Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Measurement scheduling for recursive team estimation

We consider a decentralized LQG measurement scheduling problem in which every measurement is costly, no communication between observers is permitted, and the observers' estimation errors are coupled quadratically. This setup, motivated by considerations from organization theory, models measurement scheduling problems in which cost, bandwidth, or security constraints necessitate that estimates be decentralized, although their errors are coupled. We show that, unlike the centralized case, in the decentralized case the problem of optimizing the time integral of the measurement cost and the quadratic estimation error is fundamentally stochastic, and we characterize the -optimal open-loop schedules as chattering solutions of a deterministic Lagrange optimal control problem. Using a numerical example, we describe also how this deterministic optimal control problem can be solved by nonlinear programming.This research was supported in part by ARPA Grant N00174-91-C-0116 and NSF Grant NCR-92-04419.     

A note on smoothed estimating functions

The kernel estimate of regression function in likelihood based models has been studied in Staniswalis (1989,J. Amer. Statist. Assoc.,84, 276–283). The notion of optimal estimation for the nonparametric kernel estimation of semimartingale intensity (t) is proposed. The goal is to arrive at a nonparametric estimate of ₀=(t ₀) for a fixed pointt ₀ [0, 1]. We consider the estimator that is a solution of the smoothed optimal estimating equation is the optimal estimating function as in Thavaneswaran and Thompson (1986,J. Appl. Probab.,23, 409–417).     

AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

Reflection of electrons and photons from solids bombarded by 0.1 - to 100-MeV electrons

Electron and photon reflection ratios (in number and energy) for absorbers bombarded by electrons have been computed with the ITS Monte Carlo system version 3. Electrons of energies from 0.1 to 100 MeV have been assumed normally incident on an effectively semi-infinite absorber. The absorbers considered are elemental solids of atomic numbers from 4 to 92. The data on the electron reflection ratios agree rather well with the experimental data collected from literature except some discrepancies when the number-reflection ratio is small. For photons, the number-reflection ratio increases with increasing energy, but the energy-reflection ratio shows a maximum around 10 MeV. Empirical equations for the electron reflection ratios and the photon energy-reflection ratio are given (for electrons, graphs only).     

Closer asymptotic approximations for the distributions of the power divergence goodness-of-fit statistics

Summary The members of the power divergence family of statistics all have an asymptotically equivalent χ² distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX ² statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated) expansions.     

A group additivity approach for the estimation of heat capacities of organic liquids and solids at 298 K

A group additivity method is described which provides heat capacity estimates of the condensed phase. The data base consists of 810 liquids and 446 solids. Group values for carbon in various common substitution and hybridization states and for 47 functional groups are provided. The standard error of estimation using this approach on this data base is 19.5 (liquids) and 26.9 J/ (mole K) (solids). This can be compared to typical experimental uncertainties of 8.12 and 23,4 J/ (mole K) associated with these measurements, respectively. Experimental uncertainties were estimated from the numerical differences obtained for a given substance from multiple independent literature reports.     

农残水平测试中数据多态性分析及指定值估计研究

对全国农残水平测试中毒死蜱、氯氰菊酯数据进行统计分析,在数据统计分布特征研究基础上,使用内核密度估计进行数据多态性分析,使用bootstrap模拟取样法对数据样本值重复取样,以获得稳健的水平测试样品待测物含量代表值估计、标准误差及置信区间描述,证明以bootstrap模拟取样法获取的均值与标准偏差作为有限单次样本代表值是合理、有效的,解决了四分位稳健统计方法对非正态多态分布代表值估计不稳定问题及取样理论中取样样本数限制的瓶颈,为能力验证计划指定值的获取提供了一种新方法。     

Evaluation of tocopherol recovery through simulation of molecular distillation process

DISMOL simulator was used to determine the best possible operating conditions to guide, in future studies, experimental works. This simulator needs several physical-chemical properties and often it is very difficult to determine them because of the complexity of the involved components. Their determinations must be made through correlations and/or predictions, in order to characterize the system and calculate it. The first try is to have simulation results of a system that later can be validated with experimental data. To implement, in the simulator, the necessary parameters of complex systems is a difficult task. In this work, we aimed to determe these properties in order to evaluate the tocopherol (vitamin E) recovery using a DISMOL simulator. The raw material used was the crude deodorizer distillate of soya oil. With this procedure, it is possible to determine the best operating conditions for experimental works and to evaluated the process in the separation of new systems, analyzing the profiles obtained from these simulations for the falling film molecular distillator.