Local Bootstrap Research Articles

Bootstrap inference in local polynomial regression of time series

In this paper we consider the inferential aspect of the nonparametric estimation of a conditional function \(g({\bf x};\phi)={\mathop{\mathbb E}\nolimits}[\phi(X_{t})|{\bf X}_{t,m}]\), where Xt,m represents the vector containing the m conditioning lagged values of the series. Here \(\phi\) is an arbitrary measurable function. The local polynomial estimator of order p is used for the estimation of the function g, and of its partial derivatives up to a total order p. We consider α-mixing processes, and we propose the use of a particular resampling method, the local polynomial bootstrap, for the approximation of the sampling distribution of the estimator. After analyzing the consistency of the proposed method, we present a simulation study which gives evidence of its finite sample behaviour.

Bootstrap approaches and confidence intervals for stationary and non-stationary long-range dependence processes

This paper deals with different bootstrap approaches and bootstrap confidence intervals in the fractionally autoregressive moving average ( ARFIMA ( p , d , q ) ) process [J. Hosking, Fractional differencing, Biometrika 68(1) (1981) 165–175] using parametric and semi-parametric estimation techniques for the memory parameter d. The bootstrap procedures considered are: the classical bootstrap in the residuals of the fitted model [B. Efron, R. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993], the bootstrap in the spectral density function [E. Paparoditis, D.N Politis, The local bootstrap for periodogram statistics. J. Time Ser. Anal. 20(2) (1999) 193–222], the bootstrap in the residuals resulting from the regression equation of the semi-parametric estimators [G.C Franco, V.A Reisen, Bootstrap techniques in semiparametric estimation methods for ARFIMA models: a comparison study, Comput. Statist. 19 (2004) 243–259] and the Sieve bootstrap [P. Bühlmann, Sieve bootstrap for time series, Bernoulli 3 (1997) 123–148]. The performance of these procedures and confidence intervals for d in the stationary and non-stationary ranges are empirically obtained through Monte Carlo experiments. The bootstrap confidence intervals here proposed are alternative procedures with some accuracy to obtain confidence intervals for d.

Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models

In this paper we investigate bootstrap techniques applied to the estimation of the fractional differential parameter in ARFIMA models, d. The novelty is the focus on the local bootstrap of the periodogram function. The approach is then applied to three different semiparametric estimators of d, known from the literature, based upon the periodogram function. By means of an extensive set of simulation experiments, the bias and mean square errors are quantified for each estimator and the efficacy of the local bootstrap is stated in terms of low bias, short confidence intervals, and low CPU times. Finally, a real data set is analyzed to demonstrate that the methodology may be quite effective in solving real problems.

Non parametric resampling for stationary Markov processes: The local grid bootstrap approach

A new resampling technique, referred as “local grid bootstrap” (LGB), based on nonparametric local bootstrap and applicable to a wide range of stationary general space Markov processes is proposed. This nonparametric technique resamples local neighborhoods defined around the true samples of the observed multivariate time serie. The asymptotic behavior of this resampling procedure is studied in detail. Applications to linear and nonlinear (in particular chaotic) simulated time series are presented, and compared to Paparoditis and Politis [2002. J. Statist. Plan. Inf. 108, 301–328] approach, referred as “local bootstrap” (LB) and developed in earlier similar works. The method shows to be efficient and robust even when the length of the observed time series is reasonably small.

Comparison of the performance of different options for the ITER ECRH Upper Launcher

The performance of different options for the ITER ECRH upper launcher is analysed in terms of NTM stabilisation efficiency, which is the main task for this system. The driven current at the (3,2) and (2,) resonant surfaces of ITER scenarii 2, 3a and 5 is calculated and compared with the local bootstrap current density there, which is the drive for the NTM. It is found that in terms of the figure of merit for NTM stabilisation, jECCD/jbs, a launcher concept based on front steering has much better performance than concepts based on remote steering. This can be explained by the smaller spot size of the ECRH beam at the resonant surfaces in the case of front steering. Thus, from a physics point of view, the analysed front steering option is preferable to the remote steering option.

