A Note on the Estimation of Semiparametric Two-Sample Density Ratio Models

In this paper,a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation.A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function.Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution.So we can obtain the maximum empirical likelihood estimation (MELE) of parameters.Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm.     

半参数两样本密度比率模型估计问题的一点注记

In this paper,a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation.A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function.Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution.So we can obtain the maximum empirical likelihood estimation (MELE) of parameters.Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm.     

Parametric estimation of discretely sampled Gamma-OU processes

The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.     

Zero-inflated non-central negative binomial distribution

In this article, the zero-inflated non-central negative binomial(ZINNB) distribution is introduced. Some of its basic properties are obtained. In addition, we use the maximum likelihood estimation method to estimate the parameters of the ZINNB distribution, and illustrate its application by fitting the actual data sets.     

交替迭代最大似然估计量的偏倚校正

In this paper, we give a definition of the alternating iterative maximum likelihood estimator (AIMLE) which is a biased estimator. Furthermore we adjust the AIMLE to result in asymptotically unbiased and consistent estimators by using a bootstrap iterative bias correction method as in Kuk (1995). Two examples and simulation results reported illustrate the performance of the bias correction for AIMLE.     

Empirical likelihood estimation of discretely sampled processes of OU type

This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter c...     

Bayesian estimation for generalized exponential distribution based on progressive type-I interval censoring

In this study, we consider the Bayesian estimation of unknown parameters and reliability function of the generalized exponential distribution based on progressive type-I interval censoring. The Bayesian estimates of parameters and reliability function cannot be obtained as explicit forms by applying squared error loss and Linex loss functions, respectively; thus, we present the Lindley’s approximation to discuss these estimations. Then, the Bayesian estimates are compared with the maximum likelihood estimates by using the Monte Carlo simulations.     

Parameter Estimations in BurrⅫ Model Using Masked Data

We consider a series system of two independent and non-identical components which have different BurrⅫ distributed lifetime.The maximum likelihood and Bayes estimators of the parameters of the system＇s components are obtained based on masked system life test data.The conclusion is that the Bayes estimates are better than the maximum likelihood estimates in the sense of having smaller mean squared errors.     

Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding

Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding. The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored. In this article, we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models. The proposed method allows th...     

Binomial proportion estimation in longitudinal data with non-ignorable non-response

Non-random missing data poses serious problems in longitudinal studies. The binomial distribution parameter becomes to be unidentifiable without any other auxiliary information or assumption when it suffers from ignorable missing data. Existing methods are mostly based on the log-linear regression model. In this article, a model is proposed for longitudinal data with non-ignorable non-response. It is considered to use the pre-test baseline data to improve the identifiability of the post-test parameter. Furthermore, we derive the identified estimation (IE), the maximum likelihood estimation (MLE) and its associated variance for the post-test parameter. The simulation study based on the model of this paper shows that the proposed approach gives promising results.     

Statistical Inference for the Parameter of Pareto Distribution Based on Progressively Typ e-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively typeI interval censored sample from a Pareto distribution is studied. Different methods of estimation are discussed, which include mid-point approximation estimator, the maximum likelihood estimator and moment estimator. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.     

同时序约束下保序正态均值的均方损失

For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.     

Quantile Regression for Thinning-based INAR(1) Models of Time Series of Counts

In this paper,we develop the quantile regression(QR)estimation for the first-order integer-valued autoregressive(INAR(1))models by defining the smoothing INAR(1)process.Jittering method is used to derive the QR estimators for the autoregressive coefficient and the quantile of innovations.The consistency and asymptotic normality of the proposed estimators are established.The performances of the proposed estimation procedures are evaluated by Monte Carlo simulations.The results show that the proposed procedures perform well for simulations and a real data application.     

Empirical entropy for right censored data

The maximum entropy method has been widely used in many fields, such as statistical mechanics,economics, etc. Its crucial idea is that when we make inference based on partial information, we must use the distribution with maximum entropy subject to whatever is known. In this paper, we investigate the empirical entropy method for right censored data and use simulation to compare the empirical entropy method with the empirical likelihood method. Simulations indicate that the empirical entropy method gives better coverage probability than that of the empirical likelihood method for contaminated and censored lifetime data.     

序约束下AR(p)-ARCH(q)模型参数的估计与检验

In this paper, we study a stationary AR(p)-ARCH(q) model with parameter vectors a and β. We propose a method for computing the maximum likelihood estimator (MLE) of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order: α1≥α2≥…≥αq, andβ1≥β2≥…βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio (LR) test statistic for the testing problem and derive its asymptotic null distribution.     

CONSISTENCY OF MLE OF THE PARAMETER OF EXPONENTIAL LIFETIME DISTRIBUTION FOR RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator (MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.     

独立Poisson分布的均值之MLE的改进

In this paper, we consider the simultaneous estimation of the parameters (means) of the independent Poisson distribution by using the following loss functions: L0(θ,T)=∑i=1^n(Ti-θi)^2,L1(θ,T)=∑i=1^n(Ti-θi)^2/θi We develop an estimator which is better than the maximum likelihood estimator X simultaneously under L0(θ, T) and L1(θ, T). Our estimator possesses substantially smaller risk than the usual estimator X to estimate the parameters (means) of the independent Poisson distribution.     

PROXIMAL POINT ALGORITHM FOR MINIMIZATION OF DC FUNCTION

In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the ε-subdifferentiM and the ε-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.     

SPECTRAL METHOD FOR ZAKHAROV EQUATION WITH PERIODIC BOUNDARY CONDITIONS

This paper describes the spectral method for numerically solving Zakharov equation with periodicboundary conditions. This method is spectral method for spatial variable and difference method fortime variable. We make error estimation of approximate solution and prove the convergence of spectralmethod. We had given the convergence rate. Also, we prove the stability of approximate method forinitial values.