Local asymptotic normality for long-memory process with strong mixing noises

Abstract

We will establish the local asymptotic normality (LAN) for fractional autoregressive long memory model in the case of strong mixing noises. This opens the way in future work to construct an adaptive estimator and construct optimal tests for the parameters. To check the feasibility and validity of our theoretical results a simulations study is considered.     

Prediction intervals for farima processes by bootstrap methods

In this paper we introduce a procedure to compute prediction intervals for FARIMA (p d q) processes, taking into account the variability due to model identification and parameter estimation. To this aim, a particular bootstrap technique is developed. The performance of the prediction intervals is then assessed and compared to that of stand­ard bootstrap percentile intervals. The methods are applied to the time series of Nile River annual minima.     

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

ABSTRACT

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.     

Cramér Asymptotic Efficiency in a Semiparametric Model

This article is concerned with efficient estimation in a semiparametric model. We consider pseudo maximum likelihood estimation and prove that the proposed estimator is asymptotically efficient in the sense of Cramér; that is, the estimator has the smallest mean squared error.     

Least squares estimation of varying‐coefficient hazard regression with application to breast cancer dose‐intensity data

To enhance modeling flexibility, the authors propose a nonparametric hazard regression model, for which the ordinary and weighted least squares estimation and inference procedures are studied. The proposed model does not assume any parametric specifications on the covariate effects, which is suitable for exploring the nonlinear interactions between covariates, time and some exposure variable. The authors propose the local ordinary and weighted least squares estimators for the varying‐coefficient functions and establish the corresponding asymptotic normality properties. Simulation studies are conducted to empirically examine the finite‐sample performance of the new methods, and a real data example from a recent breast cancer study is used as an illustration. The Canadian Journal of Statistics 37: 659–674; 2009 © 2009 Statistical Society of Canada     

Analysis of Deviance for Hypothesis Testing in Generalized Partially Linear Models

In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance, which admit an additivity property that reduces to analysis of variance decompositions in the Gaussian case. Chi-square tests based on integrated likelihood functions are proposed to formally test whether the nonparametric term is significant. Simulation results are shown to illustrate the proposed chi-square tests and to compare them with an existing procedure based on penalized splines. The methodology is applied to German Bundesbank Federal Reserve data.     

A Polynomial Optimization Approach to Principal–Agent Problems

This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first‐order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.     

The Effects of Multitasking on Operations Scheduling

This study considers a typical scheduling environment that is influenced by the behavioral phenomenon of multitasking. Under multitasking, the processing of a selected job suffers from interruption by other jobs that are available but unfinished. This situation arises in a wide variety of applications; for example, administration, manufacturing, and process and project management. Several classical solution methods for scheduling problems no longer apply in the presence of multitasking. The solvability of any scheduling problem under multitasking is no easier than that of the corresponding classical problem. We develop optimal algorithms for some fundamental and practical single machine scheduling problems with multitasking. For other problems, we show that they are computationally intractable, even though in some cases the corresponding problem in classical scheduling is efficiently solvable. We also study the cost increase and value gained due to multitasking. This analysis informs companies about how much it would be worthwhile to invest in measures to reduce or encourage multitasking.     

一类含有随机参数的混沌系统的Hopf分岔研究

文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.     

The k-factor GARMA Process with Infinite Variance Innovations

In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. (2008 Diongue, A.K., Guégan, D. (2008). Estimation of k-Factor GIGARCH Process: A Monte Carlo Study. Communications in Statistics-Simulation and Computation 37:2037–2049.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Stationarity and invertibility conditions of this new model are derived. Conditional Sum of Squares (CSS) and Markov Chains Monte Carlo (MCMC) Whittle methods are investigated for parameter estimation. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques. Finally, the usefulness of the model is corroborated with the application to streamflow data for Senegal River at Bakel.