Results 1  10
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12
On adaptive estimation in nonstationary ARMA models with GARCH errors
 Ann. Statist
, 2003
"... This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the loglikelihood ratio for the model is obtained. It is show ..."
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Cited by 46 (34 self)
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This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the loglikelihood ratio for the model is obtained. It is shown that the limit experiment is neither LAN nor LAMN, but is instead LABF. Adaptivity is discussed and it is found that the parameters in the model are generally not adaptively estimable if the density of the rescaled error is asymmetric. For the model with symmetric density of the rescaled error, a new efficiency criterion is established for a class of defined Mνestimators. It is shown that such efficient estimators can be constructed when the density is known. Using the kernel estimator for the score function, adaptive estimators are constructed when the density of the rescaled error is symmetric, and it is shown that the adaptive procedure for the parameters in the conditional mean part uses the full sample without splitting. These estimators are demonstrated to be
Estimating invariant laws of linear processes by Ustatistics
"... Suppose we observe an invertible linear process with independent mean zero innovations, and with coefficients depending on a finitedimensional... ..."
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Cited by 11 (10 self)
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Suppose we observe an invertible linear process with independent mean zero innovations, and with coefficients depending on a finitedimensional...
Sample Splitting With Markov Chains
 Bernoulli
, 2000
"... Sample splitting techniques play an important role in constructing estimates with prescribed influence functions in semiparametric and nonparametric models when the observations are independent and identically distributed. This paper shows how a contiguity result can be used to modify these techniqu ..."
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Cited by 9 (6 self)
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Sample splitting techniques play an important role in constructing estimates with prescribed influence functions in semiparametric and nonparametric models when the observations are independent and identically distributed. This paper shows how a contiguity result can be used to modify these techniques to the case when the observations come from a stationary and ergodic Markov chain. As a consequence, sufficient conditions for the construction of efficient estimates in semiparametric Markov chain models are obtained. The applicability of the resulting theory is demonstrated by constructing an estimate of the innovation variance in a nonparametric autoregression model, by constructing a weighted least squares estimate with estimated weights in an autoregressive model with martingale innovations, and by constructing an efficient and adaptive estimate of the autoregression parameter in a heteroscedastic autoregressive model with symmetric errors.
Adaptive estimation in time series regression models
 Journal of Econometrics
, 1992
"... This work develops adaptive estimators for a linear regression model with serially correlated errors. We show that these results continue to hold when the order of the ARMA process characterizing the errors is unknown. The finite sample results are promising, indicating that substantial efficiency ..."
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Cited by 7 (0 self)
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This work develops adaptive estimators for a linear regression model with serially correlated errors. We show that these results continue to hold when the order of the ARMA process characterizing the errors is unknown. The finite sample results are promising, indicating that substantial efficiency gains may be possible for samples as small as 50 observations. We use these estimators to investigate the behavior of the forward foreign exchange market.
Efficient Estimation in Invertible Linear Processes
"... An invertible causal linear process is a process which has infinite order moving average and autoregressive representations. We assume that the coefficients in these representations depend on a Euclidean parameter, while the corresponding innovations have an unknown centered distribution with some m ..."
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Cited by 7 (7 self)
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An invertible causal linear process is a process which has infinite order moving average and autoregressive representations. We assume that the coefficients in these representations depend on a Euclidean parameter, while the corresponding innovations have an unknown centered distribution with some moment restrictions. We discuss efficient estimation of differentiable functionals in such a semiparametric model. For this we first obtain a suitable semiparametric version of local asymptotic normality and then use Hajek's convolution theorem to characterize efficient estimators. Then we apply this result to construct efficient estimators of the Euclidean parameter and of linear functionals of the innovation distribution.
An Alternative Asymptotic Analysis of ResidualBased Statistics,” mimeo
, 2005
"... This paper offers an alternative technique to derive the limiting distribution of residualbased statistics or, more general, the limiting distribution of statistics with estimated nuisance parameters. This technique allows us to unify many known results on twostage estimators and tests and we als ..."
