## The bootstrap (2001)

Venue: | In Handbook of Econometrics |

Citations: | 110 - 2 self |

### BibTeX

@INPROCEEDINGS{Horowitz01thebootstrap,

author = {Joel L. Horowitz},

title = {The bootstrap},

booktitle = {In Handbook of Econometrics},

year = {2001},

pages = {3159--3228},

publisher = {Elsevier Science}

}

### Years of Citing Articles

### OpenURL

### Abstract

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

### Citations

3247 | An introduction to the bootstrap - Efron, Tibshirani - 1993 |

2579 | Density Estimation for Statistics and Data Analysis - Silverman - 1986 |

1852 | A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica
- White
- 1980
(Show Context)
Citation Context ... above. The experiments also investigate the RP of the t test when the HCCME is used with asymptotic critical values and when a jackknife version of the HCCME is used with asymptotic critical values (=-=MacKinnon and White 1985-=-). MacKinnon and White (1985) found through Monte Carlo experimentation that with the jackknife HCCME and asymptotic critical values, the t test had smaller distortions of RP than it did with several ... |

1693 |
Large Sample Properties of Generalized Method Moments Estimators
- Hansen
- 1982
(Show Context)
Citation Context ...lations among higher powers of components of h that persist at arbitrarily large lags (e.g., stochastic volatility). Although the restriction is satisfied in many econometric applications (see, e.g., =-=Hansen 1982-=-, Hansen and Singleton 1982), there are others in which relaxing it would be useful. The main problem in doing so is that without (4.2), it is necessary to use a kernel-type estimator of the GMM covar... |

1049 | Bootstrap methods; another look at the Jackknife”Annals of Statistics 7 - Efron - 1979 |

1043 |
A simple positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix
- Newey, West
- 1987
(Show Context)
Citation Context ...82), there are others in which relaxing it would be useful. The main problem in doing so is that without (4.2), it is necessary to use a kernel-type estimator of the GMM covariance matrix (see, e.g., =-=Newey and West 1987-=-, 1994; Andrews 1991, Andrews and Monahan 1992). Kernel-type estimators are not functions of sample moments and converge at rates that are slower than n -1/2 . However, present results on the existenc... |

818 |
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation
- Andrews
- 1991
(Show Context)
Citation Context ...ich relaxing it would be useful. The main problem in doing so is that without (4.2), it is necessary to use a kernel-type estimator of the GMM covariance matrix (see, e.g., Newey and West 1987, 1994; =-=Andrews 1991-=-, Andrews and Monahan 1992). Kernel-type estimators are not functions of sample moments and converge at rates that are slower than n -1/2 . However, present results on the existence of asymptotic expa... |

714 |
Advanced Econometrics
- Amemiya
- 1985
(Show Context)
Citation Context ...called the pseudo-true value. To 70sdefine the pseudo-true value, let ψ n be an estimator of ψ that is obtained under the incorrect assumption that H0 is true. Under regularity conditions (see, e.g.=-=, Amemiya 1985, Whit-=-e 1982), ψ n converges in probability to a limit ψ *, and n 1/2 (ψn - ψ *) = Op(1). ψ * is the pseudo-true value of ψ . Now let Tn be a statistic that is asymptotically pivotal under H0. Suppose... |

594 | Applied nonparametric regression - Härdle - 1990 |

586 | An analysis of transformation - BOX, COX - 1964 |

537 |
Testing Statistical Hypotheses
- Lehmann
- 1991
(Show Context)
Citation Context ...bability at the distribution that was, in fact, sampled. Beran (1988, p. 696) defines level to be the supremum of rejection probabilities over all distributions in the null hypothesis. Other authors (=-=Lehmann 1959-=-, p. 61; Rao 1973, p. 456) use the word size for the supremum. Lehmann defines level as a number that exceeds the rejection probability at all distributions in the null hypothesis. In this chapter, th... |

530 |
Maximum likelihood estimation of misspecified models
- White
- 1982
(Show Context)
Citation Context ...udo-true value. To 70sdefine the pseudo-true value, let ψ n be an estimator of ψ that is obtained under the incorrect assumption that H0 is true. Under regularity conditions (see, e.g., Amemiya 1985=-=, White 1982), ψ -=-n converges in probability to a limit ψ *, and n 1/2 (ψn - ψ *) = Op(1). ψ * is the pseudo-true value of ψ . Now let Tn be a statistic that is asymptotically pivotal under H0. Suppose that its ex... |

509 | Bootstrap Methods and Their Application - Davison, Hinkley - 1997 |

502 |
Generalized instrumental variables estimation of non-linear rational expectations models. Econometrica
- Hansen, Singleton
- 1982
(Show Context)
Citation Context ... higher powers of components of h that persist at arbitrarily large lags (e.g., stochastic volatility). Although the restriction is satisfied in many econometric applications (see, e.g., Hansen 1982, =-=Hansen and Singleton 1982-=-), there are others in which relaxing it would be useful. The main problem in doing so is that without (4.2), it is necessary to use a kernel-type estimator of the GMM covariance matrix (see, e.g., Ne... |

