ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475266

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475267

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475268

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

An important measure of accuracy for problems of directing projectiles at targets is the circular error probable (CEP), a bivariate version of a 50% quantile point. This article presents a Bayesian procedure for estimating CEP when the projectile impact measurements are not iid, which is the case of usual practical interest. Our interest in a Bayesian procedure is motivated by a desire to combine accuracy information from several different sources. Except for the simplest problem settings, however, it is not possible to compute the standard Bayesian conditional mean estimate due to the associated computationally infeasible high-dimensional integrals. Thus we present an estimator that is closely related to the conditional mean (based on asymptotic theory and empirical experience) but is computationally feasible in all settings of practical interest. We demonstrate the procedure on a problem in missile accuracy analysis. The article also includes some comments on the potential application of several other Bayesian techniques—namely the Laplace and Gibbs sampling integration methods—in the CEP estimation problem, as well as some comments on how our technique could apply in certain other (i.e., non-CEP) high-dimensional estimation problems.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475269

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

We discuss procedures based on nonparametric regression for estimating the dominant Lyapunov Exponent λ1from time series data generated by a nonlinear autoregressive system with additive noise. For systems with bounded fluctuations, λ1> 0 is the defining feature of chaos. Thus our procedures can be used to examine time series data for evidence of chaotic dynamics. We show that a consistent estimator of the partial derivatives of the autoregression function can be used to obtain a consistent estimator of λ1. The rate of convergence we establish is quite slow; a better rate of convergence is derived heuristically and supported by simulations. Simulation results from several implementations—one “local” (thin-plate splines) and three “global” (neural nets, radial basis functions, and projection pursuit)—are presented for two deterministic chaotic systems. Local splines and neural nets yield accurate estimates of the Lyapunov exponent; however, the spline method is sensitive to the choice of the embedding dimension. Limited results for a noisy system suggest that the thin-plate spline and neural net regression methods also provide reliable values of the Lyapunov exponent in this case.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475270

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475271

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Restricted randomizations, similar to those in split-plot type experiments, often are adapted to assign quantitative treatment factors to experimental units. Such restrictions result in the experiment having a nested error structure. Sufficient conditions are presented under which ordinary least squares (OLS) estimates of regressor parameters are uniformly minimum variance unbiased (UMVU). If one designs experiments so that these conditions are satisfied, the analysis is straightforward and easy. When these conditions are not met, three different estimators of nested regressor parameters are suggested and compared.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475272

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

This article considers multivariate causal transfer function systems with latent stationary inputs and outputs. Their observation is assumed to be disturbed by errors in variables (EV). The main identification results for such models so far consist of structure theory. Derived are descriptions of classes of EV transfer function systems compatible with given covariance structures of the observed variables under various causality constraints. The case of unique determination is treated only for one-dimensional models. The article derives a great variety of conditions under which a multivariate EV transfer function system is uniquely determined by the second-order moments of the observed variables. For this purpose it considers a general model class of nonparametric systems and subclasses of systems with some parameterized components having fixed order parameters. If parametric, the transfer function is a rational matrix. Parametric inputs or errors follow vector autoregressive moving average (ARMA) processes. Subclasses of systems with specific time series structures described by certain relations of the order parameters are shown to be identifiable. Consider for instance a subclass with parametric inputsξtand input errorsvtfollowing block identifiable ARMA processes with autoregressive (AR) orderskξ,kvand moving average (MA) ordersnξ,nv. Transfer function and output errors are nonparametric or parametric. The subclass proves to be locally identifiable if kξ>nξorkv>nv, and (globally) identifiable ifkξ>nξandkv= 0 orkv>nvandkξ= 0. Analogous conditions are given for the case that the inputs and their errors have a more detailed AR and MA structure. By also considering subclasses of a restricted model class with diagonal covariance structure of the inputs, the results reveal the effect of contemporaneous correlation among the inputs on the state of identifiability.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475273

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The problem considered is that of predicting a linear combination of the fixed and random effects of a mixed-effects linear model. More generally, the problem considered is that of predicting an unobservable random variable from a set of observable random variables. The best linear-unbiased predictor depends on parameters which generally are unknown. Various exact or approximate expressions are given for the mean squared error (MSE) of the predictor obtained by replacing the unknown parameters with estimates. Several estimators of the MSE are investigated.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475274

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

It is commonly accepted that statistical modeling should follow the parsimony principle; namely, that simple models should be given priority whenever possible. But little quantitative knowledge is known concerning the amount of penalty (for complexity) regarded as allowable. We try to understand the parsimony principle in the context of model selection. In particular, the generalized final prediction error criterion is considered, and we argue that the penalty term should be chosen between 1.5 and 5 for most practical situations. Applying our results to the cross-validation criterion, we obtain insights into how the partition of data should be done. We also discuss the small sample performance of our methods.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475275

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor