响应变量随机缺失下的变系数部分线性模型的经验似然推断

本文考虑了响应变量随机缺失下的变系数部分线性模型的估计问题。利用经验似然方法,给出了参数部分的调整经验似然比函数,证明其渐近服从标准卡方分布。进而构造了参数部分的置信域,得到了其极大经验似然估计的最优参数收敛速度和渐近半参数有效界。模拟结果表明调整经验似然方法优于未调整的经验似然方法。     

利用ARMAX模型识别结构模态参数

由振动系统的运动方程建立了描述系统输入、输出和噪声特性的外源自回归滑动平均 (ARMAX)模型。采用近似极大似然法估计ARMAX模型系数 ,克服了传统极大似然估计方法的高度计算复杂性 ,需要对参数的初值进行猜测的缺点。仿真结果表明本文方法鲁棒性较好。     

带单个变点AR(1)模型的统计推断

变点时间序列一直是计量经济学、工程学和统计学的一个重要研究课题,在金融、气象和工业等领域有着广泛的应用。研究了带单个变点一阶自回归(AR(1))模型的统计推断问题。基于极大似然(或拟似然)方法,针对带单个变点AR(1)模型给出了参数估计表达式及自相关系数估计的一致性条件,同时得到了该条件下自相关系数极大似然(或拟似然)估计的渐近分布,并依此讨论了模型是否存在变点的假设检验及自相关系数变化增量的假设检验问题。最后通过数值模拟和上证综合指数日交易量的实证分析说明了所提理论和方法的有效性。     

余重对数二元模型的似然及惩罚似然估计

对３种抽样方式讨论了余重对数二元回归概率模型的极大似然估计和极大惩罚似然估计。并对数据及模型作了进一步的推广。     

误差方差不等的变量含误差直线回归模型──参数的驻点似然估计及强相合性

本文讨论了含有一个自变量且自变量误差方差与因变量误差方差不等的变量合误差线性回归模型。由于对这种模型最大似然估计失去作用，文中提出了一种新的估计方法──驻点似然估计。这种方法就是，用使似然函数达到驻点的参数值作为参数真值的估计。作为此估计法的实际应用，本文导出了所讨论模型的参数的驻点似然估计。然后证明了所得到的估计在一定条件下是模型参数的强相合估计。     

关于模糊环境中统计参数估计

利用了模糊随机变量理论探讨多元统计分析中模型环境下总体分布未知参数的估计方法，定义新的多维模糊数据，给出参数的一致估计，无偏估计及极大似然估计的定义及相关性质。     

基于极大似然估计的多参考点模态参数识别方法

在考虑随机噪声的情况下,实现了一种基于极大似然估计的多参考点频域模态参数识别方法。该方法采用频响函数的右矩阵分式模型,通过噪声的协方差矩阵对误差向量加权,使用离散时间域中基函数改善数值求解性态。模态参数的估计过程分为两步:首先由基于最小二乘估计的polyLSCF算法获取迭代初值,然后通过Gauss-Newton方法对极大似然函数进行迭代优化,得到精度更高的模态参数识别结果。采用GARTEUR仿真算例对所给出的方法进行了验证,结果表明:在高噪声情况下,利用噪声信息的极大似然估计方法能够显著提高模态参数的识别精度,特别是阻尼的识别精度。     

非线性模型中拟似然估计的小样本性质

在一类非线性模型中，本文利用了文［３］投影似然方法，推导出了拟似然得分函数是线性无偏估计函数类中唯一最优估计函数，推广了古典线性模型中著名的Ｇａｕｓｓ－Ｍａｒｋｏｖ定理。最后，证明了拟似然估计（ＱＬＥ）比最大似然估计（ＭＬＥ）效率低，从而进一步证实了文［２］的结论。     

三参数威布尔分布在风机载荷外推中的应用

本文通过极大似然法、双线性回归法、相关系数法及概率权重矩法的威布尔估计算法对风机载荷相关变量(叶根面内弯矩、叶根面外弯矩及叶尖挠度)进行载荷外推,并通过极大似然值对该几种方法进行比较,提出适合风机载荷变量的估计算法,为使用三参数威布尔分布对风机载荷外推提供了一定的参考。     

