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72
Semiparametrically efficient rankbased inference for shape I: Optimal rankbased tests for sphericity
 Ann. Statist
, 2006
"... A class of Restimators based on the concepts of multivariate signed ranks and the optimal rankbased tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical distribution. These Restimators are rootn consistent under a ..."
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Cited by 48 (32 self)
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A class of Restimators based on the concepts of multivariate signed ranks and the optimal rankbased tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical distribution. These Restimators are rootn consistent under any radial density g, without any moment assumptions, and semiparametrically efficient at some prespecified density f. When based on normal scores, they are uniformly more efficient than the traditional normaltheory estimator based on empirical covariance matrices (the asymptotic normality of which, moreover, requires finite moments of order four), irrespective of the actual underlying elliptical density. They rely on an original rankbased version of Le Cam’s onestep methodology which avoids the unpleasant nonparametric estimation of crossinformation quantities that is generally required in the context of Restimation. Although they are not strictly affineequivariant, they are shown to be equivariant in a weak asymptotic sense. Simulations confirm their feasibility and excellent finitesample performances. 1. Introduction. 1.1. Rankbased inference for elliptical families. An elliptical density over Rk is determined by a location center θ ∈ Rk, a scale parameter σ ∈ R + 0, a realvalued positive definite symmetric k × k matrix V = (Vij) with V11 = 1,
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
Root n Consistent and Optimal Density Estimators for Moving Average Processes
"... The marginal density of a first order moving average process can be written as convolution of two innovation densities. Saavedra and Cao (2000) propose to estimate the marginal density by plugging in kernel density estimators for the innovation densities, based on estimated innovations. They obtain ..."
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Cited by 21 (17 self)
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The marginal density of a first order moving average process can be written as convolution of two innovation densities. Saavedra and Cao (2000) propose to estimate the marginal density by plugging in kernel density estimators for the innovation densities, based on estimated innovations. They obtain that for an appropriate choice of bandwidth the variance of their estimator decreases at the rate 1/n. Their estimator can be interpreted as a specific Ustatistic. We suggest a slightly simpli ed Ustatistic as estimator of the marginal density, prove that it is asymptotically normal at the same rate, and describe the asymptotic variance explicitly. We show that the estimator is asymptotically efficient if no structural assumptions are made on the innovation density. For innovation densities known to have mean zero or to be symmetric, we describe improvements of our estimator which are again asymptotically efficient.
Forecasting spot electricity prices: a comparison of parametric and semiparametric time series models
 International Journal of Forecasting
"... comparison of parametric and semiparametric time series models ..."
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Cited by 21 (0 self)
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comparison of parametric and semiparametric time series models
Weighted ResidualBased Density Estimators For Nonlinear Autoregressive Models
"... This paper considers residualbased and randomly weighted kernel estimators for innovation densities of nonlinear autoregressive models. The weights are chosen to make use of the information that the innovations have mean zero. Rates of convergence are obtained in weighted L1norms. These estimators ..."
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Cited by 18 (13 self)
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This paper considers residualbased and randomly weighted kernel estimators for innovation densities of nonlinear autoregressive models. The weights are chosen to make use of the information that the innovations have mean zero. Rates of convergence are obtained in weighted L1norms. These estimators give rise to smoothed and weighted empirical distribution functions and moments. It is shown that the latter are efficient if an efficient estimator for the autoregression parameter is used to construct the residuals.
Estimating the Innovation Distribution in Nonlinear Autoregressive Models
 Department of Mathematics, University of Siegen. http://www.math.unisiegen.de/statistik/wefelmeyer.html
"... The usual estimator for the expectation of a function under the innovation distribution of a nonlinear autoregressive model is the empirical estimator based on estimated innovations. It can be improved by exploiting that the innovation distribution has mean zero. We show that the resulting estimator ..."
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Cited by 17 (17 self)
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The usual estimator for the expectation of a function under the innovation distribution of a nonlinear autoregressive model is the empirical estimator based on estimated innovations. It can be improved by exploiting that the innovation distribution has mean zero. We show that the resulting estimator is efficient if the innovations are estimated with an efficient estimator for the autoregression parameter. Efficiency of this estimator is necessary except when the expectation of the function can be estimated adaptively. Analogous results hold for heteroscedastic models.
Deviation Probability Bound For Martingales With Applications To Statistical Estimation
, 1999
"... . Let M t be a vector martingale and #M# t denote its predictable quadratic variation. In this paper we present a bound for the probability that z # #M# 1 t M t > # # z # #M# 1 t z with a fixed vector z and discuss some its applications to statistical estimation in autoregressive and linear dif ..."
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Cited by 15 (2 self)
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. Let M t be a vector martingale and #M# t denote its predictable quadratic variation. In this paper we present a bound for the probability that z # #M# 1 t M t > # # z # #M# 1 t z with a fixed vector z and discuss some its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is nonasymptotic and does not require any ergodic assumption on the underlying model. 1. Introduction. Statistical examples Let observations Y 1 , . . . , Y T be generated by the linear regression model: Y t = X # t # + # t , t = 1, . . . , T , (1.1) where # # R p is unknown vector of parameters, X t , t = 1, . . . , T , are deterministic design points from R p , and (# t ) t#1 is a sequence of i.i.d. zero mean Gaussian random variables with the variance # 2 . Hereafter, all vectors are assumed to be vectorcolumns and a # (resp. #a# ) means the transpose (resp. the Euclidean norm) of the vector a . For estimating the vector # , one usually applies...
Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach
, 2001
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Semiparametric Duration Models
, 2001
"... In this paper we consider semiparametric duration models and efficient estimation of the parameters in a noni.i.d. environment. In contrast to classical time series models where innovations are assumed to be i.i.d., we show that, for example in the oftenused Autoregressive Conditional Duration (AC ..."
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Cited by 13 (2 self)
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In this paper we consider semiparametric duration models and efficient estimation of the parameters in a noni.i.d. environment. In contrast to classical time series models where innovations are assumed to be i.i.d., we show that, for example in the oftenused Autoregressive Conditional Duration (ACD) model, the assumption of independent innovations is too restrictive to describe financial durations accurately. Therefore, we consider semiparametric extensions of the standard specification that allow for arbitrary kinds of dependencies between the innovations. The exact nonparametric specification of these dependencies determines the flexibility of the semiparametric model. We calculate semiparametric efficiency bounds for the ACD parameters, discuss the construction of efficient estimators, and study the efficiency loss of the exponential pseudolikelihood procedure. This efficiency loss proves to be sizeable in applications. For durations observed on the Paris Bourse for the Alcatel stock in July and August 1996, the proposed semiparametric procedures clearly outperform pseudolikelihood procedures. We analyze these efficiency gains using a simulation study which confirms that, at least at the Paris Bourse, dependencies among rescaled durations can be exploited.