Petrovskaya and Leontovich (1982) proved a central limit theorem for sums of dependent random variables indexed by a graph. We apply this theorem to obtain asymptotic normality for the number of local maxima of a random function on certain graphs and for the number of edges having the same color at both endpoints in randomly colored graphs. We briefly motivate these problems, and conclude with ...

We present conditions to obtain the asymptotic normality of the maximum likelihood estimator of a loss process presented in [2]. We shall use the notations of [2], write ‖ · ‖q for the standard L norm on an arbitrary space R, d ≥ 1, and let D φ denote the k−th order di erentiation with respect to φ. Let us introduce the following hypotheses: (A4) For all i ∈ {1, . . . , r}, λi(Φ0) > 0. (A5) For...

In this article, we establish the asymptotic normality of the posterior distribution for the natural parameter in an exponential family based on independent and identically distributed data. The mode of convergence is expected Kullback-Leibler distance and the number of parameters p is increasing with the sample size n. Using this, we give an asymptotic expansion of the Shannon mutual informati...

An estimate of the second moment of the regression function is introduced. Its asymptotic normality is proved such that the asymptotic variance depends neither on the dimension of the observation vector, nor on the smoothness properties of the regression function. The asymptotic variance is given explicitly.

Poisson regression models for count variables have been utilized in many applications. However, in many problems overdispersion and zeroinflation occur. We study in this paper regression models based on the generalized Poisson distribution (Consul (1989)). These regression models which have been used for about 15 years do not belong to the class of generalized linear models considered by McCull...

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity ~ARMAGARCH! model+ The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established+ Consistency of the quasimaximum-likelihood estimator ~QMLE! is proved under only the second-order moment conditi...

This dissertation studies the least squares estimator of a trend parameter in a simple linear regression model with multiple changepoints when the changepoint times are known. The error component in the model is allowed to be autocorrelated. The least squares estimator of the trend and the variance of the trend estimator are derived. Consistency and asymptotic normality of the trend estimator a...

A wide literature is available on the asymptotic behavior of the Durbin-Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin-Watson statistic for autoregressive models with adaptive control. Our purpose is to fill the gap by establishing the asymptotic behavior of the Durbin Watson statistic for ARX models in adaptive tracking. On the one hand, we ...

For estimating the realized volatility and covariance by using high frequency data, Kunitomo and Sato (2008a,b) have proposed the Separating Information Maximum Likelihood (SIML) method when there are micro-market noises. The SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic normality (or the stable convergence in the general case) when the sample s...

We consider the asymptotic properties of the sample mean and the sample covariance sequence of a field composed of the sum of a purely-indeterministic and evanescent components. The asymptotic normality of the sample mean and sample covariances is established. A Bartlett-type formula for the asymptotic covariance matrix of the sample covariances of this field, is derived.