共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
3.
Quantile smoothing splines 总被引:7,自引:0,他引:7
4.
We compare the performances of local and global rules for smoothingparameter choice, in terms of asymptotic mean squared errorsof the resulting estimators. In some instances there is surprisinglylittle to choose between local and global approaches; our analysisidentifies contexts where the differences are small or large.This work motivates development of smoothing rules that forma half-way house between local and global smoothing.There, interpolation provides a basis for partial local smoothing.A key result shows that interpolation on even a coarse gridcan produce a very good approximation to full local smoothing.Our theoretical and numerical results lead us to suggest linearinterpolation of a bandwidth obtained by integral approximationson discrete intervals. 相似文献
5.
6.
A method is developed for fitting smooth curves through a seriesof shapes of landmarks in two dimensions using unrolling andunwrapping procedures in Riemannian manifolds. An explicit methodof calculation is given which is analogous to that of Jupp &Kent (1987) for spherical data. The resulting splines are calledshape-space smoothing splines. The method resembles that offitting smoothing splines in real spaces in that, if the smoothingparameter is zero, the resulting curve interpolates the datapoints, and if it is infinitely large the curve is a geodesicline. The fitted path to the data is defined such that its unrolledversion at the tangent space of the starting point is a cubicspline fitted to the unwrapped data with respect to that path.Computation of the fitted path consists of an iterative procedurewhich converges quickly, and the resulting path is given ina discretised form in terms of a piecewise geodesic path. Theprocedure is applied to the analysis of some human movementdata, and a test for the appropriateness of a mean geodesiccurve is given. 相似文献
7.
Bandwidth selection for the smoothing of distribution functions 总被引:3,自引:0,他引:3
8.
9.
10.
《Dendrochronologia》2014,32(4):343-356
A number of processing options associated with the use of a “regional curve” to standardise tree-ring measurements and generate a chronology representing changing tree growth over time are discussed. It is shown that failing to use pith offset estimates can generate a small but systematic chronology error. Where chronologies contain long-timescale signal variance, tree indices created by division of the raw measurements by RCS curve values produce chronologies with a skewed distribution. A simple empirical method of converting tree-indices to have a normal distribution is proposed. The Expressed Population Signal, which is widely used to estimate the statistical confidence of chronologies created using curve-fitting methods of standardisation, is not suitable for use with RCS generated chronologies. An alternative implementation, which takes account of the uncertainty associated with long-timescale as well as short-timescale chronology variance, is proposed. The need to assess the homogeneity of differently-sourced sets of measurement data and their suitability for amalgamation into a single data set for RCS standardisation is discussed. The possible use of multiple growth-rate based RCS curves is considered where a potential gain in chronology confidence must be balanced against the potential loss of long-timescale variance. An approach to the use of the “signal-free” method for generating artificial measurement series with the ‘noise’ characteristics of real data series but with a known chronology signal applied for testing standardisation performance is also described. 相似文献
11.
Linear models for field trials, smoothing and cross-validation 总被引:1,自引:0,他引:1
12.
Semiparametric smoothing for discrete data 总被引:2,自引:0,他引:2
13.
A continuous empirical Bayes smoothing technique 总被引:1,自引:0,他引:1
14.
15.
Bruno C Macchiavelli R Balzarini M 《TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik》2008,117(3):435-447
Species dispersal studies provide valuable information in biological research. Restricted dispersal may give rise to a non-random distribution of genotypes in space. Detection of spatial genetic structure may therefore provide valuable insight into dispersal. Spatial structure has been treated via autocorrelation analysis with several univariate statistics for which results could dependent on sampling designs. New geostatistical approaches (variogram-based analysis) have been proposed to overcome this problem. However, modelling parametric variograms could be difficult in practice. We introduce a non-parametric variogram-based method for autocorrelation analysis between DNA samples that have been genotyped by means of multilocus-multiallele molecular markers. The method addresses two important aspects of fine-scale spatial genetic analyses: the identification of a non-random distribution of genotypes in space, and the estimation of the magnitude of any non-random structure. The method uses a plot of the squared Euclidean genetic distances vs. spatial distances between pairs of DNA-samples as empirical variogram. The underlying spatial trend in the plot is fitted by a non-parametric smoothing (LOESS, Local Regression). Finally, the predicted LOESS values are explained by segmented regressions (SR) to obtain classical spatial values such as the extent of autocorrelation. For illustration we use multivariate and single-locus genetic distances calculated from a microsatellite data set for which autocorrelation was previously reported. The LOESS/SR method produced a good fit providing similar value of published autocorrelation for this data. The fit by LOESS/SR was simpler to obtain than the parametric analysis since initial parameter values are not required during the trend estimation process. The LOESS/SR method offers a new alternative for spatial analysis. 相似文献
16.
