Modeling mortality with a Bayesian vector autoregression

Parametric mortality models capture the cross section of mortality rates. These models fit the older ages better, because of the more complex cross section of mortality at younger and middle ages. Dynamic parametric mortality models fit a time series to the parameters, such as a Vector-auto-regression (VAR), in order to capture trends and uncertainty in mortality improvements. We consider the full age range using the Heligman and Pollard (1980) model, a cross-sectional mortality model with parameters that capture specific features of different age ranges. We make the Heligman–Pollard model dynamic using a Bayesian Vector Autoregressive (BVAR) model for the parameters and compare with more commonly used VAR models. We fit the models using Australian data, a country with similar mortality experience to many developed countries. We show how the Bayesian Vector Autoregressive (BVAR) models improve forecast accuracy compared to VAR models and quantify parameter risk which is shown to be significant.     

On large deviation expansion of distribution of maximum likelihood estimator and its application in large sample estimation

For estimating an unknown parameter , the likelihood principle yields the maximum likelihood estimator. It is often favoured especially by the applied statistician, for its good properties in the large sample case. In this paper, a large deviation expansion for the distribution of the maximum likelihood estimator is obtained. The asymptotic expansion provides a useful tool to approximate the tail probability of the maximum likelihood estimator and to make statistical inference. Theoretical and numerical examples are given. Numerical results show that the large deviation approximation performs much better than the classical normal approximation.This work is supported in part by the Natural Science and Engineering Research Council of Canada under grant NSERC A-9216.This author is also partially supported by the National Science Foundation of China.     

Estimators for alternating nonlinear autoregression

Suppose we observe a time series that alternates between different nonlinear autoregressive processes. We give conditions under which the model is locally asymptotically normal, derive a characterization of efficient estimators for differentiable functionals of the model, and use it to construct efficient estimators for the autoregression parameters and the innovation distributions. Surprisingly, the estimators for the autoregression parameters can be improved if we know that the innovation densities are equal.     

Diffusion approximation for nonparametric autoregression

A nonparametric statistical model of small diffusion type is compared with its discretization by a stochastic Euler difference scheme. It is shown that the discrete and continuous models are asymptotically equivalent in the sense of Le Cam's deficiency distance for statistical experiments, when the discretization step decreases with the noise intensity ε. Received: 12 April 1996 / Revised version: 29 October 1997     

A large deviation principle for bootstrapped sample means

A large deviation principle for bootstrapped sample means is established. It relies on the Bolthausen large deviation principle for sums of i.i.d. Banach space valued random variables. The rate function of the large deviation principle for bootstrapped sample means is the same as the classical one.

     

Variance estimation for sample quantiles using them out ofn bootstrap

We consider the problem of estimating the variance of a sample quantile calculated from a random sample of sizen. Ther-th-order kernel-smoothed bootstrap estimator is known to yield an impressively small relative error of orderO(n ^−r/(2r+1) ). It nevertheless requires strong smoothness conditions on the underlying density function, and has a performance very sensitive to the precise choice of the bandwidth. The unsmoothed bootstrap has a poorer relative error of orderO(n ^−1/4), but works for less smooth density functions. We investigate a modified form of the bootstrap, known as them out ofn bootstrap, and show that it yields a relative error of order smaller thanO(n ^−1/4) under the same smoothness conditions required by the conventional unsmoothed bootstrap on the density function, provided that the bootstrap sample sizem is of an appropriate order. The estimator permits exact, simulation-free, computation and has accuracy fairly insensitive to the precise choice ofm. A simulation study is reported to provide empirical comparison of the various methods. Supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7131/00P).     

Optimal reparametrization and large sample likelihood inference for the location-scale skew-normal model

Motivated by results in Rotnitzky et al. (2000), a family of parametrizations of the location-scale skew-normal model is introduced, and it is shown that, under each member of this class, the hypothesis H ₀: ?? = 0 is invariant, where ?? is the asymmetry parameter. Using the trace of the inverse variance matrix associated to a generalized gradient as a selection index, a subclass of optimal parametrizations is identified, and it is proved that a slight variant of Azzalini??s centred parametrization is optimal. Next, via an arbitrary optimal parametrization, a simple derivation of the limit behavior of maximum likelihood estimators is given under H ₀, and the asymptotic distribution of the corresponding likelihood ratio statistic for this composite hypothesis is determined.     

Small sample statistical condition estimation for the total least squares problem

In this paper, under the genericity condition, we study the condition estimation of the total least squares (TLS) problem based on small sample condition estimation (SCE), which can be incorporated into the direct solver for the TLS problem via the singular value decomposition (SVD) of the augmented matrix [A, b]. Our proposed condition estimation algorithms are efficient for the small and medium size TLS problem because they utilize the computed SVD of [A, b] during the numerical solution to the TLS problem. Numerical examples illustrate the reliability of the algorithms. Both normwise and componentwise perturbations are considered. Moreover, structured condition estimations are investigated for the structured TLS problem.     

Probability density estimation with surrogate data and validation sample

The probability density estimation problem with surrogate data and validation sample is considered. A regression calibration kernel density estimator is defined to incorporate the information contained in both surrogate variates and validation sample. Also, we define two weighted estimators which have less asymptotic variances but have bigger biases than the regression calibration kernel density estimator. All the proposed estimators are proved to be asymptotically normal. And the asymptotic representations for the mean squared error and mean integrated square error of the proposed estimators are established, respectively. A simulation study is conducted to compare the finite sample behaviors of the proposed estimators.     

