Showing papers on "Resampling published in 1991"

Randomization and Monte Carlo methods in biology

Abstract: Part 1 Randomization tests and confidence intervals: the idea of a randomization test examples of a randomization test aspects of randomization testing raised by the examples confidence intervals from randomization. Part 2 Monte Carlo and other computer intensive methods: Monte Carlo tests jackknifing bootstrapping bootstrap tests of significance and confidence intervals. Part 3 Some general considerations: power determining how many randomizations are needed determining a randomization distribution exactly the computer generation of pseudo-random numbers generating random permutations. Part 4 One and two sample tests: the paired comparisons design the one sample randomization test the two sample randomization test the comparison of two samples on multiple measurements. Part 5 Analysis of variance: one factor analysis of variance Bartlett's test for constant variance examples of more complicated types of analysis of variance discussion computer program. Part 6 Regrssion analysis: simple regression testing for a non-zero beta value confidence limits for beta multiple linear regression randomizing X variable values. Part 7 Distance matrices and spatial data: testing for association between distance matrices Mantel's test determining significance by sampling randomization distribution confidence limits for a matrix regression coefficient problems involving more than two matrices. Part 8 Other analyses on spatial data: the study of spatial point patterns Mead's randomization test a test based on nearest neighbour distances testing for an association between two point patterns the Besag-Diggle test tests using distances between points. Part 9 Time series: randomization and time series randomization tests for serial correlation randomization tests for trend randomization tests for periodicity irregularly spaced series tests on times of occurence discussion of procedures for irregular series bootstrap and Monte Carlo tests. Part 10 Multivariate data: univariate and multivariate tests sample means and covariance matrices comparison on sample means vectors chi-squared analyses for count data principal component analysis and other one sample methods discriminate function analysis. Part 11 Ad hoc methods: the construction of tests in non-standard situations testing for randomness of species co-occurences on islands examining time change in niche ovelap probing multivariate data with random skewers other examples. Part 12 Conclusion: randomization methods bootstrap and Monte Carlo methods.

Empirical Likelihood for Linear Models

Abstract: Empirical likelihood is a nonparametric method of inference. It has sampling properties similar to the bootstrap, but where the bootstrap uses resampling, it profiles a multinomial likelihood supported on the sample. Its properties in i.i.d. settings have been investigated in works by Owen, by Hall and by DiCiccio, Hall and Romano. This article extends the method to regression problems. Fixed and random regressors are considered, as are robust and heteroscedastic regressions. To make the extension, three variations on the original idea are considered. It is shown that when some functionals of the distribution of the data are known, one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization. The result is first order equivalent to conditioning on a sample value of the known functional. The use of a Euclidean alternative to the likelihood function is investigated. A triangular array version of the empirical likelihood theorem is given. The one-way ANOVA and heteroscedastic regression models are considered in detail. An example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model.

Two guidelines for bootstrap hypothesis testing

Abstract: Two guidelines for nonparametric bootstrap hypothesis testing are highlighted. The first recommends that resampling be done in a way that reflects the null hypothesis, even when the true hypothesis is distant from the null. The second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction. Violation of the first guideline can seriously reduce the power of a test. Sometimes this reduction is spectacular, since it is most serious when the null hypothesis is grossly in error. The second guideline is of some importance when the conclusion of a test is equivocal. It has no direct bearing on power, but improves the level accuracy of a test.

Bootstrap Simultaneous Error Bars for Nonparametric Regression

Abstract: Simultaneous error bars are constructed for nonparametric kernel estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated residual distribution. The error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints. Applications to an economic problem are given and comparison to both pointwise and Bonferroni-type bars is presented through a simulation study.

Plastic transformation of PET images

Abstract: A theory and technique are presented that allow nonlinear resampling of positron emission tomography data to remove nonlinear differences in brain shape. The resampling is determined empirically by a function relating the observed image and a desired template. The validity, reliability, and precision of the plastic transformation are compared with linear rescaling alone, within, and between subjects.

