Forward search outlier detection in data envelopment analysis

In this paper we tackle the problem of outlier detection in data envelopment analysis (DEA). We propose a procedure where we merge the super-efficiency DEA and the forward search. Since DEA provides efficiency scores which are not parameters to fit the model to the data, we introduce a distance, to be monitored along the search. This distance is obtained through the integration of a regression model and the super-efficiency DEA. We simulate a Cobb-Douglas production function and we compare the super-efficiency DEA and the forward search analysis in both uncontaminated and contaminated settings. For inference about outliers, we exploit envelopes obtained through Monte Carlo simulations.     

Testing covariates in high-dimensional regression

In a high-dimensional linear regression model, we propose a new procedure for testing statistical significance of a subset of regression coefficients. Specifically, we employ the partial covariances between the response variable and the tested covariates to obtain a test statistic. The resulting test is applicable even if the predictor dimension is much larger than the sample size. Under the null hypothesis, together with boundedness and moment conditions on the predictors, we show that the proposed test statistic is asymptotically standard normal, which is further supported by Monte Carlo experiments. A similar test can be extended to generalized linear models. The practical usefulness of the test is illustrated via an empirical example on paid search advertising.     

Bayesian Variable and Transformation Selection in Linear Regression

This article suggests a method for variable and transformation selection based on posterior probabilities. Our approach allows for consideration of all possible combinations of untransformed and transformed predictors along with transformed and untransformed versions of the response. To transform the predictors in the model, we use a change-point model, or “change-point transformation,” which can yield more interpretable models and transformations than the standard Box–Tidwell approach. We also address the problem of model uncertainty in the selection of models. By averaging over models, we account for the uncertainty inherent in inference based on a single model chosen from the set of models under consideration. We use a Markov chain Monte Carlo model composition (MC³) method which allows us to average over linear regression models when the space of models under consideration is very large. This considers the selection of variables and transformations at the same time. In an example, we show that model averaging improves predictive performance as compared with any single model that might reasonably be selected, both in terms of overall predictive score and of the coverage of prediction intervals. Software to apply the proposed methodology is available via StatLib.     

失混合效应模型的分位回归及变量选择

纵向数据常常用正态混合效应模型进行分析.然而,违背正态性的假定往往会导致无效的推断.与传统的均值回归相比较,分位回归可以给出响应变量条件分布的完整刻画,对于非正态误差分布也可以给稳健的估计结果．本文主要考虑右删失响应下纵向混合效应模型的分位回归估计和变量选择问题．首先,逆删失概率加权方法被用来得到模型的参数估计．其次,结合逆删失概率加权和LASSO惩罚变量选择方法考虑了模型的变量选择问题.蒙特卡洛模拟显示所提方法要比直接删除删失数据的估计方法更具优势．最后,分析了一组艾滋病数据集来展示所提方法的实际应用效果．     

Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates

In this paper, we discuss Bayesian joint quantile regression of mixed effects models with censored responses and errors in covariates simultaneously using Markov Chain Monte Carlo method. Under the assumption of asymmetric Laplace error distribution, we establish a Bayesian hierarchical model and derive the posterior distributions of all unknown parameters based on Gibbs sampling algorithm. Three cases including multivariate normal distribution and other two heavy-tailed distributions are considered for fitting random effects of the mixed effects models. Finally, some Monte Carlo simulations are performed and the proposed procedure is illustrated by analyzing a group of AIDS clinical data set.     

Penalized quadratic inference functions for single-index models with longitudinal data

In this paper, we focus on single-index models for longitudinal data. We propose a procedure to estimate the single-index component and the unknown link function based on the combination of the penalized splines and quadratic inference functions. It is shown that the proposed estimation method has good asymptotic properties. We also evaluate the finite sample performance of the proposed method via Monte Carlo simulation studies. Furthermore, the proposed method is illustrated in the analysis of a real data set.     

On Dynamic Generalized Linear Models with Applications

In this paper we combine the idea of ‘power steady model’, ‘discount factor’ and ‘power prior’, for a general class of filter model, more specifically within a class of dynamic generalized linear models (DGLM). We show an optimality property for our proposed method and present the particle filter algorithm for DGLM as an alternative to Markov chain Monte Carlo method. We also present two applications; one on dynamic Poisson models for hurricane count data in Atlantic ocean and the another on the dynamic Poisson regression model for longitudinal count data.     