A Frictionless Steering Mechanism for the Front Steering ECCD ITER Upper Port Launcher

A FS launcher is being designed for the ITER upper port, which offers enhanced physics performance over the RS launcher. A two mirror system is used to decouple the focusing and steering aspects of the launcher and provide a relatively small beam waist (<20 mm) projected far into the plasma (>1.6 m from the steering mirror). The resulting NTM stabilization efficiency (maximum CD density divided by the local bootstrap current >1.6) is above marginal for the q = 2 and 3/2 rational flux surfaces of the relevent ITER equilibria (scenarios 2, 3a and 5) and a factor of ∼3 relative to an equivalent RS launcher. The performance of the FS launcher strongly depends on the reliability of the steering mechanism, which is used to rotate the plasma facing steering mirror. CRPP has designed a frictionless steering mechanism assembled in a compact cartridge capable of up to ±10° rotation (corresponding to a poloidal steering range of up to ±20° for the microwave beam around a fixed axis of rotation) that offers a high operation reliability despite the close proximity to the thermal and neutron flux coming from the ITER plasma.

Bootstrap techniques in semiparametric estimation methods for ARFIMA models: A comparison study

This paper considers different bootstrap procedures for investigating the estimation of the fractional parameter d in a particular case of long memory processes, i.e. for ARFIMA models withd in (0.0, 0.5). We propose two bootstrap techniques to deal with semiparametric estimation methods of d. One approach consists of the local bootstrap method for time frequency initially suggested for the ARMA case by Paparoditis and Politis (1999), and the other consists of the bootstrapping in the residuals of the frequency-domain regression equation. Through Monte Carlo simulation, these alternative bootstrap methods are compared, based on the mean and the mean square error of the estimators, with the well-known parametric and nonparametric bootstrap techniques for time series models.

Neoclassical tearing modes on ASDEX Upgrade: improved scaling laws, high confinement at high \U0001d6c3N and new stabilization experiments

In this paper, recent results on the physics of neoclassical tearing modes (NTMs) achieved on ASDEX Upgrade are reported. A scaling law for NTM decay has been found, showing that the minimum local bootstrap current density required for mode growth is proportional to the ion gyro radius. As this scaling law does not depend on the seed island size, and thus on the background MHD activity, it is more reliable than previously derived scaling laws for the NTM onset. Furthermore, the recently reported frequently interrupted regime is discussed. In this new regime (m,n) NTMs are characterized by frequent amplitude drops caused by interaction with (m+1, n+1) background MHD activity. Due to the resulting reduced time averaged island size this leads to lower confinement degradation compared to that caused by the usual NTMs. As shown here, the transition into this regime can actively be triggered by lowering the magnetic shear at the q = (m+1)/(n+1) rational surface. Further investigations regard mechanisms to increase the βN value for NTM onset such as plasma shaping, seed island size and density profile control. Using these studies, a scenario with high βN (βN = 3.5) at high density (n/nGW = 0.83) and confinement (H98(y,2) = 1.2) has been developed. Moreover, this scenario is characterized by type II ELM activity and thus by moderate heat load to the target plates. Finally, new NTM stabilization experiments are reported, demonstrating an increase in βN after NTM stabilization.

Local block bootstrap

For time series that are not stationary, the block bootstrap method is not directly applicable. However, if the underlying stochastic structure is slowly changing with time, one may employ a local block-resampling procedure. We define such a procedure, and give an example of its applicability. To cite this article: E. Paparoditis, D.N. Politis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 959–962.

Risk Estimation for Classification Trees

This article is a study of techniques for bias reduction of estimates of risk both globally and within terminal nodes of CARTR classification trees. In Section 5.4 of Classification and Regression Trees, Leo Breiman presented an estimator that has two free parameters. An empirical Bayes method was put forth for estimating them. Here we explain why the estimator should be successful in the many examples for which it is. We give numerical evidence from simulations in the two-class case with attention to ordinary resubstitution and seven other methods of estimation. There are 14 sampling distributions, all but one simulated and the remaining concerning E. coli promoter regions. We report on varying minimum node sizes of the trees; prior probabilities and misclassification costs; and, when relevant, the numbers of bootstraps or cross-validations. A variation of Breiman's method in which repeated cross-validation is employed to estimate global rates of misclassification was the most accurate from among the eight methods. Exceptions are cases for which the Bayes risk of the Bayes rule is small. For them, either a local bootstrap .632 estimate or Breiman's method modified to use a bootstrap estimate of the global misclassification rate is most accurate.

Complete sequence of the Japanese quail (Coturnix japonica) mitochondrial genome and its genetic relationship with related species.