Spatial autoregression and related spatio-temporal models

We propose a spatial autoregressive random field of order p on the spatial domain for p?2 in this paper, whose univariate margins are the continuous-time autoregression of order p on the real line, and introduce a class of semiparametric spatio-temporal covariance models stationary in space with the spatial autoregressive margin.     

The empirical characteristic function and large sample hypothesis testing

The empirical characteristic function is considered as a tool for large sample testing of a hypothesis that can be characterized in terms of the characteristic function. Two test statistics based upon the empirical characteristic function are proposed. The limiting distributions of these test statistics are obtained and methods are suggested for using these limiting distributions to calculate critical regions.     

Modeling of induced anisotropy at large deformations for polymers

In this work we develop a model to describe the induced plasticity of polymers at large deformations. Polymers such as stretch films exhibit a pronounced strength in the loading direction. The undeformed state of the films is isotropic, whereas after the uni-axial loading the material becomes anisotropic. In order to consider this induced anisotropy during the stretch process, a spectral decomposition of the inelastic right CAUCHY-GREEN tensor is done. Therefore, the yield function can be formulated as a function of the anisotropic tensor, where again the anisotropic tensor is a function of the maximum eigenvalue. A backward EULER scheme is used for updating the evolution equations, and the algorithmic tangent operator is derived. The numerical implementation of the resulting set of constitutive equations is used in a finite element program and for parameter identification. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation

In this paper,we investigate the effective condition numbers for the generalized Sylvester equation(AX-YB,DX-YE)=(C,F),where A,D∈R m×m,B,E∈R n×n and C,F ∈ R m×n.We apply the small sample statistical method for the fast condition estimation of the generalized Sylvester equation,which requires O(m2n+mn2) flops,comparing with O(m3+n3) flops for the generalized Schur and generalized HessenbergSchur methods for solving the generalized Sylvester equation.Numerical examples illustrate the sharpness of our perturbation bounds.     

非线性自回归序列L1估计的渐近分布

由于时间序列数据中经常出现的厚尾特征使得通常的估计方法不再具有渐近的正态分布,在误差项二阶矩有限的条件下考虑了非线性自回归序列的L_1估计.采用局部线性近似的方法得到了具有凸样本路径的随机过程,在此基础上利用凸样本路径随机过程弱收敛的性质证明了非线性自回归序列L_1估计的渐近正态性及无偏性.     

Modeling and simulation of metabolic networks for estimation of biomass accumulation parameters

Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled such as flux-balance analysis that considers the steady state nature of the cell. However, it is important to consider the dynamic behavior of a cell since the environmental conditions change continuously. Sometimes due to the critical changes in the environment some of the reactions exhibit completely different behavior leading to discrete changes in the metabolic network. Therefore, a cell exhibits discrete-continuous behavior in continuous time. Since hybrid systems exhibit the same characteristics modeling a cell as a hybrid system gives an accurate representation. The aim of this paper is to develop a simulation framework to model the evolving structure of the cell metabolism under changes in the environment. The metabolic responses that cell gives, against multiple changes in the environment are not fully understood. Therefore, in this study, a cell is modeled as a hybrid system that is composed of a system of differential and algebraic equations. The changes in the concentration of metabolites in the environment are represented by Ordinary Differential Equations and the intracellular cell metabolism is represented by a set of algebraic equations. To understand the feedback relationship between intracellular and extracellular changes, the system is solved considering the effects of extracellular stresses on the metabolic responses.     

Asymptotic results for polygonal processes related to an autoregression

We establish functional central limit theorems for polygonal process constructed from consecutive estimators of a simple AR(1) model. We consider both stationary and unit root cases. The results are applied to change segment analysis.     

Strong law of large numbers for the middle part of a sample

Let {X_n} _n=1 be a sequence of independent, symmetric random variables and let {X_in} _i=1 ⁿ be the absolute order statistics. The rate of growth of and X_2,n is investigated for n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 166, pp. 25–31, 1988.     

Eigenvectors of some large sample covariance matrix ensembles

We consider sample covariance matrices ${S_N=\frac{1}{p}\Sigma_N^{1/2}X_NX_N^* \Sigma_N^{1/2}}$ where X _N is a N ×? p real or complex matrix with i.i.d. entries with finite 12th moment and ?? _N is a N ×? N positive definite matrix. In addition we assume that the spectral measure of ?? _N almost surely converges to some limiting probability distribution as N ?? ?? and p/N ?? ?? >?0. We quantify the relationship between sample and population eigenvectors by studying the asymptotics of functionals of the type ${\frac{1}{N}\text{Tr} ( g(\Sigma_N) (S_N-zI)^{-1}),}$ where I is the identity matrix, g is a bounded function and z is a complex number. This is then used to compute the asymptotically optimal bias correction for sample eigenvalues, paving the way for a new generation of improved estimators of the covariance matrix and its inverse.     

Some large sample results for a class of functionals of Kaplan-Meier estimator

In this paper, a class of functionals of Kaplan-Meier estimator is investigated. Counting process martingale methods are used to show the asymptotic normality, and we establish a mean square error inequality and a probability inequality of them without the assumption thatF, G are continuous, where,F, G are survival time distribution and censoring time distribution respectively. This project is supported by China Postdoctoral Science Foundation