498 |
The Dynamic Effects of Aggregate Demand and Supply Disturbances
- Blanchard, Quah
- 1989
(Show Context)
Citation Context ...finiteness of income-effect matrices, the conditional Kolmogorov test of Andrews (1997), Stute’s (1997) specification test for parametric regression models, and certain functions of time-series data=-= (Blanchard and Quah 1989-=-, Runkle 1987, West 1990) are examples in which evaluating the asymptotic distribution is difficult and bootstrapping has been used as an alternative. In fact, the bootstrap is often more accurate in ... |

442 |
The Bootstrap and Edgeworth Expansion
- Hall
- 1992
(Show Context)
Citation Context ...2 1 2 −2 Φ( zn, α / 2*) − + g2( zn, α / 2*, Fn ) = 1− α + O( n ) n almost surely. Equations (3.21) and (3.22) can be solved to yield Cornish-Fisher expansions for zn,α/2 and zn,α/2*. The r=-=esults are (Hall 1992a, p. 111) 1 g2 ( z∞, -=-α / 2, F0) −2 (3.23) zn, α / 2 = z∞, α / 2 − + O( n ) , n φ( z ) ∞, α / 2 28swhere φ is the standard normal density function, and 1 g2( z∞, α / 2 , Fn ) −2 (3.24) zn, α / 2* = z∞... |

327 | The Jackknife and Bootstrap - Shao, Tu - 1995 |

277 | The jackknife and the bootstrap for general stationary observations.” Annuls of Statistics 17:1217–1241 - Künsch - 1989 |

225 |
Introduction to the Theory of Coverage Processes
- Hall
- 1988
(Show Context)
Citation Context ...because the moment conditions on which GMM estimation is based usually do not specify the dependence structure of the GMM residuals. The blocks may be non-overlapping (Carlstein 1986) or overlapping (=-=Hall 1985, K-=-ünsch 1988, Politis and Romano 1994). To describe these blocking methods more precisely, let the data consist of observations {Xi: i = 1, … , n}. With non-overlapping blocks of length l, block 1 is... |

203 | Automatic lag selection in covariance matrix estimation - Newey, West - 1994 |

202 | Some asymptotic theory for the bootstrap - Bickel, Freedman - 1981 |

192 | Small Sample Bias in GMM Estimation of Covariance Structures - Altonji, Segal - 1996 |

182 | Least Absolute Deviation Estimation for Censored Regression Model - Powell - 1984 |

175 | Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts,Review of Economic Studies - Heckman, Smith, et al. - 1997 |

163 | Comparing Nonparametric versus Parametric Regression Fits - Härdle, Mammen - 1993 |

136 |
Bootstrap Critical Values for Tests Based on Generalized Method of Moments Estimators
- Hall, Horowitz
- 1996
(Show Context)
Citation Context ...y, therefore, that empirical-likelihood recentering can be extended to GMM estimation with dependent data. The recentering method based on (3.29) requires no modification for use with dependent data (=-=Hall and Horowitz 1996-=-). Section 4.1 provides further discussion of the use of the bootstrap with dependent data. 4. EXTENSIONS This section explains how the bootstrap can be used to obtain asymptotic refinements in certai... |

131 | Maximum score estimation of the stochastic utility model of choice - Manski - 1975 |

127 | A smoothed maximum score estimator for the binary response model - Horowitz - 1992 |

126 | Cube root asymptotics - Kim, Pollard - 1990 |

125 |
Better bootstrap confidence intervals
- Efron
- 1987
(Show Context)
Citation Context ...approximations to the distributions of statistics that are not asymptotically pivotal can be obtained through the use of bootstrap iteration (Beran 1987, 1988; Hall 1992a) or bias-correction methods (=-=Efron 1987-=-). Bias correction methods are not applicable to symmetrical tests and confidence intervals. Bootstrap iteration is discussed in Section 4.4. Bootstrap iteration is highly computationally intensive, w... |

124 | Censored Regression Quantiles - Powell - 1986 |

124 |
The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One
- Nelson, Startz
- 1990
(Show Context)
Citation Context ...s instrumental-variables estimation with poorly correlated instruments and regressors. It is well known that first-order asymptotic approximations are especially poor in this situation (Hillier 1985, =-=Nelson and Startz 1990-=-ab, Phillips 1983). The bootstrap does not offer a solution to this problem. With poorly correlated instruments and regressors, Edgeworth expansions of estimators and test statistics involve denominat... |

