Quadratic prediction and quadratic sufficiency in finite populations

The problem of quadratic prediction for population quadratic quantities in finite populations has been considered in the literature. In this paper, we mainly aim at extending the ordinary quadratic prediction problems to a general case, and derive the representations of the two essentially unique optimal predictors: one is an optimal invariant quadratic unbiased predictor, and the other is an optimal invariant quadratic (potentially) biased predictor. Further, we show that the two predictors are nonnegative and reasonable by considering an extreme situation, and apply resulting conclusions to a special model with a compound symmetric variance matrix. In addition, we propose a notion of quadratic sufficiency with regard to the optimal prediction problems by employing materials derived in the first part, and investigate corresponding characterizations in detail.     

Moderate deviations for finite population student's statistic

In this paper, moderate deviations for finite population are given under weaker conditions. As by-products, some exponential inequalities for finite population are also established.     

A numerical method for nonlinear age-structured population models with finite maximum age

We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin-MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.     

任意秩有限总体中无偏预测和估计的构造关系

研究了有限总体均值向量的无偏估计和线性可预测变量的无偏预测之间的关系,利用分块矩阵广义逆直接对加权风险函数进行分解,提出了一种由均值向量的无偏估计来构造无偏预测的新方法,并找到了它们之间的构造关系.特别地,线性可预测变量的最优线性无偏预测(BLUP)可由均值向量的最佳线性无偏估计(BLUE)惟一地表示(有关惟一性在几乎处处意义下理解).     

Prediction of diameter errors in bar turning: a computationally effective model

Machining accuracy can be considerably affected by the deflections of the machine–workpiece–tool system as well as the thermal expansion of material during machining. An improved model for predicting dimensional errors in turning process is presented. This model uses a geometric analysis in the machine frame, in which the elastic deflections of the machine–workpiece–tool system due to the cutting force are studied. In this paper, our workpiece deflection model [A.-V. Phan, G. Cloutier, J.R.R. Mayer, International Journal of Production Research 37 (1999) 4039–4051; G. Cloutier, J.R.R. Mayer, A.-V. Phan, Computer Modeling and Simulation in Engineering 4 (1999) 133–137] earlier developed is employed. As described in Phan et al. (1999), this deflection model is general, accurate and computationally effective thanks to its closed-form solutions derived from the finite element technique. Also, due to the coupling between the cutting force and actual depth of cut, iterative computations are performed to obtain the coupling value of this force which provides further accuracy to the prediction. Finally, via numerical examples, the predicted diameter error on a workpiece, the ratio between the coupled cutting force and its nominal value along the part axis as well as the influence of the cutting force components on the error prediction are computed using the proposed model. The results provide additional insight into the error formation in the turning process.     

On the distribution of sample mean in finite populations. I

We obtain Bergström-type [2] asymptotic expansions for sample mean in finite population [8]. Analogues of the Cornish-Fisher transformation are obtained in the cases of limit distributions from class $\mathcal{L}$ and distributions of sums of independent identically distributed random variables (in [2], the Bergström equality is used).     

A predictive estimator of finite population mean using nonparametric regression

The paper considers the problem of estimating the population mean using auxiliary information. We propose a new model-based estimator of the population mean, based on local polynomial regression. This estimator exhibits several attractive properties under the model-based approach. The estimator is compared to a number of methods which have been proposed in the literature via a simulation study based on several populations.     

Local a posteriori estimates for pointwise gradient errors in finite element methods for elliptic problems

We prove local a posteriori error estimates for pointwise gradient errors in finite element methods for a second-order linear elliptic model problem. First we split the local gradient error into a computable local residual term and a weaker global norm of the finite element error (the ``pollution term'). Using a mesh-dependent weight, the residual term is bounded in a sharply localized fashion. In specific situations the pollution term may also be bounded by computable residual estimators. On nonconvex polygonal and polyhedral domains in two and three space dimensions, we may choose estimators for the pollution term which do not employ specific knowledge of corner singularities and which are valid on domains with cracks. The finite element mesh is only required to be simplicial and shape-regular, so that highly graded and unstructured meshes are allowed.

     

On interactive chains with finite populations

An Interactive Markov Chain is a population process in which each individuals's transitions depend on the population's distribution over the various states. We investigate a certain aspect of such process’ dynamics for a fixed population size. Conditions for convergence to steady‐state regardless of population size are provided.     

