We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressions for the asymptotic covariance matrix. We develop in detail the martingale estimating function ap...

In canonical correlation analysis, canonical vectors are used in the interpretation of the canonical variables. We are interested in the asymptotic representation of the expectation, the variance and the distribution of the canonical vector. In this study, we derive the asymptotic distribution of the canonical vector under nonnormality. To obtain the asymptotic expansion of the canonical vector...

Huber’s gross-errors contamination model considers the class Fε of all noise distributions F = (1 − ε)Φ + εH, with Φ standard normal, ε ∈ (0, 1) the contamination fraction, and H the contaminating distribution. A half century ago, Huber evaluated the minimax asymptotic variance in scalar location estimation, min ψ max F∈Fε V (ψ, F ) = 1 I(F ∗ ε ) (1) where V (ψ,F ) denotes the asymptotic varian...

This paper deals with the problem of blind estimation of the carrier frequency offset of a linearly modulated noncircular transmission through an unknown frequency-selective channel. A frequency estimator is developed based on the unique conjugate cyclic frequency of the received signal, which is equal to twice the frequency offset. Consistency and asymptotic normality of the frequency estimato...

Clustered binary data with a large number of covariates have become increasingly more common in many scientific disciplines. This paper develops an asymptotic theory for generalized estimating equations (GEE) analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters. In this “large n, diverging p” framework, we provide appropriate regularity c...

The length of the future horizon is one of the principal “user choices” in subspace identification. It is well known that for the CCA algorithm the asymptotic variance decreases as the future horizon increases when input signals are white (or absent). There are also examples, when the input is not white, in which the asymptotic variance is minimized when the future horizon is equal to the syste...

We calculate the finite sample probability mass-at-zero and the probability of underestimating the true ratio between random effects variance and error variance in a LMM with one variance component. The calculations are expedited by simple matrix diagonalization techniques. One possible application is to compute the probability that the log of the likelihood ratio (LRT), or residual likelihood ...

High frequency inference has generated a wave of research interest among econometricians and practitioners, as indicated from the increasing number of estimators based on intra-day data. However, we also witness a scarcity of methodology to assess the uncertainty – standard error– of the estimator. The root of the problem is that whether with or without the presence of microstructure, standard ...

In this paper, we study (Q > x), the tail of the steady-state queue length distribution at a high-speed multiplexer. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. We provide two asymptotic upper bounds for the tail probability and an asymptotic result that emphasizes the importance of the dominant time sc...