Estimation of the intensity of a Poisson point process by means of nearest neighbor distances

A new unbiased consistent asymptotically normal estimator U _k of the intensity λ of a stationary multivariate Poisson point process is exhibited. This estimate is based on a combination of the j -th nearest neighbor (possibly non Euclidean) distances ( j =1, ..., k ) to a single fixed site x . A simple closed form containing logarithmic terms is obtained for E ( U ^l _k )(0< l < k ).     

Extending design-optimality from an initial model to augmented models

We consider an initial linear model E(Y)=B a and an augmented model E(Y)=B a+C b. We show that, if a design is optimal for estimating K a in the initial model, then there exists a matrix L such that this design is also optimal for estimating K a+L b in the augmented model. Received: December 1998     

On the construction of <Emphasis Type="Italic">E</Emphasis>(<Emphasis Type="Italic">s</Emphasis><Superscript>2</Superscript>)-optimal supersaturated designs

Supersaturated designs are an important class of factorial designs in which the number of factors is larger than the number of runs. These designs supply an economical method to perform and analyze industrial experiments. In this paper, we consider generalized Legendre pairs and their corresponding matrices to construct E(s ²)-optimal two-level supersaturated designs suitable for screening experiments. Also, we provide some general theorems which supply several infinite families of E(s ²)-optimal two-level supersaturated designs of various sizes.      

Efficiencies of Rounded Optimal Approximate Designs for Small Samples

Optimal exact designs are notoriously hard to study and only a few of them are known for polynomial models. Using recently obtained optimal exact designs (I mhof , 1997), we show that the efficiency of the frequently used rounded optimal approximate designs can be sensitive if the sample size is small. For some criteria, the efficiency of the rounded optimal approximate design can vary by as much as 25% when the sample size is changed by one unit. The paper also discusses lower efficiency bounds and shows that they are sometimes the best possible bounds for the rounded optimal approximate designs.     

Algorithms for optimal design with application to multiple polynomial regression

The approximate theory of optimal linear regression design leads to specific convex extremum problems for numerical solution. A conceptual algorithm is stated, whose concrete versions lead us from steepest descent type algorithms to improved gradient methods, and finally to second order methods with excellent convergence behaviour. Applications are given to symmetric multiple polynomial models of degree three or less, where invariance structures are utilized. A final section is devoted to the construction of efficientexact designs of sizeN from the optimal approximate designs. For the multifactor cubic model and some of the most popular optimality criteria (D-, A-, andI-criteria) fairly efficient exact designs are obtained, even for small sample sizeN. AMS Subject Classification: 62K05.Abbreviated Title: Algorithms for Optimal Design.Invited paper presented at the International Conference on Mathematical Statistics,ProbaStat '94, Smolenice, Slovakia.     

Agreement and consensus in a Q-mode research design: an empirical comparison of measures,and an application

Subject of this paper is the analysis of consensus within small groups of respondents, based on a proportionally large number of variables. The target group is researchers who are interested in Q-mode research. Measures of agreement are compared, and an application from a recent project is presented. Cohen’s κ is the preferable measure, Krippendorff’s α is an alternative, which is based on a different concept of expected disagreement. At group level, along with κ and α for multiple raters, additional measures are r _wg, intraclass correlation, and κ _SC. Predictions about level differences between groups can be assessed by a t-test and θ     

Optimality and efficiency of circular neighbor balanced designs for correlated observations

The purpose of this paper is to apply the Kunert and Martins (2000b) method for finding optimal designs into the case of dependence. Using this method we study optimality of circular neighbor balanced designs at distances 1 and 2 under the one-dimensional interference model with errors correlated according to a circular autoregressive process. We determine the efficiency of binary designs for specified values of correlation coefficient, for which these designs are not optimal.Research partially supported by the KBN Grant Number 5 P03A 041 21.     

重庆动物园笼舍生态丰容设计与实践

通过对重庆动物园涉禽馆、两爬馆、熊猫馆、金鱼馆等动物笼舍的生态化丰容改造,改善了动物圈养生存的环境质量,提高了其生殖率和适应性等生物学功能,增强了福利水平。是动物笼舍自然化、生态化发展做有益的探索。有助于动物的健康和繁殖,也为游客提供良好的视觉享受,提高展出与观赏效果。具有重要的推广应用价值。     

Distance optimality design criterion in linear models

Properties of the most familiar optimality criteria, for example A-, D- and E-optimality, are well known, but the distance optimality criterion has not drawn much attention to date. In this paper properties of the distance optimality criterion for the parameter vector of the classical linear model under normally distributed errors are investigated. DS-optimal designs are derived for first-order polynomial fit models. The matter of how the distance optimality criterion is related to traditional D- and E-optimality criteria is also addressed. Received: June 1999     

On some properties of the linear function Poisson binomial and negative binomial distributions

Summary A general model in fluctuations of sums of random variables leading, under certain assumptions, to each of the generalized and linear function Poisson, binomial and negative binomial distributions is presented. Moreover the generating functions and the factorial moments of the linear function Poisson, binomial and negative binomial distributions are obtained in close forms and certain distributional properties are discussed.     