Least median of squares estimation in power systems

Abstract: An algorithm for solving LMS (least median of squares) in nonlinear systems has been proposed. The solutions are found through resampling methods based on linear approximations. These methods are suitable for parallel processing. The robustness of the LMS estimator has been verified on several test systems and illustrated on the IEEE 14-bus system. The concept of leverage points shed new light on the meter placement issue as well as the concepts of local redundancy and local breakdown point. A preliminary conclusion is that shorter lines have to be provided with enough measurements in order to increase their local redundancy. Indeed, they tend to be isolated in the factor space and weakly coupled with the surrounding measurements. >

Quantifying Precision of Mark-Recapture Estimates Using the Bootstrap and Related Methods

Abstract: SUMMARY Bootstrap techniques yield variance estimates under any model for which parameter estimates can be calculated, and are useful in cases where analytic variances are not available in closed form, or are available only if more restrictive assumptions are made. Here the application of bootstrap techniques to mark-recapture models is discussed. The approach also allows generation of robust confidence intervals, which extend beyond the permissible parameter range only if the mark-recapture model itself allows out-of-range parameter estimates. If an animal population is assumed to be closed (i.e., no death, birth, or migration), two further methods of obtaining confidence limits for population size are suggested. The first is based on a Robbins-Monro search for each limit, and the second applies the concept of a randomisation or permutation test. In the absence of nuisance parameters, both methods are exact apart from Monte Carlo variation and the limitations imposed by a discrete distribution. For the second, if all possible permutations are enumerated, Monte Carlo variation is eliminated.

Bootstrap statistics for paleomagnetic data

Abstract: The power and utility of paleomagnetic analyses stem largely from the ability to quantify such parameters as the degree of rotation of a rock body, or the orientation of an anisotropy axis. Until recently, estimates for uncertainty in these paleomagnetically determined parameters derived from assumptions concerning the underlying parametric distribution functions of the data. In many geologically important situations, the commonly used parametric distribution functions fail to model the data adequately and the uncertainty estimates so obtained are unreliable. Such essentials as the test for common mean require data sets consistent with a spherically symmetric underlying distribution; their application in inappropriate circumstances can result in flawed interpretations. Moreover, the almost universally used approximation for a cone of 95% confidence for the mean of a sample drawn from a Fisher distribution is quite biased even for moderate dispersions (K = 25). The availablity of inexpensive, powerful computers makes possible the empirical estimation of confidence regions by means of data resampling techniques such as the bootstrap. These resampling schemes replace analytical solutions with repeated simple calculations. We describe a bootstrap approach for the calculation of uncertainties for means or principal directions of paleomagnetic data. The method is tested on means of simulated Fisher distributions with known parameters and is found to be reliable for data sets with more than about 25 elements. Because a Fisher distribution is not assumed, the approach is applicable to a wide range of paleomagnetic data and can be used equally well on directions or associated virtual poles. We also illustrate bootstrap techniques for the discrimination of directions and for the fold test which enable the use of these powerful tests on the wider range of data sets commonly obtained in paleomagnetic investigations.

Robust Distances: Simulations and Cutoff Values

Abstract: It is possible to detect outliers in multivariate point clouds by computing distances based on robust estimates of location and scale. It has been suggested to use the Minimum Volume Ellipsoid estimator, which can be computed using a resampling algorithm. In this paper the small sample behavior of the robust distances is studied by means of simulation. We obtain a correction factor yielding approximately correct coverage percentages for the corresponding ellipsoids. In addition, a projection-type algorithm is considered to overcome the computational complexity of the resampling algorithm. Advantages and disadvantages of the second algorithm are discussed.

Small Sample Properties of Robust Analyses of Linear Models Based on R-Estimates: A Survey

Abstract: Analyses of linear models based on robust estimates of regression coefficients offers the user an attractive robust alternative to the classical least squares analysis in analyzing linear models. Much of the work done on robust analyses of linear models has concerned their asymptotic properties. To be of practical interest, though, the small sample properties of these analyses need to be ascertained. This article discusses studentization of these robust analyses and surveys past studies of it. With increasing speed of computation, resampling techniques have become feasible solutions to this studentizing problem. Some discussion of these techniques is also offered. To illustrate the discussion a Monte Carlo study of several experiments is included.

Prediction and tolerance intervals with transformation and/or weighting

Abstract: We consider estimation of quantiles and construction of prediction and tolerance intervals for a new response following a possibly nonlinear regression fit with transformation and/or weighting. We consider the case of normally distributed errors and, to a lesser extent, the nonparametric case in which the error distribution is unknown. Quantile estimation here follows standard theory, although we introduce a simple computational device for likelihood ratio testing and confidence intervals. Prediction and tolerance intervals are somewhat more difficult to obtain. We show that the effect of estimating parameters when constructing tolerance intervals can be expected to be greater than the effect in the prediction problem. Improved prediction and tolerance intervals are constructed based on resampling techniques. In the tolerance interval case, a simple analytical correction is introduced. We apply these methods to the prediction of automobile stopping distances and salmon production using, respectively, a he...

