Unbiastld estimation of parametric functions in sampling from two two-truncation parameter families

We consider the problem of UMVU estimation of a U-estimable function of four unknown truncation parameters based on two independent random samples from two two-truncation parameter families. In particular, we obtain the UMVU estimator of functional, P (Y > X). Also the confidence intervals for some parametric functions are obtained.     

Asymptotic distribution of regression type estimators of parameters of stable laws

Asymptotic distributions of regression-type estimators for the parameters of stable distributions am obtained. The asymptotic normalized standard deviations of the estimators are computed for various values of the parameters and various choices of the number of points used in getting the regression estimates.     

Bandwidth selection for local linear regression smoothers

Summary. The paper presents a general strategy for selecting the bandwidth of nonparametric regression estimators and specializes it to local linear regression smoothers. The procedure requires the sample to be divided into a training sample and a testing sample. Using the training sample we first compute a family of regression smoothers indexed by their bandwidths. Next we select the bandwidth by minimizing the empirical quadratic prediction error on the testing sample. The resulting bandwidth satisfies a finite sample oracle inequality which holds for all bounded regression functions. This permits asymptotically optimal estimation for nearly any regression function. The practical performance of the method is illustrated by a simulation study which shows good finite sample behaviour of our method compared with other bandwidth selection procedures.     

光盘扫描高斯光束的研究

讨论了扫描光束对高斯参数扫描光点强度分布的影响；给出了高斯参数与中心峰值强度及光点直径的定量关系；展示出焦平面上的三维光强分布图；提出了光盘存贮中高斯参数的选择依据；有效利用无能，获得高性能扫描光点。     

A weighted polynomial regression method for local fitting of spatial data

Typically, parametric approaches to spatial problems require restrictive assumptions. On the other hand, in a wide variety of practical situations nonparametric bivariate smoothing techniques has been shown to be successfully employable for estimating small or large scale regularity factors, or even the signal content of spatial data taken as a whole.We propose a weighted local polynomial regression smoother suitable for fitting of spatial data. To account for spatial variability, we both insert a spatial contiguity index in the standard formulation, and construct a spatial-adaptive bandwidth selection rule. Our bandwidth selector depends on the Gearys local indicator of spatial association. As illustrative example, we provide a brief Monte Carlo study case on equally spaced data, the performances of our smoother and the standard polynomial regression procedure are compared.This note, though it is the result of a close collaboration, was specifically elaborated as follows: paragraphs 1 and 2 by T. Sclocco and the remainder by M. Di Marzio. The authors are grateful to the referees for constructive comments and suggestions.     

Sequential experimental design and response optimisation

We consider the situation where one wants to maximise a functionf(θ,x) with respect tox, with θ unknown and estimated from observationsy _k . This may correspond to the case of a regression model, where one observesy _k =f(θ,x _k )+ε _k , with ε _k some random error, or to the Bernoulli case wherey _k ∈{0, 1}, with Pr[y _k =1|θ,x _k |=f(θ,x _k ). Special attention is given to sequences given by , with an estimated value of θ obtained from (x₁, y₁),...,(x _k ,y _k ) andd _k (x) a penalty for poor estimation. Approximately optimal rules are suggested in the linear regression case with a finite horizon, where one wants to maximize ∑ _i=1 ^N w _i f(θ, x _i ) with {w _i } a weighting sequence. Various examples are presented, with a comparison with a Polya urn design and an up-and-down method for a binary response problem.     

A study on cyclic bandwidth sum

Suppose G is a graph of p vertices. A proper labeling f of G is a one-to-one mapping f:V(G)→{1,2,…,p}. The cyclic bandwidth sum of G with respect to f is defined by CBS _f (G)=∑ _uv∈E(G)|f(v)−f(u)| _p , where |x| _p =min {|x|,p−|x|}. The cyclic bandwidth sum of G is defined by CBS(G)=min {CBS _f (G): f is a proper labeling of G}. The bandwidth sum of G with respect to f is defined by BS _f (G)=∑ _uv∈E(G)|f(v)−f(u)|. The bandwidth sum of G is defined by BS(G)=min {BS _f (G): f is a proper labeling of G}. In this paper, we give a necessary and sufficient condition for BS(G)=CBS(G), and use this to show that BS(T)=CBS(T) when T is a tree. We also find cyclic bandwidth sums of complete bipartite graphs. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. Supported in part by the National Science Council under grants NSC91-2115-M-156-001.     

Quantile plots for mean effects in the presence of variance effects for 2k-p designs

In robust parameter design, variance effects and mean effects in a factorial experiment are modelled simultaneously. If variance effects are present in a model, correlations are induced among the naive estimators of the mean effects. A simple normal quantile plot of the mean effects may be misleading because the mean effects are no longer iid under the null hypothesis that they are zero. Adjusted quantiles are computed for the case when one variance effect is significant and examples of 8-run and 16-run fractional factorial designs are examined in detail. We find that the usual normal quantiles are similar to adjusted quantiles for all but the largest and smallest ordered effects for which they are conservative. Graphically, the qualitative difference between the two sets of quantiles is negligible (even in the presence of large variance effects) and we conclude that normal probability plots are robust in the presence of variance effects.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.     

Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths

We obtain the rates of pointwise and uniform convergence of multivariate kernel density estimators using a random bandwidth vector obtained by some data-based algorithm. We are able to obtain faster rate for pointwise convergence. The uniform convergence rate is obtained under some moment condition on the marginal distribution. The rates are obtained under i.i.d. and strongly mixing type dependence assumptions.