122 |
Prepivoting test statistics: a bootstrap view of asymptotic refinements
- Beran
- 1988
(Show Context)
Citation Context ...g bootstrap samples from bootstrap samples as well as using the bootstrap to create an asymptotically pivotal statistic. The discussion here concentrates on the use of prepivoting to test hypotheses (=-=Beran 1988-=-). Beran (1987) explains how to use prepivoting to form confidence regions. Hall (1986b) describes an alternative approach to bootstrap iteration. Let Tn be a statistic for testing a hypothesis H0 abo... |

122 |
New Methods for Analyzing Structural Models of Labor Force Dynamics
- Flinn, Heckman
- 1982
(Show Context)
Citation Context ...ng may also be useful in situations where checking the consistency of the bootstrap is difficult. Examples of this include inference about the parameters of certain kinds of structural search models (=-=Flinn and Heckman 1982),-=- auction models (Donald and Paarsch 1996), and binary-response models that are estimated by Manski’s (1975, 1985) maximum score method. 3. ASYMPTOTIC REFINEMENTS The previous section described condi... |

116 |
Sibling Models and Data in Economics: Beginnings of a Survey
- Griliches
- 1979
(Show Context)
Citation Context ...ated or tested are variances or covariances of a distribution. This happens, for example, in estimation of covariance structures of economic processes (Abowd and Card 1987, 1988; Behrman et al. 1994; =-=Griliches 1979-=-; Hall and Mishkin 1982). In such cases Studentization is carried out with an estimator of the variance of an estimated variance. Imprecise estimation of a variance also affects the finite-sample perf... |

105 | Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator - Manski - 1985 |

102 | Subsampling - Politis, Romano, et al. - 1999 |

100 |
Vector Autoregressions and Reality
- Runkle
- 1987
(Show Context)
Citation Context ...ct matrices, the conditional Kolmogorov test of Andrews (1997), Stute’s (1997) specification test for parametric regression models, and certain functions of time-series data (Blanchard and Quah 1989=-=, Runkle 1987-=-, West 1990) are examples in which evaluating the asymptotic distribution is difficult and bootstrapping has been used as an alternative. In fact, the bootstrap is often more accurate in finite sample... |

94 | On blocking rules for the bootstrap with dependent data - Hall, Horowitz, et al. - 1995 |

93 |
Some further results on the exact small sample properties of the instrumental variables estimator
- Nelson, Startz
- 1990
(Show Context)
Citation Context ...s instrumental-variables estimation with poorly correlated instruments and regressors. It is well known that first-order asymptotic approximations are especially poor in this situation (Hillier 1985, =-=Nelson and Startz 1990-=-ab, Phillips 1983). The bootstrap does not offer a solution to this problem. With poorly correlated instruments and regressors, Edgeworth expansions of estimators and test statistics involve denominat... |

91 |
Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions.” The Annals of Statistics 22
- Politis, Romano
- 1994
(Show Context)
Citation Context ...ce, Nnm is likely to be very large, which makes Gnm hard to compute. This problem can be overcome by replacing the average over all Nnm subsamples with the average over a random sample of subsamples (=-=Politis and Romano 1994).-=- These can be obtained by sampling the data {Xi: i = 1, … , n} randomly without replacement. It is not difficult to show that the conditions of Theorem 2.3 are satisfied in all of the statistics con... |

88 | Bootstrapping regression models - Freedman - 1981 |

82 | Bootstrap and Wild Bootstrap for High-Dimensional Linear Models - Mammen - 1993 |

76 | Bootstrap Methods and their Application (Cambridge - Davison, Hinkley - 1997 |

75 | On the asymptotic accuracy of Efron's bootstrap - Singh - 1981 |

72 | Bootstrap Procedures Under Some Non-i.i.d Models - Liu - 1988 |

69 | Sieve bootstrap for time series - Bühlmann - 1997 |

65 |
Endowments and the Allocation of Schooling in the Family and in the Marriage Market: The Twins Experiment
- Behrman, Rosenzweig, et al.
- 1994
(Show Context)
Citation Context ...arameters being estimated or tested are variances or covariances of a distribution. This happens, for example, in estimation of covariance structures of economic processes (Abowd and Card 1987, 1988; =-=Behrman et al. 1994-=-; Griliches 1979; Hall and Mishkin 1982). In such cases Studentization is carried out with an estimator of the variance of an estimated variance. Imprecise estimation of a variance also affects the fi... |

65 |
Bootstrapping Time Series Models
- Li, Maddala
- 1996
(Show Context)
Citation Context ...almost surely as n → ∞. Ferretti and Romo (1996) also show n n n n how this result can be extended to the case in which {Ui} in (4.4) follows an AR(1) process. The results of Monte Carlo experiments (=-=Li and Maddala 1996-=-, 1997) suggest that the differences between the true and nominal RP’s of tests of hypotheses about integrated or cointegrated data-generation processes are smaller with bootstrap-based critical value... |

61 | Theoretical comparison of bootstrap confidence intervals - Hall - 1988 |