The problem of a covariate-time qualitative interaction in a survival study.

Abstract: We introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards. Although this kind of alternative is somewhat rare, designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures, upon which we can call in those few cases where such departures are suspected. Furthermore, the proposed test and an approximate version of the test are seen to suffer only moderate losses in power, when compared with their optimal counterparts, should the alternative be one of proportional hazards. Our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail. The model we use in this work is a special case of the one introduced by Anderson and Senthilselvan (1982. Applied Statistics 31, 44-51). We propose overcoming an inferential problem stemming from their model by using the methods of Davies (1977, Biometrika 64, 247-254; 1987, Biometrika 74, 33-43) backed up by resampling techniques. We also look at an approach relying directly on resampling techniques. The distributional aspects of this approach under the null hypothesis are interesting but, practically, its behaviour is such that its use cannot be generally recommended. Outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory.

On importance resampling for the bootstrap

Abstract: SUMMARY We introduce an empirical method of importance resampling, which does not require analytical calculation of the resampling probabilities. Our method can easily be used as part of a general algorithm for Monte Carlo calculation of bootstrap confidence intervals and hypothesis tests. It produces consistent, efficient and unbiased Monte Carlo approximations. We also present a very general but elementary account of importance resampling, which shows that even optimal importance resampling cannot improve on uniform resampling for calculating bootstrap estimates of bias, variance, skewness and related quantities. This result demonstrates a major difference between importance resampling and other approaches to efficient bootstrap simulation, such as balanced resampling and antithetic resampling, which produce significant improvements in efficiency for a wide range of problems involving the bootstrap.

Some Bootstrap Tests of Symmetry for Univariate Continuous Distributions

Abstract: The Kolmogorov distance between the empirical $\operatorname{cdf} F_n$ and its symmetrization $sF_n$ with respect to an adequate estimator of the center of symmetry of $P$ is a natural statistic for testing symmetry. However, its limiting distribution depends on $P$. Using critical values from the symmetrically bootstrapped statistic (where the resampling is made from $sF_n$) produces tests that can be easily implemented and have asymptotically the correct levels as well as good consistency properties. This article deals with the asymptotic theory that justifies this procedure in particular for a test proposed by Schuster and Barker. Because of lack of smoothness (in some cases implying non-Gaussianness of the limiting processes), these tests do not seem to fall into existing general frameworks.

Detection of density-dependent effects on caribou numbers from a series of census data

Abstract: The main objective of this paper is to review and discuss the applicability of statistical procedures for the detection of density dependence based on a series of annual or multi-annual censuses. Regression models for which the statistic value under the null hypothesis of density independence is set a priori (slope = 0 or 1), generate spurious indications of density dependence. These tests are inappropriate because low sample sizes, high variance, and sampling error consistently bias the slope when applied to a finite number of population estimates. Two distribution-free tests are reviewed for which the rejection region for the hypothesis of density independence is derived intrinsically from the data through a computer-assisted permutation process. The "randomization test" gives the best results as the presence of a pronounced trend in the sequence of population estimates does not affect test results. The other non-parametric test, the "permutation test", gives reliable results only if the population fluctuates around a long-term equilibrium density. Both procedures are applied to three sets of data (Pukaskwa herd, Avalon herd, and a hypothetical example) that represent quite divergent population trajectories over time.

A sequential approximation to a permutation test

Abstract: A sequential method for approximating a general permutation test (SAPT) is proposed and evaluated. Permutations are randomly generated from some set G, and a sequential probability ratio test (SPRT) is used to determine whether an observed test statistic falls sufficiently far in the tail of the permutation distribution to warrant rejecting some hypothesis. An estimate and bounds on the power function of the SPRT are used to find bounds on the effective significance level of the SAPT. Guidelines are developed for choosing parameters in order to obtain a desired significance level and minimize the number of permutations needed to reach a decision. A theoretical estimate of the average number of permutations under the null hypothesis is given along with simulation results demonstrating the power and average number of permutations for various alternatives. The sequential approximation retains the generality of the permutation test,- while avoiding the computational complexities that arise in attempting to co...