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Cited by 5 (1 self)
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This paper offers an alternative technique to derive the limiting distribution of residualbased statistics or, more general, the limiting distribution of statistics with estimated nuisance parameters. This technique allows us to unify many known results on twostage estimators and tests and we also derive new results. The technique is especially useful in situations where smoothness of the statistic of interest with respect to the parameters to be estimated does not hold or is difficult to establish, e.g., rankbased statistics. We essentially replace this differentiability condition with a distributional invariance property that is often satisfied in specification tests. Our results on statistics that have not been considered before all use nonparametric statistics. On the technical side, we provide a novel approach to the preestimation problem using Le Cam’s third lemma. The resulting formula for the correction in the limiting variance as a result of preestimation some parameters is a simple expression involving some appropriate covariances. The regularity conditions required fairly minimal. Numerous examples show the strength and wide applicability of our approach.
On Asymptotic Differentiability Of Averages
, 1999
"... This paper proves an asymptotic expansion useful in the construction of estimates with a prescribed influence function in parametric and semiparametric models. ..."
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Cited by 2 (1 self)
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This paper proves an asymptotic expansion useful in the construction of estimates with a prescribed influence function in parametric and semiparametric models.
Efficient Estimation in a Semiparametric Autoregressive Model
, 1998
"... . This paper constructs efficient estimates of the parameter ae in the semiparametric autoregression model X t = aeX t\Gamma1 + fl(X t\Gamma2 ) + ffl t with a smooth function fl and independent and identically distributed innovations ffl t with zero means and finite variances. This will be done un ..."
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Cited by 1 (1 self)
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. This paper constructs efficient estimates of the parameter ae in the semiparametric autoregression model X t = aeX t\Gamma1 + fl(X t\Gamma2 ) + ffl t with a smooth function fl and independent and identically distributed innovations ffl t with zero means and finite variances. This will be done under the assumptions that jaej + lim sup jxj!1 jfl(x)j jxj ! 1 and that the errors have a density with finite Fisher information for location. The former condition guarantees that the process can be chosen to be stationary and ergodic. AMS 1991 subject classification: Primary 62G05, 62G20; Secondary 62M05, 62G07 Keywords and phrases: Stationary Markov chains; ergodicity; V uniform ergodicity; local asymptotic normality; local asymptotic minimaxity, contiguity, sample splitting 1. Introduction In this paper we consider a stationary and ergodic semiparametric additive autoregression model with observations X \Gamma1 ; X 0 ; : : : ; X n . This model is defined by the structural relation (...
Semiparametric Efficiency Bound and MEstimation in TimeSeries Models for Conditional Quantiles
"... Abstract: In this paper we derive the semiparametric efficiency bound in time series models of conditional quantiles under a sole strong mixing assumption. We moreover provide an expression of Stein’s (1956) least favorable parametric submodel. Our approach can be summarized as follows: first, we ch ..."
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Cited by 1 (0 self)
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Abstract: In this paper we derive the semiparametric efficiency bound in time series models of conditional quantiles under a sole strong mixing assumption. We moreover provide an expression of Stein’s (1956) least favorable parametric submodel. Our approach can be summarized as follows: first, we characterize the class of M–estimators that are consistent for the the conditional quantile parameter. We show that these estimators are asymptotically normal, and determine the minimum of their asymptotic covariance matrices. Second, we construct a fully parametric submodel that satisfies the conditional quantile restriction and contains the data generating process. Finally, we show that this submodel is the least favorable, i.e. the asymptotic covariance matrix of its maximum likelihood estimator is equal to the above minimum. 1.
Efficient estimation in a semiparametric heteroscedastic autoregressive model
, 1999
"... In this paper we characterize and construct efficient estimators of the autoregression parameter in the heteroscedastic autoregression model of order 1 with unknown innovation density and unknown volatility function. ..."
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In this paper we characterize and construct efficient estimators of the autoregression parameter in the heteroscedastic autoregression model of order 1 with unknown innovation density and unknown volatility function.