞ filter design are proposed in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of the desired filter is given. A simulation example will be given to show the efficiency of the proposed methods.

Estimation of Sparse MIMO Channels with Common Support

Abstract: We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of sparse common support (SCS) channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.

RE-EM trees: a data mining approach for longitudinal and clustered data

Abstract: Longitudinal data refer to the situation where repeated observations are available for each sampled object. Clustered data, where observations are nested in a hierarchical structure within objects (without time necessarily being involved) represent a similar type of situation. Methodologies that take this structure into account allow for the possibilities of systematic differences between objects that are not related to attributes and autocorrelation within objects across time periods. A standard methodology in the statistics literature for this type of data is the mixed effects model, where these differences between objects are represented by so-called "random effects" that are estimated from the data (population-level relationships are termed "fixed effects," together resulting in a mixed effects model). This paper presents a methodology that combines the structure of mixed effects models for longitudinal and clustered data with the flexibility of tree-based estimation methods. We apply the resulting estimation method, called the RE-EM tree, to pricing in online transactions, showing that the RE-EM tree is less sensitive to parametric assumptions and provides improved predictive power compared to linear models with random effects and regression trees without random effects. We also apply it to a smaller data set examining accident fatalities, and show that the RE-EM tree strongly outperforms a tree without random effects while performing comparably to a linear model with random effects. We also perform extensive simulation experiments to show that the estimator improves predictive performance relative to regression trees without random effects and is comparable or superior to using linear models with random effects in more general situations.

Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter

Abstract: Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature as to whether such parametric assumptions are important or innocuous. In the context of generalized linear mixed models used to analyze clustered or longitudinal data, we examine the impact of random effects distribution misspecification on a variety of inferences, including prediction, inference about covariate effects, prediction of random effects and estimation of random effects variances. We describe examples, theoretical calculations and simulations to elucidate situations in which the specification is and is not important. A key conclusion is the large degree of robustness of maximum likelihood for a wide variety of commonly encountered situations.

New Concepts in Adaptive Control Using Multiple Models

Abstract: The concept of using multiple models to cope with transients which arise in adaptive systems with large parametric uncertainties was introduced in the 1990s. Both switching between multiple fixed models, and switching and tuning between fixed and adaptive models was proposed, and the stability of the resulting schemes was established. In all cases, the number of models needed is generally large (cn where n is the dimension of the parameter vector and c an integer), and the models do not “cooperate” in any real sense. In this paper, a new approach is proposed which represents a significant departure from past methods. First, it requires (n+1) models (in contrast to cn) which is significantly smaller, when “n ” is large. Second, while each of the (n+1) models chosen generates an estimate of the plant parameter vector, the new approach provides an estimate which depends on the collective outputs of all the models, and can be viewed as a time-varying convex combination of the estimates. It is then shown that control based on such an estimate results in a stable overall system. Further, arguments are given as to why such a procedure should result in faster convergence of the estimate to the true value of the plant parameter as compared to conventional adaptive controllers, resulting in better performance. Simulation studies are included to practically verify the arguments presented, and demonstrate the improvement in performance.

A Survey on Time-Varying Copulas: Specification, Simulations, and Application

Abstract: The aim of this article is to bring together different specifications for copula models with time-varying dependence structure Copula models are widely used in financial econometrics and risk management They are considered to be a competitive alternative to the Gaussian dependence structure The dynamic structure of the dependence between the data can be modeled by allowing either the copula function or the dependence parameter to be time-varying First, we give a brief description of eight different models, among which there are fully parametric, semiparametric, and adaptive methods The purpose of this study is to compare the applicability of each particular model in different cases We conduct a simulation study to show the performance for model selection, to compare the model fit for different setups and to study the ability of the models to estimate the (latent) time-varying dependence parameter Finally, we provide an illustration by applying the competing models on the same financial dataset and

