Márton Ispány

Fluctuation limit of branching processes with immigration and estimation of the means

We investigate a sequence of Galton-Watson branching processes with immigration, where the offspring mean tends to its critical value 1 and the offspring variance tends to 0. It is shown that the fluctuation limit is an Ornstein-Uhlenbeck-type process. As a consequence, in contrast to the case in which the offspring variance tends to a positive limit, it transpires that the conditional least-squares estimator of the offspring mean is asymptotically normal. The norming factor is n 3/2, in contrast to both the subcritical case, in which it is n 1/2, and the nearly critical case with positive limiting offspring variance, in which it is n.

Asymptotic behavior of unstable INAR(p) processes

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unstable autoregressive processes of order p. An application for Boston armed robberies data set is presented.

Promises and Pitfalls of Anchoring Vignettes in Health Survey Research.

Data harmonization is a topic of growing importance to demographers, who increasingly conduct domestic or international comparative research. Many self-reported survey items cannot be directly compared across demographic groups or countries because these groups differ in how they use subjective response categories. Anchoring vignettes, already appearing in numerous surveys worldwide, promise to overcome this problem. However, many anchoring vignettes have not been formally evaluated for adherence to the key measurement assumptions of vignette equivalence and response consistency. This article tests these assumptions in some of the most widely fielded anchoring vignettes in the world: the health vignettes in the World Health Organization (WHO) Study on Global AGEing and Adult Health (SAGE) and World Health Survey (WHS) (representing 10 countries; n = 52,388), as well as similar vignettes in the Health and Retirement Study (HRS) (n = 4,528). Findings are encouraging regarding adherence to response consistency, but reveal substantial violations of vignette equivalence both cross-nationally and across socioeconomic groups. That is, members of different sociocultural groups appear to interpret vignettes as depicting fundamentally different levels of health. The evaluated anchoring vignettes do not fulfill their promise of providing interpersonally comparable measures of health. Recommendations for improving future implementations of vignettes are discussed.

Asymptotic Behavior of Critical Primitive Multi-Type Branching Processes with Immigration

Under natural assumptions a Feller-type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly toward a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix.

Asymptotic Behaviour of Estimators of the Parameters of Nearly Unstable INAR(1) Models

A sequence of first-order integer-valued autoregressive type (INAR(1)) processes is investigated, where the autoregressive type coefficients converge to 1. It is shown that the limiting distribution of the joint conditional least squares estimators for this coefficient and for the mean of the innovation is normal. Consequences for sequences of Galton-Watson branching processes with unobservable immigration, where the mean of the offspring distribution converges to 1 (which is the critical value), are discussed.

Functionals of complex Ornstein-Uhlenbeck processes

Abstract The exact distribution of the sufficient statistics and distribution of the maximum likelihood estimator of the drift (damping) parameter in a stationary complex Ornstein-Uhlenbeck process, given by (1.1), is investigated. Complete tables of the distribution function for different levels are given by the help of MATLAB. The comparison with the earlier calculations are discussed. The relation of the famous model of Chandler Wobble proposed by Kolmogorov is investigated [1].

Asymptotic behavior of CLS estimators for 2-type doubly symmetric critical Galton-Watson processes with immigration

In this paper, the asymptotic behavior of the conditional least squares (CLS) estimators of the offspring means (α, β) and of the criticality parameter � := α + β for a 2-type critical doubly symmetric positively regular Galton–Watson branching process with immigration is described.

OOCWC: The robocar world championship initiative

Robocar World Championship or briefly OOCWC is a new initiative to create a community of people who share their interest in investigating the relationship between smart cities and robot cars with particular attention to the spread of robot cars in the near future. At the heart of this initiative is the Robocar City Emulator. It is intended to offer a common research platform for the investigation of the smart city simulations. In this paper, we review the recent advances of OOCWC.

A Poisson INAR(1) process with a seasonal structure

This paper introduces a non-negative integer-valued autoregressive (INAR) process with seasonal structure of first order, which is an extension of the standard INAR(1) model proposed by Al-Osh and Alzaid [First-order integer-valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8:261–275]. The main properties of the model are derived such as its stationarity and autocorrelation function (ACF), among others. The conditional least squares and conditional maximum likelihood estimators of the model parameters are studied and their asymptotic properties are established. Some detailed discussion is dedicated to the case where the marginal distribution of the process is Poisson. A Monte Carlo experiment is conducted to evaluate and compare the performances of these estimators for finite sample sizes. The standard Yule–Walker approach is also considered for comparison purposes. The empirical results indicate that, in general, the conditional maximum likelihood estimator presents much better performance in terms of bias and mean square error. The model is illustrated using a real data set.

Divergence minimization under prior inequality constraints

Motivated by problems in robust statistics we first give a simple proof of the following: Given a probability measure P and positive measures /spl mu/</spl nu/, the /spl gamma/-divergence from P of probability measures Q satisfying /spl mu//spl les/Q or /spl mu//spl les/Q/spl les//spl nu/ is minimized by an explicitly determined Q/sup */ not depending on (the convex function) /spl gamma/. Next we address /spl gamma/-divergence minimization under the above inequality constraint and additional moment constraints.