Parametric Resampling Research Articles

A Note on Bias Correction for the Standard Two‐Sided Power Distribution

AbstractIt is verified that the maximum likelihood (ML) estimators of the standard two‐sided power distribution (STSP) parameters introduced by van Dorp and Kotz on the interval (0,1) can be severely biased. Since the usual analytical methods of bias correction cannot be applied in such a parametric distribution, bootstrap bias correction methods are proposed. The numerical study favors a particular bootstrap estimator based on parametric resampling. Real data applications are also considered to illustrate the impact of bias correction of the usual maximum likelihood estimators of the standard two‐sided power distribution parameters when the sample size is small.

Group linear non-Gaussian component analysis with applications to neuroimaging

Independent component analysis (ICA) is an unsupervised learning method popular in functional magnetic resonance imaging (fMRI). Group ICA has been used to search for biomarkers in neurological disorders including autism spectrum disorder and dementia. However, current methods use a principal component analysis (PCA) step that may remove low-variance features. Linear non-Gaussian component analysis (LNGCA) enables simultaneous dimension reduction and feature estimation including low-variance features in single-subject fMRI. A group LNGCA model is proposed to extract group components shared by more than one subject. Unlike group ICA methods, this novel approach also estimates individual (subject-specific) components orthogonal to the group components. To determine the total number of components in each subject, a parametric resampling test is proposed that samples spatially correlated Gaussian noise to match the spatial dependence observed in data. In simulations, estimated group components achieve higher accuracy compared to group ICA. The method is applied to a resting-state fMRI study on autism spectrum disorder in 342 children (252 typically developing, 90 with autism), where the group signals include resting-state networks. The discovered group components appear to exhibit different levels of temporal engagement in autism versus typically developing children, as revealed using group LNGCA. This novel approach to matrix decomposition is a promising direction for feature detection in neuroimaging.

Management of Portfolio Depletion Risk through Optimal Life Cycle Asset Allocation

Members of defined contribution (DC) pension plans must take on additional responsibilities for their investments, compared to participants in defined benefit (DB) pension plans. The transition from DB to DC plans means that more employees are faced with these responsibilities. We explore the extent to which DC plan members can follow financial strategies that have a high chance of resulting in a retirement scenario that is fairly close to that provided by DB plans. Retirees in DC plans typically must fund spending from accumulated savings. This leads to the risk of depleting these savings, that is, portfolio depletion risk. We analyze the management of this risk through life cycle optimal dynamic asset allocation, including the accumulation and decumulation phases. We pose the asset allocation strategy as an optimal stochastic control problem. Several objective functions are tested and compared. We focus on the risk of portfolio depletion at the terminal date, using such measures as conditional value at risk (CVAR) and probability of ruin. A secondary consideration is the median terminal portfolio value. The control problem is solved using a Hamilton-Jacobi-Bellman formulation, based on a parametric model of the financial market. Monte Carlo simulations that use the optimal controls are presented to evaluate the performance metrics. These simulations are based on both the parametric model and bootstrap resampling of 91 years of historical data. The resampling tests suggest that target-based approaches that seek to establish a safety margin of wealth at the end of the decumulation period appear to be superior to strategies that directly attempt to minimize risk measures such as the probability of portfolio depletion or CVAR. The target-based approaches result in a reasonably close approximation to the retirement spending available in a DB plan. There is a small risk of depleting the retiree’s funds, but there is also a good chance of accumulating a buffer that can be used to manage unplanned longevity risk or left as a bequest.

Automation and Evaluation of the SOWH Test with SOWHAT.