Two ge neral classes of search designs for factor screening experiments with factors at three levels

In this paper, we are presenting general classes of factor screening designs for identifying a few important factors from a list of m (≥ 3) factors each at three levels. A design is a subset of 3^m possible runs. The problem of finding designs with small number of runs is considered here. A main effect plan requires at least (2m + 1) runs for estimating the general mean, linear and quadratic effects of m factors. An orthogonal main effect plan requires, in addition, the number of runs as a multiple of 9. For example, when m=5, a main effect plan requires at least 11 runs and an orthogonal main effect plan requires 18 runs. Two general factor screening designs presented here are nonorthogonal designs with (2m− 1) runs. These designs, called search designs permit us to search for and identify at most two important factors out of m factors under the search linear model introduced in Srivastava (1975). For example, when m=5, the two new plans given in this paper have 9 runs, which is a significant improvement over an orthogonal main effect plan with 18 runs in terms of the number of runs and an improvement over a main effect plan with at least 11 runs. We compare these designs, for 4≤m≤ 10, using arithmetic and geometric means of the determinants, traces, and maximum characteristic roots of certain matrices. Two designs D1 and D2 are identical for m=3 and this design is an optimal design in the class of all search designs under the six criteria discussed above. Designs D1 and D2 are also identical for m=4 under some row and column permutations. Consequently, D1 and D2 are equally good for searching and identifying one important factor out of m factors when m=4. The design D1 is marginally better than the design D2 for searching and identifying one important factor out of m factors when m=5, … , 10. The design D1 is marginally better than the D2 for searching and identifying two important factors out of m factors when m=5, 7, 9. The design D2 is somewhat better than the design D1 for m=6, 8. For m=10, D1 is marginally better than D2 w.r.t. the geometric mean and D2 is marginally better than D1 w.r.t. the arithmetic mean of the maximum characteristic roots.     

Analytic moments for GJR-GARCH (1, 1) processes

For a GJR-GARCH(1, 1) specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moments for the most commonly used GARCH models are stated as special cases. We also derive the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. A simulation study using these analytic moments produces approximate predictive distributions which are free from the bias affecting simulations. An empirical study using almost 30 years of daily equity index, exchange rate and interest rate data applies Johnson SU and Edgeworth expansion distribution fitting to our closed-form formulae for higher moments of returns.     

To sigmoid-based functional description of the volatility smile

We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied volatilities which demonstrate smile or skew. An arbitrage-free calibration algorithm is considered that constructs the implied volatility surface as a grid in the strike-expiration space and guarantees a lack of arbitrage at every node of this grid. We also demonstrate how to construct an arbitrage-free interpolation and extrapolation in time, as well as build a local volatility and implied pdf surfaces. Asymptotic behavior of this parameterization is discussed, as well as results on stability of the calibrated parameters are presented. Numerical examples show robustness of the proposed approach in building all these surfaces as well as demonstrate a better quality of the fit as compared with some known models.     

On randomization, modeling and experimental design: some remarks on a paper by De Vos

De Vos (1991) claims to have discovered a new example from agricultural field experimentation which shows that a simple robust spatial model may lead to inference and systematic experimental design that outperforms the inference from randomized experiments by far. In this reaction it is shown that: (1) the example is not new; (2) the gains in efficiency are exaggerated due to comparison with an inefficient randomization method; (3) the paper is over-optimistic with respect to robustness of model-based methods and throws unjustified doubts on the validity of randomization methods; (4) the choice between randomization methods and model-based methods depends on the relative importance attached to efficiency and validity.     

The Early History of the Cumulants and the Gram-Charlier Series

The early history of the Gram-Charlier series is discussed from three points of view: (1) a generalization of Laplace's central limit theorem, (2) a least squares approximation to a continuous function by means of Chebyshev-Hermite polynomials, (3) a generalization of Gauss's normal distribution to a system of skew distributions. Thiele defined the cumulants in terms of the moments, first by a recursion formula and later by an expansion of the logarithm of the moment generating function. He devised a differential operator which adjusts any cumulant to a desired value. His little known 1899 paper in Danish on the properties of the cumulants is translated into English in the Appendix.     

Lattices of capacities,and related topologies1

Capacities are defined as set functions with regularity properties in terms of two general families K and G of ‘inner’ and ‘outer’ sets (K = compact sets, G= open sets in the standard case). The space C of all such capacities is a complete lattice with respect to its natural partial order. The lattice structure of C is studied in combination with the natural topology of C. Also some subspaces are investigated.