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Smoothing Methods (smoothing + methods)

Distribution by Scientific Domains
Mathematics and Statistics83%

Selected Abstracts

Test of Marginal Compatibility and Smoothing Methods for Exchangeable Binary Data with Unequal Cluster Sizes

BIOMETRICS, Issue 1 2007
Zhen Pang
Summary Exchangeable binary data are often collected in developmental toxicity and other studies, and a whole host of parametric distributions for fitting this kind of data have been proposed in the literature. While these distributions can be matched to have the same marginal probability and intra-cluster correlation, they can be quite different in terms of shape and higher-order quantities of interest such as the litter-level risk of having at least one malformed fetus. A sensible alternative is to fit a saturated model (Bowman and George, 1995, Journal of the American Statistical Association90, 871,879) using the expectation-maximization (EM) algorithm proposed by Stefanescu and Turnbull (2003, Biometrics59, 18,24). The assumption of compatibility of marginal distributions is often made to link up the distributions for different cluster sizes so that estimation can be based on the combined data. Stefanescu and Turnbull proposed a modified trend test to test this assumption. Their test, however, fails to take into account the variability of an estimated null expectation and as a result leads to inaccurate p -values. This drawback is rectified in this article. When the data are sparse, the probability function estimated using a saturated model can be very jagged and some kind of smoothing is needed. We extend the penalized likelihood method (Simonoff, 1983, Annals of Statistics11, 208,218) to the present case of unequal cluster sizes and implement the method using an EM-type algorithm. In the presence of covariate, we propose a penalized kernel method that performs smoothing in both the covariate and response space. The proposed methods are illustrated using several data sets and the sampling and robustness properties of the resulting estimators are evaluated by simulations. [source]

Semiparametric approaches to flow normalization and source apportionment of substance transport in rivers

ENVIRONMETRICS, Issue 3 2001
Per Stålnacke
Abstract Statistical analysis of relationships between time series of data exhibiting seasonal variation is often of great interest in environmental monitoring and assessment. The present study focused on regression models with time-varying intercept and slope parameters. In particular, we derived and tested semiparametric models in which rapid interannual and interseasonal variation in the intercept were penalized in the search for a model that combined a good fit to data with smoothly varying parameters. Furthermore, we developed a software package for efficient estimation of the parameters of such models. Test runs on time series of runoff data and riverine loads of nutrients and chloride in the Rhine River showed that the proposed smoothing methods were particularly useful for analysis of time-varying linear relationships between time series of data with both seasonal variation and temporal trends. The predictivity of the semiparametric models was superior to that of conventional parametric models. In addition, normalization of observed annual loads to mean or minimum runoff produced smooth curves that provided convincing evidence of human impact on water quality. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Application of smoothing methods to flash problems

AICHE JOURNAL, Issue 4 2004
John Slaby
[source]

Parameter estimation for differential equations: a generalized smoothing approach

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2007
J. O. Ramsay
Summary., We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations. Such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation. The paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non-linear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive estimates and confidence intervals, and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology. The performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus. [source]

A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2004
F. J. Gaspar
Abstract In this paper, we present efficient multigrid methods for the system of poroelasticity equations discretized on a staggered grid. In particular, we compare two different smoothing approaches with respect to efficiency and robustness. One approach is based on the coupled relaxation philosophy. We introduce ,cell-wise' and ,line-wise' versions of the coupled smoothers. They are compared with a distributive relaxation, that gives us a decoupled system of equations. It can be smoothed equation-wise with basic iterative methods. All smoothing methods are evaluated for the same poroelasticity test problems in which parameters, like the time step, or the Lamé coefficients are varied. Some highly efficient methods result, as is confirmed by the numerical experiments. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Nonparametric Inference for Local Extrema with Application to Oligonucleotide Microarray Data in Yeast Genome

BIOMETRICS, Issue 2 2006
Peter X.-K.
Summary Identifying local extrema of expression profiles is one primary objective in some cDNA microarray experiments. To study the replication dynamics of the yeast genome, for example, local peaks of hybridization intensity profiles correspond to putative replication origins. We propose a nonparametric kernel smoothing (NKS) technique to detect local hybridization intensity extrema across chromosomes. The novelty of our approach is that we base our inference procedures on equilibrium points, namely those locations at which the first derivative of the intensity curve is zero. The proposed smoothing technique provides both point and interval estimation for the location of local extrema. Also, this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points. We illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome, in that the locations of autonomous replication sequence (ARS) elements are identified through the equilibrium points of the smoothed intensity profile curve. Our method found a few ARS elements that were not detected by the current smoothing methods such as the Fourier convolution smoothing. [source]