In this contribution we study the statistical properties of a number of closed-loop identiication methods and parameterizations. A focus will be on asymptotic variance expressions for these methods and by studying the asymptotic variance for the parameter vector estimates we show that indirect methods fail to give better accuracy than the direct method.

Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown nuisance parameter. We establish an asymptotic approximation to the nonparametric regression experiment when the value of the variance is an additional paramete...

This paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms. Based on the …xed-bandwidth asymptotic variance and the pre-asymptotic variance, we propose a heteroskedasticity and autocorrelation robust (HAR) variance estimator that achieves double robustness — it is asymptotically valid regardless of whether the temporal ...

In this paper we derive asymptotic tests for general linear hypotheses on variance components using repeated variance components models In two examples the two way nested classi cation model and the two way crossed classi cation model with interaction we explicitly investigate the properties of the asymptotic tests in small sample sizes

Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown nuisance parameter. We establish an asymptotic approximation to the nonparametric regression experiment when the value of the variance is an additional paramete...

We consider the asymptotic variance of the departure counting processD(t) of the GI/G/1 queue;D(t) denotes the number of departures up to time t. We focus on the case that the system load % equals 1, and prove that the asymptotic variance rate satisfies lim t→∞ VarD(t) t = λ ( 1− 2 π )( ca + c 2 s ) , where λ is the arrival rate and ca, cs are squared coefficients of variation of the inter-arri...

We present a new CuSum chart for monitoring shifts in the mean of autocorrelated data. The monitoring statistic is the plain cumulative sum of differences between the observations and the target value, and the control limits are a function of the asymptotic variance constant and target in-control average run length. Our method uses a variety of non-parametric techniques that are popular in the ...

Recently, Aumüller and Dietzfelbinger proposed a version of a dual-pivot quicksort, called “Count”, which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this note we provide further probabilistic analysis of “Count”. We derive an exact formula for the average number of swaps needed by “Count” as well as an asymptotic formula for the varia...

The asymptotic bias and variance are important deter minants of the quality of a simulation run In particu lar the asymptotic bias can be used to approximate the bias introduced by starting the collection of a measure in a particular state distribution and the asymptotic variance can be used to compute the simulation time re quired to obtain a statistically signi cant estimate of a measure Whil...

In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by Pitt and Shephard (1999a). Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we also derive bounds on the L p error and bias of the same for a finite particle sample size. By examining the recursive formula for the asymptotic variance o...