Sojourn times with finite time-horizon in finite semi-markov processes

Let Y = {Y_t:t ≥ 0} be a semi-Markov process with finite state space S. Assume that Y is either irreducible and S is then partitioned into two classes A and B, or, that Y is absorbing and S is partitioned into A, B and C, where C is the set of all absorbing states of Y. Denote by T_{A, m}(t) the mth sojourn time of Y in A during [0, t]. T_{A, m}(t) is thus defined as the duration in [0, t] of the mth visit of Y to A if A is visited by Y during [0, t] at least m times; T_{A, m}(t) = 0 otherwise. We derive a recurrence relation for the vectors of double Laplace transforms g_m**(T₁,T₂) = {g_m**(T₁, T₂;S):sSC}, m = 1,2,… which are defined by with T₁, T₂, Re(T₁), Re(T₂) > 0. This result is then applied to alternating renewal processes. Symbolic Laplace transform inversion with MAPLE is used to obtain the first two moments of T_{A, m}(t). The assumed holding time distributions are exponential and Erlang respectively. This paper is a continuation of some of the author's recent work on the distribution theory of sojourn times in a subset of the finite state space of a (semi-)Markov process where the time horizon t = + ∞. The practical importance of considering a finite time horizon for semi-Markov reliability models has been discussed recently by Jack (1991), Jack and Dagpunar (1992), and Christer and Jack (1991).     

On finite groups with non-subnormal subgroups

For a finite group G, let n(G) denote the number of conjugacy classes of non-subnormal subgroups of G. In this paper, we show that a finite group G satisfying n(G)≤2|π(G)| is solvable, and for a finite non-solvable group G, n(G) = 2|π(G)|+1 if and only if G?A₅.     

Measurement errors in multivariate measurement scales

Our aim is to construct a general measurement framework for analyzing the effects of measurement errors in multivariate measurement scales. We define a measurement model, which forms the core of the framework. The measurement scales in turn are often produced by methods of multivariate statistical analysis. As a central element of the framework, we introduce a new, general method of estimating the reliability of measurement scales. It is more appropriate than the classical procedures, especially in the context of multivariate analyses. The framework provides methods for various topics related to the quality of measurement, such as assessing the structural validity of the measurement model, estimating the standard errors of measurement, and correcting the predictive validity of a measurement scale for attenuation. A proper estimate of reliability is a requisite in each task. We illustrate the idea of the measurement framework with an example based on real data.     

Prediction of the dynamic response of a mini-cantilever beam partially submerged in viscous media using finite element method

In this work, the use of mini cantilever beams for characterization of rheological properties of viscous materials is demonstrated. The dynamic response of a mini cantilever beam partially submerged in air and water is measured experimentally using a duel channel PolyTec scanning vibrometer. The changes in dynamic response of the beam such as resonant frequency, and frequency amplitude are compared as functions of the rheological properties (density and viscosity) of fluid media. Next, finite element analysis (FEA) method is adopted to predict the dynamic response of the same cantilever beam. The numerical prediction is then compared with experimental results already performed to validate the FEA modeling scheme. Once the model is validated, further numerical analysis was conducted to investigate the variation in vibration response with changing fluid properties. Results obtained from this parametric study can be used to measure the rheological properties of any unknown viscous fluid.     

Dedekind sums with a parameter in finite fields

We first introduce the multiple Dedekind–Rademacher sum with a parameter in finite fields and establish its reciprocity law. We then construct an analog of the higher-dimensional Apostol–Dedekind sums, and establish their reciprocity laws using the parameterized Dedekind sum.     

Bayesian linear prediction in finite populations

In this paper, Bayesian linear prediction of the total of a finite population is considered in situations where the observation error variance is parameter dependent. Connections with least squares prediction (Royall (1976, J. Amer. Statist. Assoc., 71, 657–664)) in mixed linear models (Theil (1971, Principles of Econometrics, Wiley, New York)), are established. Extensions to the case of dynamic (state dependent) superpopulation models are also proposed.     

On finite capacity queues with time dependent arrival rates

We consider the finite capacity M/M/1−K$M/M/1-K$ queue with a time dependent arrival rate λ(t)$\lambda \left(t\right)$. Assuming that the capacity K$K$ is large and that the arrival rate varies slowly with time (as t/K$t/K$), we construct asymptotic approximations to the probability of finding n$n$ customers in the system at time t$t$, as well as the mean number. We consider various time ranges, where the system is nearly empty, nearly full, or is filled to a fraction of its capacity. Extensive numerical studies are used to back up the asymptotic analysis.     

A cyclic-service finite source model with round-robin scheduling

A cyclic-service finite source model with round-robin scheduling is considered. A single server scans sources in a cyclic manner whether there is a request or not. Each request consists of multiple tasks and only one task can be served when the server scans. We provide the exact analysis of the average response time in a heterogeneous finite source model, where the service times of tasks are distributed according to general probability distributions which may be different from one source to another. Further, we derive the Laplace-Stieltjes transform of the probability distribution function of the waiting time.     

Partial linear single index models with distortion measurement errors

We study partial linear single index models when the response and the covariates in the parametric part are measured with errors and distorted by unknown functions of commonly observable confounding variables, and propose a semiparametric covariate-adjusted estimation procedure. We apply the minimum average variance estimation method to estimate the parameters of interest. This is different from all existing covariate-adjusted methods in the literature. Asymptotic properties of the proposed estimators are established. Moreover, we also study variable selection by adopting the coordinate-independent sparse estimation to select all relevant but distorted covariates in the parametric part. We show that the resulting sparse estimators can exclude all irrelevant covariates with probability approaching one. A simulation study is conducted to evaluate the performance of the proposed methods and a real data set is analyzed for illustration.