The Japanese quail (Coturnix japonica; JQ) is one of the domesticated fowl species of Japan. To provide DNA sequence information for examination of its phylogenetic position in the order Galliformes, the complete sequence of the JQ mitochondria was determined. Sequence analysis revealed that the JQ mitochondrial genome is a circular DNA of 16 697 basepairs (bp), which is smaller than the chicken mitochondrial DNA of 16 775 bp, but the genomic structure of JQ mitochondria was the same as that of the chicken. The sequence homologies of all mitochondrial genes including those for 12S and 16S ribosomal RNA (rRNA), between Japanese quail and chicken ranged from 78.0 to 89.9%. Because the sequences of NADH dehydrogenase subunit 2 and cytochrome b genes had been reported in five species [Phasianus colchicus (ring-neck pheasant: RP), Gallus gallus domesticus (chicken: CH), Perdix perdix (grey partridge: GP), Bambusicola thoracia (Chinese bamboo partridge: CP), and Aythya americana (redhead: RH)], the concatenated nucleotide sequences (2184 bp) and amino acid sequences of these two genes were used in a phylogenetic analysis of JQ against these five species using a maximum likelihood (ML) method. Using the first and second bases of the codons, and the third base of the codons indicated a phylogenic tree of [RH, (RP, GP), (JQ, (CH, CP))]. A phylogenic tree of [RH, JQ, (RP, GP), (CH, CP)] was determined using amino acid sequences. Because the local bootstrap values for the JQ branch in these trees are not high, additional sequence is necessary for construction of a reliable tree.

Nonparametric testing the similarity of two unknown density functions: local power and bootstrap analysis

In this paper, we compare two kernel-based tests for testing the closeness between two unknown density functions, one test has a smoothing parameter h that goes to zero as sample size tends to infinity, the other one has a fixed smoothing parameter. We show that the former test (with a shrinking h) can be more powerful than the later for “singular” local alternatives considered by Rosenblatt (1975). We also demonstrate that bootstrap procedure provide a better approximation than the asymptotic normal approximation. Monte Carlo simulations are reported to examine the finite sample performances of the nonparametric kernel-based tests based on both the asymptotic and bootstrap critical values.

Phylogeny of Eurasian Soricine Shrews (Insectivora, Mammalia) Inferred from the Mitochondrial CytochromebGene Sequences

Abstract Phylogenetic relationships among 31 operational taxonomic units of shrews (Soricidae, Mammalia), mainly from eastern Eurasia, were inferred from partial nucleotide sequences of the mitochondrial cytochrome b gene by maximum likelihood (ML) and neighbor joining (NJ) methods. Eleven monophyletic groups were recognized among the soricine shrews examined in the ML tree. However, branching orders of the groups were obscure judging from the local bootstrap values, and two out of the 11 groups were not monophyletic in the NJ tree. The phylogenetic relationships among Sorex caecutiens, S. shinto, and S. sadonis in the Japanese and Sakhalin islands, whose taxonomy was controversial, were clarified. S. shinto in the Honshu and Shikoku Islands is genetically differentiated enough to be considered a separate species from S. caecutiens, while S. sadonis could be treated as a subspecies of S. shinto. Some other taxonomic problems are also discussed.

Survey of pellet enhanced performance in JET discharges

Pellet enhanced performance (PEP) has been observed in a number of JET discharges at various plasma conditions, in both L and H modes, with the H multiplier (the confinement enhancement factor over the Goldston confinement time) covering the range from 1 to 4, and with plasma currents from 1 MA to 4.1 MA. Most of the PEP plasmas have been created by refuelling with pellets of 4 mm diameter injected at 1.2 km/s. PEPs show an improved central confinement with an effective heat conductivity reduced by factors of approximately 2-5 relative to otherwise comparable discharges. This is possibly related to the inverted shear in the plasma core due to the large local bootstrap current density. The limitations in the PEP performance seem to be set by at least two mechanisms: impurity behaviour, MHD activity or a combination of both. In certain discharges, MHD modes seem to be able to check the often observed impurity accumulation. Too much MHD mode activity, however, easily destroys the enhanced confinement of the PEP discharge. The stability of the ballooning modes has been studied and the PEP plasma core is found to be in the second stability region against ballooning modes or close to marginal stability. In a number of discharges complex high (m,n) modes have been observed with the soft X-ray cameras. The behaviour of the low (m,n) MHD modes can only be understood by considering the detailed evolution of the inverted q profile, which exists in a given discharge

On the distributions of some test criteria for a covariance matrix under local alternatives and bootstrap approximations

The asymptotic distribution of some test criteria for a covariance matrix are derived under local alternatives. Except for the existence of some higher moments, no assumption as to the form of the distribution function is made. As an illustration, a case of t distribution included normal model is considered and the power of the likelihood ratio test and Nagao's test for sphericity, as described in Srivastava and Khatri and Anderson, is computed. Also, the power is computed using the bootstrap method. In the case of t distribution, the bootstrap approximation does not appear to be as good as the one obtained by the asymptotic expansion method.

Local bootstrap

Local bootstrap