Weak Convergence of Randomly Weighted Dependent Residual Empiricals with Applications to Autoregression

Koul, Hira L.; Ossiander, Mina

doi:10.1214/aos/1176325383

Cited by 61 publications

(59 citation statements)

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“…(His assumption that f is almost everywhere positive can be omitted). See also Koul and Ossiander (1994), Koul (2002) and Koul and Ling (2006). We therefore have the following result.…”

Section: Conditional Distribution Functionmentioning

confidence: 67%

Prediction in moving average processes

Schίck¹,

Wefelmeyer²

2008

Journal of Statistical Planning and Inference

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Abstract. For the stationary invertible moving average process of order one with unknown innovation distribution F , we construct root-n consistent plug-in estimators of conditional expectations E(h(Xn+1)|X1, . . . , Xn). More specifically, we give weak conditions under which such estimators admit Bahadur type representations, assuming some smoothness of h or of F . For fixed h it suffices that h is locally of bounded variation and locally Lipschitz in L2(F ), and that the convolution of h and F is continuously differentiable. A uniform representation for the plug-in estimator of the conditional distribution function P (Xn+1 ≤ · |X1, . . . , Xn) holds if F has a uniformly continuous density. For a smoothed version of our estimator, the Bahadur representation holds uniformly over each class of functions h that have an appropriate envelope and whose shifts are F -Donsker, assuming some smoothness of F . The proofs use empirical process arguments.

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“…(His assumption that f is almost everywhere positive can be omitted). See also Koul and Ossiander (1994), Koul (2002) and Koul and Ling (2006). We therefore have the following result.…”

Section: Conditional Distribution Functionmentioning

confidence: 67%

Prediction in moving average processes

Schίck¹,

Wefelmeyer²

2008

Journal of Statistical Planning and Inference

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“…n is a weighted absolute empirical distribution function similar to those studied by Koul and Ossiander (1994). When also b = 0 then b G 1;0 n equals the empirical distribution function b G n of (2.7).…”

Section: Absolute Empirical Process Representationmentioning

confidence: 85%

“…It is useful to consider an auxiliary class of weighted and marked empirical distribution functions for errors " i as opposed to absolute errors j" i j: The analysis of this class generalises that of Koul and Ossiander (1994) in two respects. First, the standardised estimation error b is permitted to diverge at a rate of n 1=4 rather than being bounded.…”

Section: A Class Of Auxiliary Weighted and Marked Empirical Processesmentioning

confidence: 99%

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Asymptotic Analysis of the Forward Search

Johansen

Nielsen

2013

SSRN Journal

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Summary:The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made. The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a …xed point argument to describe the iterative element of the procedure.

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“…Results in the previous section were based on the properties of weighted empirical processes constructed from residuals whose distance from the true innovations is in…nitesimal uniformly in t, in probability. This is analogous to the setup of Koul and Ossiander (1994). Here, however, under our hypotheses on@ @, it need not hold that max t=1;:::;T j y t 1 j = o (b T ), so max t=1;:::;T j ŷ t uy t 1 " t j need not be o P (1) even if the true value u = d 1 T c is inserted (in fact, it is not o P (1) if@ is the OLS estimator).…”

Section: Extension To Higher-order Autoregressionsmentioning

confidence: 91%

Exploiting Infinite Variance Through Dummy Variables in Nonstationary Autoregressions

Cavaliere

Georgiev

2013

Econom. Theory

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We consider estimation and testing in …nite-order autoregressive models with a (near) unit root and in…nite-variance innovations. We study the asymptotic properties of estimators obtained by dummying out "large"innovations, i.e., exceeding a given threshold. These estimators re ‡ect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterative versions of the dummy-variable estimator are also discussed. We provide conditions on the preliminary parameter estimator and on the threshold which ensure that (i) the dummy-based estimator is consistent at higher rates than the OLS estimator, (ii) an asymptotically normal test statistic for the unit root hypothesis can be derived, and (iii) order of magnitude gains of local power are obtained.

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Weak Convergence of Randomly Weighted Dependent Residual Empiricals with Applications to Autoregression

Cited by 61 publications

References 0 publications

Prediction in moving average processes

Prediction in moving average processes

Asymptotic Analysis of the Forward Search

Exploiting Infinite Variance Through Dummy Variables in Nonstationary Autoregressions

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