Implementations of the Monte Carlo EM Algorithm

The Monte Carlo EM (MCEM) algorithm is a modification of the EM algorithm where the expectation in the E-step is computed numerically through Monte Carlo simulations. The most exible and generally applicable approach to obtaining a Monte Carlo sample in each iteration of an MCEM algorithm is through Markov chain Monte Carlo (MCMC) routines such as the Gibbs and Metropolis–Hastings samplers. Although MCMC estimation presents a tractable solution to problems where the E-step is not available in closed form, two issues arise when implementing this MCEM routine: (1) how do we minimize the computational cost in obtaining an MCMC sample? and (2) how do we choose the Monte Carlo sample size? We address the first question through an application of importance sampling whereby samples drawn during previous EM iterations are recycled rather than running an MCMC sampler each MCEM iteration. The second question is addressed through an application of regenerative simulation. We obtain approximate independent and identical samples by subsampling the generated MCMC sample during different renewal periods. Standard central limit theorems may thus be used to gauge Monte Carlo error. In particular, we apply an automated rule for increasing the Monte Carlo sample size when the Monte Carlo error overwhelms the EM estimate at any given iteration. We illustrate our MCEM algorithm through analyses of two datasets fit by generalized linear mixed models. As a part of these applications, we demonstrate the improvement in computational cost and efficiency of our routine over alternative MCEM strategies.     

基于贝叶斯MCMC算法的美式期权定价

鉴于美式期权的定价具有后向迭代搜索特征,本文结合Longstaff和Schwartz提出的美式期权定价的最小二乘模拟方法,研究基于马尔科夫链蒙特卡洛算法对回归方程系数的估计,实现对美式期权的双重模拟定价.通过对无红利美式看跌股票期权定价进行大量实证模拟,从期权价值定价误差等方面同著名的最小二乘蒙特卡洛模拟方法进行对比分析,结果表明基于MCMC回归算法给出的美式期权定价具有更高的精确度.模拟实证结果表明本文提出的对美式期权定价方法具有较好的可行性、有效性与广泛的适用性.该方法的不足之处就是类似于一般的蒙特卡洛方法,会使得求解的计算量有所加大.     

Recentered Importance Sampling With Applications to Bayesian Model Validation

Since its introduction in the early 1990s, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This article examines problems associated with its application to repeated evaluation of related posterior distributions with a particular focus on Bayesian model validation. We demonstrate that, in certain applications, the curse of dimensionality can be reduced by a simple modification of IS. In addition to providing new theoretical insight into the behavior of the IS approximation in a wide class of models, our result facilitates the implementation of computationally intensive Bayesian model checks. We illustrate the simplicity, computational savings, and potential inferential advantages of the proposed approach through two substantive case studies, notably computation of Bayesian p-values for linear regression models and simulation-based model checking. Supplementary materials including the Appendix and the R code for Section are available online.     

Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and that only have limited spatial regularity. We extend the finite element error analysis for this type of equation, carried out in Charrier et al. (SIAM J Numer Anal, 2013), to more difficult problems, posed on non-smooth domains and with discontinuities in the coefficient. For this wider class of model problem, we prove convergence of the multilevel Monte Carlo algorithm for estimating any bounded, linear functional and any continuously Fréchet differentiable non-linear functional of the solution. We further improve the performance of the multilevel estimator by introducing level dependent truncations of the Karhunen–Loève expansion of the random coefficient. Numerical results complete the paper.     

Influence measures in ridge regression when the error terms follow an Ar(1) process

Influence concepts have an important place in linear regression models and case deletion is a useful method for assessing the influence of single case. The influence measures in the presence of multicollinearity were discussed under the linear regression models when the errors structure is uncorrelated and homoscedastic. In contrast to other article on this subject, we consider the influence measures in ridge regression with autocorrelated errors. Theoretical results are illustrated with a numerical example and a Monte Carlo simulation is conducted to see the effect autocorrelation coefficient, strength of multicollinearity and sample size on leverage points and influential observations.     

对稳健回归尺度参数估计的一种改进

常对线性回归模型的稳健 M估计中 ,尺度参数使用绝对离差中位数 MAD.将 Rousseeuw等人对单变量尺度参数的一种稳健估计 Sn引入到回归问题中 ,讨论了此估计的一些优良性质 ,并通过一个小规模的模拟研究 ,说明使用 Sn比使用 MAD做尺度参数将会较大地提高回归估计的估计效率 .     

A modified Hooke and Jeeves algorithm with likelihood ratio performance extrapolation for simulation optimization

The Hooke and Jeeves algorithm (HJ) is a pattern search procedure widely used to optimize non-linear functions that are not necessarily continuous or differentiable. The algorithm performs repeatedly two types of search routines; an exploratory search and a pattern search. The HJ algorithm requires deterministic evaluation of the function being optimized. In this paper we consider situations where the objective function is stochastic and can be evaluated only through Monte Carlo simulation. To overcome the problem of expensive use of function evaluations for Monte Carlo simulation, a likelihood ratio performance extrapolation (LRPE) technique is used. We extrapolate the performance measure for different values of the decision parameters while simulating a single sample path from the underlying system. Our modified Hooke and Jeeves algorithm uses a likelihood ratio performance extrapolation for simulation optimization. Computational results are provided to demonstrate the performance of the proposed modified HJ algorithm.     

