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48
The bootstrap
 In Handbook of Econometrics
, 2001
"... The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an a ..."
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Cited by 75 (1 self)
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The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an approximation to the distribution of an estimator or test statistic that is at least as accurate as the
The Impact of Bootstrap Methods on Time Series Analysis
 Statistical Science
, 2003
"... Sparked by Efron’s seminal paper, the decade of the 1980s was a period of active research on bootstrap methods for independent data— mainly i.i.d. or regression setups. By contrast, in the 1990s much research was directed towards resampling dependent data, for example, time series and random field ..."
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Cited by 21 (5 self)
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Sparked by Efron’s seminal paper, the decade of the 1980s was a period of active research on bootstrap methods for independent data— mainly i.i.d. or regression setups. By contrast, in the 1990s much research was directed towards resampling dependent data, for example, time series and random fields. Consequently, the availability of valid nonparametric inference procedures based on resampling and/or subsampling has freed practitioners from the necessity of resorting to simplifying assumptions such as normality or linearity that may be misleading.
Block length selection in the bootstrap for time series
 Comput. Statist. Data Anal
, 1999
"... The blockwise bootstrap is a modification of Efron's bootstrap designed to give correct results for dependent stationary observations. One drawback of the method is that it depends critically on a block length which had to be chosen by the user. Here we propose a fully datadriven method to select t ..."
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Cited by 14 (3 self)
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The blockwise bootstrap is a modification of Efron's bootstrap designed to give correct results for dependent stationary observations. One drawback of the method is that it depends critically on a block length which had to be chosen by the user. Here we propose a fully datadriven method to select this block length. It is based on the equivalence of the blockwise bootstrap variance to a lag weight estimator of a spectral density at the origin. The relevant spectral density is the one of the process given by the influence function of the statistic to be bootstrapped. In this equivalence the block length is the inverse of the bandwidth. We thus apply a recently developed local bandwidth selection procedure to the time series given by the estimated influence function. Simulations show that this procedure gives good results in a wide range of situations.
Inference of Trends in Time Series
 J. the Royal Statistical Society: Series B (Statistical Methodology
, 2007
"... Summary. We consider statistical inference of trends in mean nonstationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically cor ..."
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Cited by 14 (4 self)
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Summary. We consider statistical inference of trends in mean nonstationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities. The results are applied to global warming temperature data and Nile river flow data. Our confidence band of the trend of the global warming temperature series supports the claim that the trend is increasing over the last 150 years.
The design and analysis of benchmark experiments
 JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
, 2005
"... The assessment of the performance of learners by means of benchmark experiments is an established exercise. In practice, benchmark studies are a tool to compare the performance of several competing algorithms for a certain learning problem. Crossvalidation or resampling techniques are commonly used ..."
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Cited by 13 (6 self)
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The assessment of the performance of learners by means of benchmark experiments is an established exercise. In practice, benchmark studies are a tool to compare the performance of several competing algorithms for a certain learning problem. Crossvalidation or resampling techniques are commonly used to derive point estimates of the performances which are compared to identify algorithms with good properties. For several benchmarking problems, test procedures taking the variability of those point estimates into account have been suggested. Most of the recently proposed inference procedures are based on special variance estimators for the crossvalidated performance. We introduce a theoretical framework for inference problems in benchmark experiments and show that standard statistical test procedures can be used to test for differences in the performances. The theory is based on well defined distributions of performance measures which can be compared with established tests. To demonstrate the usefulness in practice, the theoretical results are applied to regression and classification benchmark studies based on artificial and real world data.
Weak Dependence beyond Mixing and Asymptotics for Nonparametric Regression
, 2000
"... We consider a new concept of weak dependence, introduced by Doukhan and Louhichi ([9]), which is more general than the classical frameworks of mixing or associated sequences. The new notion is broad enough to include many interesting examples such as very general Bernoulli shifts, Markovian models o ..."
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Cited by 11 (3 self)
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We consider a new concept of weak dependence, introduced by Doukhan and Louhichi ([9]), which is more general than the classical frameworks of mixing or associated sequences. The new notion is broad enough to include many interesting examples such as very general Bernoulli shifts, Markovian models or time series bootstrap processes with discrete innovations. Under such a weak dependence assumption, we investigate nonparametric regression which represents one (among many) important statistical estimation problem. We justify in this more general setting the `whitening by windowing principle' for nonparametric regression, saying that asymptotic properties remain in rst order the same as for independent samples. The proofs borrow previously used strategies, but precise arguments are developed under the new aspect of general weak dependence. Key Words and phrases. Bernoulli shift, bootstrap, central limit theorem, Lindeberg method, Markov process, mixing, nonparametric estimation, positiv...
European Central Bank
, 2008
"... New Keynesian Phillips Curves (NKPC) have been extensively used in the analysis of monetary policy, but yet there are a number of issues of concern about how they are estimated and then related to the underlying macroeconomic theory. The first is whether such equations are identified. To check ident ..."
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Cited by 10 (0 self)
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New Keynesian Phillips Curves (NKPC) have been extensively used in the analysis of monetary policy, but yet there are a number of issues of concern about how they are estimated and then related to the underlying macroeconomic theory. The first is whether such equations are identified. To check identification requires specifying the process for the forcing variables (typically the output gap) and solving the model for inflationintermsoftheobservables. Inpractice,theequationisestimatedby GMM, relying on statistical criteria to choose instruments. This may result in failure of identification or weak instruments. Secondly, the NKPC is usually derived as a part of a DSGE model, solved by loglinearising around a steady state and the variables are then measured in terms of deviations from the steady state. In practice the steady states, e.g. for output, are usually estimated by some statistical procedure such as the HodrickPrescott (HP) filter that might not be appropriate. Thirdly, there are arguments that other variables, e.g. interest rates, foreign inflation and foreign output gaps should enter the Phillips curve. This paper examines these three issues and argues that all three benefit from a global perspective. The global perspective provides additional instruments to alleviate the weak instrument problem, yields a theoretically consistent measure of the steady state and provides a natural route for foreign inflation or output gap to enter the NKPC. Keywords: Global VAR (GVAR), identification, New Keynesian Phillips Curve, TrendCycle decomposition.
Mixing property and functional central limit theorems for a sieve bootstrap in time series
, 1995
"... We study a bootstrap method for stationary realvalued time series, which is based on the method of sieves. We restrict ourselves to autoregressive sieve bootstraps. Given a sample X1;:::;X n from a linear process fX tg t2 Z, we approximate the underlying process by an autoregressive model with orde ..."
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Cited by 7 (1 self)
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We study a bootstrap method for stationary realvalued time series, which is based on the method of sieves. We restrict ourselves to autoregressive sieve bootstraps. Given a sample X1;:::;X n from a linear process fX tg t2 Z, we approximate the underlying process by an autoregressive model with order p = p(n), where p(n)!1;p(n) =o(n) as the sample size n!1. Based on such a model a bootstrap process fX t g t2 Z is constructed from which one can draw samples of any size. We giveanovel result which says that with high probability,such a sieve bootstrap process fX t g t2 Z satis es a new type of mixing condition. This implies that many results for stationary, mixing sequences carry over to the sieve bootstrap process. As an example we derive a functional central limit theorem under a bracketing condition.