We consider the asymptotic behavior of additive functionals of linear processes with infinite variance innovations. Applying the central limit theory for Markov chains, we establish asymptotic normality for short-range dependent processes. A non-central limit theorem is obtained when the processes are long-range dependent and the innovations are in the domain of attraction of stable laws.

Sample selection models are important for correcting for the effects of nonrandom sampling in microeconomic data. This note is about semiparametric estimation using a series approximation to the selection correction term. Regression spline and power series approximations are considered. Consistency and asymptotic normality are shown, as well as consistency of an asymptotic variance estimator. J...

In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nosé-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of the conjugate momentum vector. Numerical experiments with a double well potential corroborate the as...

Denote by Zν the number of critical points of a random trigonometric polynomial of degree ≤ ν. We prove that as ν → ∞ the expectation of Zν is asymptotic to 2ν √ 3 5 while its variance is asymptotic to δ∞ν where δ∞ ≈ 0.35. Mathematics Subject Classification 2010: 33B10, 42A61, 60D99.

We provide an estimate of the score function for rank regression using compactly supported wavelets. This estimate is then used to find a rank-based asymptotically efficient estimator for the slope parameter of a linear model. We also provide a consistent estimator of the asymptotic variance of the rank estimator. For related mixed models, the asymptotic relative efficiency is also discussed

In many applications of generalized linear mixed models to clustered correlated or longitudinal data, often we are interested in testing whether a random effects variance component is zero. The usual asymptotic mixture of chi-square distributions of the score statistic for testing constrained variance components does not necessarily hold. In this paper, we propose and explore a parametric boots...

This paper proposes a new test for the presence of jumps in asset prices. The test is derived from a direct application of Itô’s lemma to the semi-martingale process of asset prices. Intuitively, the proposed test measures the impact of jumps on the third and higher order return moments and is also directly related to the profit/loss function of a variance swap replication strategy. We derive i...

We use the sample covariation to develop asymptotic tests for independence for data in the normal domain of attraction of a stable law. The tests can be used for finite or infinite variance processes. In a simulation study we compare the finite sample performance of the proposed tests to the Portmanteau test commonly used in time series modeling. The null convergence of the test statistics to t...

In this paper we demonstrate that standard methods of asymptotic inference will break down in a binary choice duration model in a time series setting. This comes about because the dependent variable has a degenerate limit distribution, which makes the asymptotic variance-covariance matrix singular. This result has implications for discrete choice duration panel data models under large N and T a...

We compare the asymptotic covariance matrix of the ML estimator in a nonlinear measurement error model to the asymptotic covariance matrices of the CS and SQS estimators studied in Kukush et al (2002). For small measurement error variances they are equal up to the order of the measurement error variance and thus nearly equally efficient.