极大似然高分辨波达估计新方法

极大似然估计器是波达方向估计中公认的最佳估计器,但是计算量很大。为了解决极大似然估计器由于进行多维格形搜索而带来的计算量大的不足,将粒子滤波方法与极大似然估计相结合,提出了一种基于粒子滤波的极大似然波达方向估计器(Maximum Likelihood DOA Estimator Based on Particle Filtering,简称MLE-PF)。研究结果表明,MLE-PF不但保持了原极大似然估计方法的优良性能,大大减小了计算量,计算复杂度由O(LK)降至O(K×Ns),而且在低信噪比时也具有比MUSIC以及MiniNorm方法更加优越的估计性能。     

半参数回归模型的泛补偿最小二乘估计

本文首先提出泛补偿最小二乘法：接着,使用该法考虑半参数回归模型,得到了参数及非参数的估计。然后,将泛补偿最小二乘法与补偿最小二乘法进行了比较;最后用模拟的算例说明了该方法的有效性。     

Asymptotic behavior of robust estimators in partially linear models with missing responses: the effect of estimating the missing probability on the simplified marginal estimators

In this paper, we consider a semiparametric partially linear regression model where missing data occur in the response. We derive the asymptotic behavior of the robust estimators for the regression parameter and of the weighted simplified location estimator introduced in Bianco et al. (Comput. Stat. Data Anal. 54:546–564, 2010a). For the latter, consistency results and the asymptotic distribution are derived when the missing probability is known and also when it is estimated.     

Wavelet penalized likelihood estimation in generalized functional models

The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in a functional influence of some covariates, we authorize others to be modeled linearly. We thus consider a generalized partially linear regression model with unknown regression coefficients and an unknown nonparametric function. We present a maximum penalized likelihood procedure to estimate the components of the model introducing penalty based wavelet estimators. Asymptotic rates of the estimates of both the parametric and the nonparametric part of the model are given and quasi-minimax optimality is obtained under usual conditions in literature. We establish in particular that the ? ¹-penalty leads to an adaptive estimation with respect to the regularity of the estimated function. An algorithm based on backfitting and Fisher-scoring is also proposed for implementation. Simulations are used to illustrate the finite sample behavior, including a comparison with kernel- and spline-based methods.     

A dimension reduction approach for conditional Kaplan–Meier estimators

Many quantities of interest in survival analysis are smooth, closed-form functionals of the law of the observations. For instance, the conditional law of a lifetime of interest under random right censoring, and the conditional probability of being cured. In such cases, one can easily derive nonparametric estimators for the quantities of interest by plugging-into the functional the nonparametric estimators of the law of the observations. However, with multivariate covariates, the nonparametric estimation suffers from the curse of dimensionality. Here, a new dimension reduction approach for survival analysis is proposed and investigated in the right-censored lifetime case. First, we consider a single-index hypothesis on the conditional law of the observations and propose a \(\sqrt{n}-\)asymptotically normal semiparametric estimator. Next, we apply the smooth functionals to this estimator. This results in semiparametric estimators of the quantities of interest that avoid the curse of dimensionality. Confidence regions for the index and the functional of interest are built by bootstrap. The new methodology allows to test the dimension reduction assumption, can be extended to other dimension reduction methods and can be applied to closed-form functionals of more general censoring mechanisms.     

The Robust Regression Methods for Estimating of Finite Population Mean Based on SRSWOR in Case of Outliers

The ordinary least square (OLS) method is commonly used in regression analysis. But in the presence of outlier in the data, its results are unreliable. Hence, the robust regression methods have been suggested for a long time as alternatives to the OLS to solve the outliers problem. In the present study, new ratio type estimators of finite population mean are suggested using simple random sampling without replacement (SRSWOR) utilizing the supplementary information in Bowley’s coefficient of skewness with quartiles. For these proposed estimators, we have used the OLS, Huber-M, Mallows GM-estimate, Schweppe GM-estimate, and SIS GM-estimate methods for estimating the population parameters. Theoretically, the mean square error (MSE) equations of various estimators are obtained and compared with the OLS competitor. Simulations for skewed distributions as the Gamma distribution support the results, and an application of real data set containing outliers is considered for illustration.     