A copula based Bayesian approach for paid–incurred claims models for non-life insurance reserving

Our article considers the class of recently developed stochastic models that combine claims payments and incurred losses information into a coherent reserving methodology. In particular, we develop a family of hierarchical Bayesian paid–incurred claims models, combining the claims reserving models of Hertig (1985) and Gogol (1993). In the process we extend the independent log-normal model of Merz and Wüthrich (2010) by incorporating different dependence structures using a Data-Augmented mixture Copula paid–incurred claims model.In this way the paper makes two main contributions: firstly we develop an extended class of model structures for the paid–incurred chain ladder models where we develop precisely the Bayesian formulation of such models; secondly we explain how to develop advanced Markov chain Monte Carlo sampling algorithms to make inference under these copula dependence PIC models accurately and efficiently, making such models accessible to practitioners to explore their suitability in practice. In this regard the focus of the paper should be considered in two parts, firstly development of Bayesian PIC models for general dependence structures with specialised properties relating to conjugacy and consistency of tail dependence across the development years and accident years and between Payment and incurred loss data are developed. The second main contribution is the development of techniques that allow general audiences to efficiently work with such Bayesian models to make inference. The focus of the paper is not so much to illustrate that the PIC paper is a good class of models for a particular data set, the suitability of such PIC type models is discussed in Merz and Wüthrich (2010) and Happ and Wüthrich (2013). Instead we develop generalised model classes for the PIC family of Bayesian models and in addition provide advanced Monte Carlo methods for inference that practitioners may utilise with confidence in their efficiency and validity.     

Imperfect debugging in software reliability: A Bayesian approach

The objective of studying software reliability is to assist software engineers in understanding more of the probabilistic nature of software failures during the debugging stages and to construct reliability models. In this paper, we consider modeling of a multiplicative failure rate whose components are evolving stochastically over testing stages and discuss its Bayesian estimation. In doing so, we focus on the modeling of parameters such as the fault detection rate per fault and the number of faults. We discuss how the proposed model can account for “imperfect debugging” under certain conditions. We use actual inter-failure data to carry out inference on model parameters via Markov chain Monte Carlo methods and present additional insights from Bayesian analysis.     

Bayesian Methods for Wavelet Series in Single-Index Models

Single-index models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. This article proposes a nonparametric estimation approach that combines wavelet methods for nonequispaced designs with Bayesian models. We consider a wavelet series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform shrinkage on wavelet coefficients and use Markov chain Monte Carlo methods for a posteriori inference. We investigate an independence-type Metropolis-Hastings algorithm to produce samples for the direction parameter. Our method leads to simultaneous estimates of the link function and of the index parameters. We present results on both simulated and real data, where we look at comparisons with other methods.     

Adaptive integration for multi-factor portfolio credit loss models

We propose algorithms of adaptive integration for calculation of the tail probability in multi-factor credit portfolio loss models. We first modify the classical Genz-Malik rule, a deterministic multiple integration rule suitable for portfolio credit models with number of factors less than 8. Later on we arrive at the adaptive Monte Carlo integration, which essentially replaces the deterministic integration rule by antithetic random numbers. The latter can not only handle higher-dimensional models but is also able to provide reliable probabilistic error bounds. Both algorithms are asymptotic convergent and consistently outperform the plain Monte Carlo method.     

Technical efficiency estimation with multiple inputs and multiple outputs using regression analysis

Regression and linear programming provide the basis for popular techniques for estimating technical efficiency. Regression-based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error. In contrast, linear programming models are nonparametric and allow multiple inputs and outputs. The purported disadvantage of the regression-based models is the inability to allow multiple outputs without additional data on input prices. In this paper, deterministic cross-sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed. Notably, technical efficiency can be estimated using regression models characterized by multiple input, multiple output environments without input price data. We provide multiple examples including a Monte Carlo analysis.     

A Monte Carlo Filtering Approach for Estimating the Term Structure of Interest Rates

We develop new methodology for estimation of general class of term structure models based on a Monte Carlo filtering approach. We utilize the generalized state space model which can be naturally applied to the estimation of the term structure models based on the Markov state processes. It is also possible to introduce measurement errors in the general way without any bias. Moreover, the Monte Carlo filter can be applied even to the models in which the zero-coupon bonds' prices can not be analytically obtained. As an example, we apply the method to LIBORs (London Inter Bank Offered Rates) and interest rates swaps in the Japanese market and show the usefulness of our approach.