The Swofford–Olsen–Waddell–Hillis (SOWH) test evaluates statistical support for incongruent phylogenetic topologies. It is commonly applied to determine if the maximum likelihood tree in a phylogenetic analysis is significantly different than an alternative hypothesis. The SOWH test compares the observed difference in log-likelihood between two topologies to a null distribution of differences in log-likelihood generated by parametric resampling. The test is a well-established phylogenetic method for topology testing, but it is sensitive to model misspecification, it is computationally burdensome to perform, and its implementation requires the investigator to make several decisions that each have the potential to affect the outcome of the test. We analyzed the effects of multiple factors using seven data sets to which the SOWH test was previously applied. These factors include a number of sample replicates, likelihood software, the introduction of gaps to simulated data, the use of distinct models of evolution for data simulation and likelihood inference, and a suggested test correction wherein an unresolved “zero-constrained” tree is used to simulate sequence data. To facilitate these analyses and future applications of the SOWH test, we wrote SOWHAT, a program that automates the SOWH test. We find that inadequate bootstrap sampling can change the outcome of the SOWH test. The results also show that using a zero-constrained tree for data simulation can result in a wider null distribution and higher p-values, but does not change the outcome of the SOWH test for most of the data sets tested here. These results will help others implement and evaluate the SOWH test and allow us to provide recommendations for future applications of the SOWH test. SOWHAT is available for download from https://github.com/josephryan/SOWHAT.

Nonparametric resampling of random walks for spectral network clustering

Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.

Resampling Effects on Significance Analysis of Network Clustering and Ranking

Community detection helps us simplify the complex configuration of networks, but communities are reliable only if they are statistically significant. To detect statistically significant communities, a common approach is to resample the original network and analyze the communities. But resampling assumes independence between samples, while the components of a network are inherently dependent. Therefore, we must understand how breaking dependencies between resampled components affects the results of the significance analysis. Here we use scientific communication as a model system to analyze this effect. Our dataset includes citations among articles published in journals in the years 1984–2010. We compare parametric resampling of citations with non-parametric article resampling. While citation resampling breaks link dependencies, article resampling maintains such dependencies. We find that citation resampling underestimates the variance of link weights. Moreover, this underestimation explains most of the differences in the significance analysis of ranking and clustering. Therefore, when only link weights are available and article resampling is not an option, we suggest a simple parametric resampling scheme that generates link-weight variances close to the link-weight variances of article resampling. Nevertheless, when we highlight and summarize important structural changes in science, the more dependencies we can maintain in the resampling scheme, the earlier we can predict structural change.

Inference for a Simple Step-Stress Model with Type-I Censoring and Lognormally Distributed Lifetimes

Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows the experimenter to obtain failure data more quickly at increased stress levels than under normal operating conditions. A step-stress model is one special class of ALT, and in this article we consider a simple step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-I censoring. We then discuss inferential methods for the unknown parameters of the model by the maximum likelihood estimation method. Some numerical methods, such as the Newton–Raphson and quasi-Newton methods, are discussed for solving the corresponding non-linear likelihood equations. Next, we discuss the construction of confidence intervals for the unknown parameters based on (i) the asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study is carried out to examine the performance of these methods of inference. Finally, a numerical example is presented in order to illustrate all the methods of inference developed here.

Undercoverage of Wavelet-Based Resampling Confidence Intervals

The decorrelating property of the discrete wavelet transformation (DWT) appears valuable because one can avoid estimating the correlation structure in the original data space by bootstrap resampling of the DWT. Several authors have shown that the wavestrap approximately retains the correlation structure of observations. However, simply retaining the same correlation structure of original observations does not guarantee enough variation for regression parameter estimators. Our simulation studies show that these wavestraps yield undercoverage of parameters for a simple linear regression for time series data of the type that arise in functional MRI experiments. It is disappointing that the wavestrap does not even provide valid resamples for both white noise sequences and fractional Brownian noise sequences. Thus, the wavestrap method is not completely valid in obtaining resamples related to linear regression analysis and should be used with caution for hypothesis testing as well. The reasons for these undercoverages are also discussed. A parametric bootstrap resampling in the wavelet domain is introduced to offer insight into these previously undiscovered defects in wavestrapping.