Roberts AM 《International journal of biometeorology》2008,52(6):463-470
Stepwise regression is often used to draw associations between phenological records and weather data. For example, the dates that a species first flowers each year might be regressed on monthly mean temperatures for a period preceding flowering. The months that 'best' explain the variation in first flowering dates would be selected by stepwise regression. However, daily records of weather are usually available. Stepwise regression on daily temperatures would not be appropriate because of high correlations between neighbouring days. Smoothing methods provide a way of avoiding such difficulties. Regression coefficients can be smoothed by penalising differences in slopes between neighbouring regressors. The resultant curve of regression gradients is intuitively attractive. Various possible approaches to smoothing regression coefficients are discussed. We illustrate the use of one method, P-spline signal regression, which is particularly appropriate when there are many more regressors than observations. Smoothing can be applied to more than one set of regressors. This results in a multi-dimensional surface of regression coefficients. We use this approach to investigate how the time of year that a plant species tends to flower affects its relationship with temperature records. Using this method, we found that later species tend to be affected by later temperatures. 相似文献
17.
Endpoint error in smoothing and differentiating raw kinematic data: An evaluation of four popular methods 总被引:1,自引:0,他引:1
‘Endpoint error’ describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's (1982, J. Biomechanics 15, 99–105) modification of the Pezzack et al. (1977, J. Biomechanics, 10, 377–382) raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack et al. (1977) data set. In fact, the quintic spline performed best with non-padded data (cumulative error=48.0 rad s−2). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error=226.6 rad s−2). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error=68.8 rad s−2) than when applied to analogous subsets padded by reflection (average cumulative error=86.1 rad s−2). 相似文献
18.
Nonparametric smoothing methods are used to model longitudinal data, but the challenge remains to incorporate correlation into nonparametric estimation procedures. In this article, we propose an efficient estimation procedure for varying-coefficient models for longitudinal data. The proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models. The proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified. For varying-coefficient models, it is often of interest to test whether coefficient functions are time varying or time invariant. We propose a unified and efficient nonparametric hypothesis testing procedure, and further demonstrate that the resulting test statistics have an asymptotic chi-squared distribution. In addition, the goodness-of-fit test is applied to test whether the model assumption is satisfied. The corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion. We evaluate the finite sample performance of the proposed procedures with Monte Carlo simulation studies. The proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome (AIDS) data set. 相似文献
19.
Exact likelihood ratio tests for penalised splines 总被引:4,自引:0,他引:4
20.
The cubic smoothing spline has been a popular method for detrending tree-ring data since the 1980s. The common implementation of this procedure (e.g., ARSTAN, dplR) uses a unique method for determining the smoothing parameter that is widely known as the %n criterion. However, this smoothing parameter selection method carries the assumption that end point effects are ignorable. In this paper, we complete the mathematical derivation and show how the original method differs from the complete version, both in the interpretation of the smoothing parameter and in the spline fit. Frequency response curves (FRC) demonstrate how the smoothing parameter is affected by the original assumption. For example, the FRC results indicate that a tree core of 250-year length has a 14% difference in the cut-off frequency when looking at the 67%n criterion. The FRC analysis shows that the existing approach produces a more flexible fit than anticipated, i.e., it is removing more variance than previously thought. For example, a 67%n spline under the existing approach corresponds to a 53%n spline fit. By using both simulated tree-core sequences and a dataset from a Midwest forest, we discuss which conditions result in greater differences between the spline fits and which conditions will have small differences. Tree-core sequences that have more curvature, such as a large-amplitude growth release, will lead to greater differences. Finally, we provide approximations to the end-point effect procedure. For example, using an 83%n criterion under the original approach produces a spline fit approximating the 67%n fit under the complete approach. These approximations could be easily implemented within existing programs like ARSTAN. 相似文献