Optimal equivariant prediction for high-dimensional linear models with arbitrary predictor covariance
نویسندگان
چکیده
منابع مشابه
High-dimensional autocovariance matrices and optimal linear prediction
A new methodology for optimal linear prediction of a stationary time series is introduced. Given a sample X1, . . . , Xn, the optimal linear predictor of Xn+1 is X̃n+1 = φ1(n)Xn + φ2(n)Xn−1 + . . .+φn(n)X1. In practice, the coefficient vector φ(n) ≡ (φ1(n), φ2(n), . . . , φn(n)) is routinely truncated to its first p components in order to be consistently estimated. By contrast, we employ a consi...
متن کاملREJOINDER: High-dimensional autocovariance matrices and optimal linear prediction
We would like to sincerely thank all discussants for their kind remarks and insightful comments. To start with, we wholeheartedly welcome the proposal of Rob Hyndman for a “better acf” plot based on our vector estimator γ̂∗(n) from Section 3.2. As mentioned, the sample autocovariance is not a good estimate for the vector γ(n), and this is especially apparent in the wild excursions it takes at hi...
متن کاملDiscussion of “ High - dimensional autocovariance matrices and optimal linear prediction ” ∗ , †
First, we would like to congratulate Prof. McMurry and Prof. Politis for their thought-provoking paper on the optimal linear prediction based on full time series sample (hereafter, referred as [MP15]). [MP15] considered the one-step optimal linear predictor X∗ n+1 = ∑n i=1 φi(n)Xn+1−i of a univariate time series X1, . . . , Xn in the ` 2 sense which is given by the solution of the Yule-Walker e...
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Spatial covariance matrix estimation is of great significance in many applications in climatology, econometrics and many other fields with complex data structures involving spatial dependencies. High dimensionality brings new challenges to this problem, and no theoretical optimal estimator has been proved for the spatial high-dimensional covariance matrix. Over the past decade, the method of re...
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This paper considers testing a covariance matrix in the high dimensional setting where the dimension p can be comparable or much larger than the sample size n. The problem of testing the hypothesis H0 : = 0 for a given covariance matrix 0 is studied from a minimax point of view. We first characterize the boundary that separates the testable region from the non-testable region by the Frobenius n...
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2013
ISSN: 1935-7524
DOI: 10.1214/13-ejs826