Analysis of left-truncated right-censored or doubly censored data with linear transformation models

We analyze left-truncated right-censored (LTRC) data or doubly censored data using semiparametric transformation models. It is demonstrated that the extended estimating equations of both?Cheng et al. (Biometrika 82:835?C845,?1995) and?Chen et al. (Biometrika 89:659?C668,?2002) can be used to analyze LTRC data or doubly censored data when left-censored variables are always observed. The asymptotic properties of the proposed estimators are derived. A simulation study is conducted to investigate the performance of the proposed estimators.     

Tail Estimation for Window-Censored Processes

This article develops methods to estimate the tail and full distribution of the lengths of the 0-intervals in a continuous time stationary ergodic stochastic process that takes the values 0 and 1 in alternating intervals. The setting is that each of many such 0–1 processes has been observed during a short time window. Thus, the observed 0-intervals could be noncensored, right-censored, left-censored, or doubly-censored, and the lengths of 0-intervals that are ongoing at the beginning of the observation window have a length-biased distribution. We exhibit parametric conditional maximum likelihood estimators for the full distribution, develop maximum likelihood tail estimation methods based on a semiparametric generalized Pareto model, and propose goodness-of-fit plots. Finite sample properties are studied by simulation, and asymptotic normality is established for the most important case. The methods are applied to estimation of the length of off-road glances in the 100-car study, a big naturalistic driving experiment. Supplementary materials that include MatLab code for the estimation routines and a simulation study are available online.     

A semiparametric technique for the multi‐response optimization problem

Multi‐response optimization (MRO) in response surface methodology is quite common in applications. Before the optimization phase, appropriate fitted models for each response are required. A common problem is model misspecification and occurs when any of the models built for the responses are misspecified resulting in an erroneous optimal solution. The model robust regression (MRR) technique, a semiparametric method, has been shown to be more robust to misspecification than either parametric or nonparametric methods. In this study, we propose the use of MRR to improve the quality of model estimation and adapt its fits of each response to the desirability function approach, one of the most popular MRO techniques. A case study and simulation studies are presented to illustrate the procedure and to compare the semiparametric method with the parametric and nonparametric methods. The results show that MRR performs much better than the other two methods in terms of model comparison criteria in most situations during the modeling stage. In addition, the simulated optimization results for MRR are more reliable during the optimization stage. Copyright © 2010 John Wiley & Sons, Ltd.     

On the Relationship of Sample Size and Moments of Estimators in Simple Linear Regression

Methods are developed for determining minimum sample size in simple linear regression (when residuals are nonnormal) that permit use of the classical normality-based analyses. The methods are based on behavior of standardized third and fourth moments of regression estimators. The case of symmetric independent variable values with one observation at each is considered. All other regression assumptions are assumed to be true.     

Estimation of the Shape Parameter of the Weibull Distribution Using Linear Regression Methods: Non‐Censored Samples

The two‐parameter Weibull distribution is one of the most widely applied probability distributions, particularly in reliability and lifetime modelings. Correct estimation of the shape parameter of the Weibull distribution plays a central role in these areas of statistical analysis. Many different methods can be used to estimate this parameter, most of which utilize regression methods. In this paper, we presented various regression methods for estimating the Weibull shape parameter and an experimental study using classical regression methods to compare the results of the methods. A complete list of the parameter estimators considered in this study is as follows: ordinary least squares (OLS), weighted least squares (WLS, Bergman, F&T, Lu), non‐parametric robust Theil's (Theil) and weighted Theil's (WeTheil), robust Winsorized least squares (WinLS), and M‐estimators (Huber, Andrew, Tukey, Cauchy, Welsch, Hampel and Logistic). Estimator performances were compared based on bias and mean square error criteria using Monte‐Carlo simulations. The simulation results demonstrated that for small, complete, and non‐outlier data sets, the Bergman, F&T, and Lu estimators are more efficient than the others. When the data set contains one or two outliers in the X direction, Theil is the most efficient estimator. Copyright © 2012 John Wiley & Sons, Ltd.