Bootstrap-based improved estimators for the two-parameter Birnbaum–Saunders distribution

In this paper, we consider the two-parameter Birnbaum–Saunders distribution proposed by Birnbaum and Saunders [Birnbaum, Z.W. and Saunders, S.C., 1969, A new family of life distributions. Journal of Applied Probability, 6, 319–327], which is commonly used for modeling the lifetime of materials and equipment. We consider different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the distribution via bootstrap (parametric and nonparametric). The numerical evidence favors a particular bootstrap estimator based on parametric resampling. Finally, an example with real data is presented and discussed.

A Maximum Entropy Method for Particle Filtering

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.

Late Carboniferous remagnetisation of Palaeozoic rocks in the NE Rhenish Massif, Germany

During stepwise thermal and alternating field demagnetisation experiments on Devonian and Lower Carboniferous carbonate and clastic rocks from the north-eastern part of the Rhenish Massif, Germany, three components of magnetisation (A, B, C) are identified. Component A is a recent viscous overprint that parallels the local present day geomagnetic field. Component B is mainly observed from 260 up to 550 °C during thermal demagnetisation and is carried by magnetite. In two localities, where red siltstones and red carbonate rocks were sampled, component B is stable up to 670 °C, indicating the presence of hematite. Three clusters of in situ B directions can be identified, which are controlled by the tectonic position of the sampling areas. These are from NW to SE: the Remscheid anticline (RA), the Lüdenscheid syncline (LS) and the Attendorn and Wittgenstein synclines (AS/WS). Standard and inclination-only fold tests, using parametric resampling, yield optimal statistical parameters at increasing amounts of untilting ranging from 0% in the South up to 57% in the North of the NE Rhenish Massif. Despite the variations in optimal untilting, the resulting site mean directions of component B do not differ significantly in inclination. These results are interpreted to reflect the acquisition of magnetisation during progressive northward migration of the deformation front in Late Carboniferous times. The resulting palaeolatitudes (RA: 1°S +2° −3°; LS: 2°S +3° −2°; AS/WS: 1°S +3° −4°) are in good agreement with the predicted position of the sampling area in the Late Carboniferous, as derived from a published Apparent Polar Wander Path for Baltica and Laurentia. The unblocking temperature spectra and the synfolding nature of B yield strong evidence that chemical processes, possibly driven by fluid migration during orogenesis, caused this remagnetisation. A third component C was observed in zones of tight folding with steeply dipping to overturned bedding planes and is dominantly carried by hematite. The resulting palaeolatitude (27°N +10° −8°) suggest a Late Triassic to Early Jurassic age of component C, which is interpreted to be caused by either hematite-bearing post-Variscan mineralisation or oxidising fluids percolating from the weathering surface and penetrating zones of enhanced permeability in the Mesozoic.

Resampling m-Dependent Random Variables with Applications to Forecasting

Resampling methods are proposed to estimate the distributions of sums of m-dependent possibly differently distributed real-valued random variables. The random variables are allowed to have varying mean values. A non parametric resampling method based on the moving blocks bootstrap is proposed for the case in which the mean values are smoothly varying or ‘asymptotically equal’. The idea is to resample blocks in pairs. It is also confirmed that a ‘circular’ block resampling scheme can be used in the case where the mean values are ‘asymptotically equal’. A central limit resampling theorem for each of the two cases is proved. The resampling methods have a potential application to time series analysis, to distinguish between two different forecasting models. This is illustrated with an example using Swedish export prices of coated paper products.

A simulation study of iterated and non-iterated bootstrap methods for bias reduction and confidence interval estimation

We describe a simulation study of the application of bootstrap methods with nonparametric, symmetrized nonparametric and parametric resampling to the problems of a) reducing the bias of an parameter estimate and b) estimating a confidence interval. The populations simulated were N(2,5) and 2x 2 1. In problem a), first- and second-order additive corrections and Efron's 1990 bias correction were applied to an initial bootstrap estimate of jU3; the second-order additive correction was superior to Efron's 1990 bias correction in all cases, including that of the 2xf population with parametric resampling, for which the theoretical prediction of poor performance by the iterated additive method was borne out in practice. In problem b), symmetric 95% confidence intervals for the means of the same populations as above were calculated from initial samples i) by applying a first-order additive correction to a initial bootstrap confidence interval.