One-step Bootstrapping for Smooth Iterative Procedures

Abstract: SUMMARY Resampling techniques have the potential to provide useful information about the sampling distribution of estimators of many population characteristics. Ambitious schemes such as the bootstrap and iterated bootstrap imply a substantial increase in computational effort. For some iterative procedures, such as generalized least squares or the EM algorithm, it is possible to avoid fully iterating each bootstrap replication to convergence. By analysing expansions of the defining equation, we can extract asymptotically correct bootstrap estimates from a single step for each replication. In this paper we demonstrate the large sample validity of this computationally efficient approach and illustrate its small sample applicability. Whether or not the adjustment represents an adequate replacement for full iteration depends on the nature of the problem and the desired accuracy for the bootstrap quantiles. If subsequent iterations are adjusted, then greater enhancement of the rate is achieved and the practical increase in accuracy is significant.

Bahadur Representations for Uniform Resampling and Importance Resampling, with Applications to Asymptotic Relative Efficiency

Abstract: We derive Bahadur-type representations for quantile estimates obtained from two different types of nonparametric bootstrap resampling--the commonly used uniform resampling method, where each sample value is drawn with the same probability, and importance resampling, where different sample values are assigned different resampling weights. These results are applied to obtain the relative efficiency of uniform resampling and importance resampling and to derive exact convergence rates, both weakly and strongly, for either type of resampling.

The performance of minimax spatial resampling filters for focussing wide-band arrays

Abstract: The design and performance of linear shift-variant filters for coherent wideband processing are examined via spatial resampling. In particular, a minimax error criterion is used to obtain realizable resampling filters, and an approximate statistical analysis of wideband spatially resampled minimum variance spatial spectral estimation is presented. Simulation results indicate that spatial resampling provides a computationally efficient means of reducing the threshold observation time required to obtain high-resolution estimates of source location. >

Expected Response to Selection in Synthetic Populations of Perennial Ryegrass

Abstract: Confidence intervals for heritability and expected genetic advance of seven agronomic traits in two populations of perennial ryegrass have been computed in two ways (a = bootstrap method; b = parametric method) for five different combinations of selection. Two conclusions can be drawn from our results: — Superiority of individual selection over family or every combination of selection. — Usefulness of methods based on resampling to estimate confidence intervals for genetic parameters without particular statistical hypotheses.

An adaptive and powerful randomization test

Abstract: Reference STAP-ARTICLE-1992-005View record in Web of Science Record created on 2006-04-04, modified on 2017-05-12

Variance estimation for sample autocovariances: direct and resampling approaches

Abstract: Summary The usual covariance estimates for data n-1 from a stationary zero-mean stochastic process {Xt} are the sample covariances Both direct and resampling approaches are used to estimate the variance of the sample covariances. This paper compares the performance of these variance estimates. Using a direct approach, we show that a consistent windowed periodogram estimate for the spectrum is more effective than using the periodogram itself. A frequency domain bootstrap for time series is proposed and analyzed, and we introduce a frequency domain version of the jackknife that is shown to be asymptotically unbiased and consistent for Gaussian processes. Monte Carlo techniques show that the time domain jackknife and subseries method cannot be recommended. For a Gaussian underlying series a direct approach using a smoothed periodogram is best; for a non-Gaussian series the frequency domain bootstrap appears preferable. For small samples, the bootstraps are dangerous: both the direct approach and frequency domain jackknife are better.

Antialiasing-warped imagery using lookup-table-based methods for adaptive resampling

Abstract: In a previous paper, the authors demonstrated how image warping could be implemented using a pair of two-dimensional (2-D) spatial look-up tables. In that paper, the focus was on generating the tables, not on antialiasing the results. In this paper, the authors present a method for generating resampling kernels from the spatial look-up tables for the purpose of reducing aliasing. The method generates resampling kernels based on the reduction in spatial frequency content that must take place in order to produce an antialiased warped result. Since the reduction in spatial frequency required for each output pixel can be unique, the method is adaptive.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Quasi-random resampling for the bootstrap

Abstract: Quasi-random sequences are known to give efficient numerical integration rules in many Bayesian statistical problems where the posterior distribution can be transformed into periodic functions on then-dimensional hypercube. From this idea we develop a quasi-random approach to the generation of resamples used for Monte Carlo approximations to bootstrap estimates of bias, variance and distribution functions. We demonstrate a major difference between quasi-random bootstrap resamples, which are generated by deterministic algorithms and have no true randomness, and the usual pseudo-random bootstrap resamples generated by the classical bootstrap approach. Various quasi-random approaches are considered and are shown via a simulation study to result in approximants that are competitive in terms of efficiency when compared with other bootstrap Monte Carlo procedures such as balanced and antithetic resampling.