Two sample tests for high-dimensional covariance matrices

Abstract: We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance-covariance matrices, and the other is on offdiagonal sub-matrices which define the covariance between two non-overlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the “large p, small n” situations and (ii) without assuming parametric distributions for the two populations. These two aspects surpass the capability of the conventional likelihood ratio test. The proposed tests can be used to test on covariances associated with gene ontology terms.

parfm: Parametric Frailty Models in R

Abstract: Frailty models are getting more and more popular to account for overdispersion and/or clustering in survival data. When the form of the baseline hazard is somehow known in advance, the parametric estimation approach can be used advantageously. Nonetheless, there is no unified widely available software that deals with the parametric frailty model. The new parfm package remedies that lack by providing a wide range of parametric frailty models in R. The gamma, inverse Gaussian, and positive stable frailty distributions can be specified, together with five different baseline hazards. Parameter estimation is done by maximising the marginal log-likelihood, with right-censored and possibly left-truncated data. In the multivariate setting, the inverse Gaussian may encounter numerical difficulties with a huge number of events in at least one cluster. The positive stable model shows analogous difficulties but an ad-hoc solution is implemented, whereas the gamma model is very resistant due to the simplicity of its Laplace transform.

Patch complexity, finite pixel correlations and optimal denoising

Abstract: Image restoration tasks are ill-posed problems, typically solved with priors. Since the optimal prior is the exact unknown density of natural images, actual priors are only approximate and typically restricted to small patches. This raises several questions: How much may we hope to improve current restoration results with future sophisticated algorithms? And more fundamentally, even with perfect knowledge of natural image statistics, what is the inherent ambiguity of the problem? In addition, since most current methods are limited to finite support patches or kernels, what is the relation between the patch complexity of natural images, patch size, and restoration errors? Focusing on image denoising, we make several contributions. First, in light of computational constraints, we study the relation between denoising gain and sample size requirements in a non parametric approach. We present a law of diminishing return, namely that with increasing patch size, rare patches not only require a much larger dataset, but also gain little from it. This result suggests novel adaptive variable-sized patch schemes for denoising. Second, we study absolute denoising limits, regardless of the algorithm used, and the converge rate to them as a function of patch size. Scale invariance of natural images plays a key role here and implies both a strictly positive lower bound on denoising and a power law convergence. Extrapolating this parametric law gives a ballpark estimate of the best achievable denoising, suggesting that some improvement, although modest, is still possible.

Identification strategy of error parameter in volumetric error compensation of machine tool based on laser tracker measurements

Abstract: This paper presents a new method for volumetric verification of machine tools. Beyond the consideration of a particular machine, a general verification methodology is presented based on the type of machine to verify the number and movement of axes and different techniques that can be used. A scheme and kinematic model with the inclusion of the measurement system depending on the kinematics of the machine are presented. The model describes the geometry and kinematics of a real milling machine based on a parametric synthetic data generator, which generates a test with known geometric errors and noise to enable a study of different optimisation techniques and models. Similarly, different errors identification techniques and volumetric verification models are presented and analysed. The paper shows the improvement that occurs in verification by considering optimisation phases, the appropriateness of using new techniques of feedback, and the influence of optimisation parameters. Chebyshev polynomials and its characteristics are presented, as well as a regression function for the new verification model. The new developed technique allows the characterisation of the different errors in the whole workspace of the machine and in less time than direct verification methods.

Robust Fuzzy Fault-Tolerant Control of Wind Energy Conversion Systems Subject to Sensor Faults

Abstract: In this paper, we propose a multiobserver switching control strategy for robust active fault tolerant fuzzy control (RAFTFC) of variable-speed wind energy conversion systems (WECS) in the presence of wide wind variation, wind disturbance, parametric uncertainties, and sensors faults. The Takagi-Sugeno (TS) fuzzy model with parametric uncertainties is adopted for modeling the nonlinear WECS and establishing fuzzy state observers. Sufficient conditions are derived for robust stabilization in the sense of Taylor series stability and are formulated in linear matrix inequalities (LMIs). Application to WECS, subject to uncertain parameters and sensor faults illustrate the effectiveness of the proposed controllers.