Parallel tempering for dynamic generalized linear models

ABSTRACT

Markov chain Monte Carlo (MCMC) methods can be used for statistical inference. The methods are time-consuming due to time-vary. To resolve these problems, parallel tempering (PT), as a parallel MCMC method, is tried, for dynamic generalized linear models (DGLMs), as well as the several optimal properties of our proposed method. In PT, two or more samples are drawn at the same time, and samples can exchange information with each other. We also present some simulations of the DGLMs in the case and provide two applications of Poisson-type DGLMs in financial research.     

Establishing decision tree-based short-term default credit risk assessment models

ABSTRACT

Traditional credit risk assessment models do not consider the time factor; they only think of whether a customer will default, but not the when to default. The result cannot provide a manager to make the profit-maximum decision. Actually, even if a customer defaults, the financial institution still can gain profit in some conditions. Nowadays, most research applied the Cox proportional hazards model into their credit scoring models, predicting the time when a customer is most likely to default, to solve the credit risk assessment problem. However, in order to fully utilize the fully dynamic capability of the Cox proportional hazards model, time-varying macroeconomic variables are required which involve more advanced data collection. Since short-term default cases are the ones that bring a great loss for a financial institution, instead of predicting when a loan will default, a loan manager is more interested in identifying those applications which may default within a short period of time when approving loan applications. This paper proposes a decision tree-based short-term default credit risk assessment model to assess the credit risk. The goal is to use the decision tree to filter the short-term default to produce a highly accurate model that could distinguish default lending. This paper integrates bootstrap aggregating (Bagging) with a synthetic minority over-sampling technique (SMOTE) into the credit risk model to improve the decision tree stability and its performance on unbalanced data. Finally, a real case of small and medium enterprise loan data that has been drawn from a local financial institution located in Taiwan is presented to further illustrate the proposed approach. After comparing the result that was obtained from the proposed approach with the logistic regression and Cox proportional hazards models, it was found that the classifying recall rate and precision rate of the proposed model was obviously superior to the logistic regression and Cox proportional hazards models.     

A variance shift model for detection of outliers in the linear mixed measurement error models

ABSTRACT

In this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990 Nakamura, T. (1990). Corrected score function for errors in variables models: methodology and application to generalized linear models. Biometrika 77:127–137.[Crossref], [Web of Science ®] , [Google Scholar]). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests.     

Modeling of covariance structures of random effects and random errors in linear mixed models

Abstract

In this paper, we discuss how to model the mean and covariancestructures in linear mixed models (LMMs) simultaneously. We propose a data-driven method to modelcovariance structures of the random effects and random errors in the LMMs. Parameter estimation in the mean and covariances is considered by using EM algorithm, and standard errors of the parameter estimates are calculated through Louis’ (1982 Louis, T.A. (1982). Finding observed information using the EM algorithm. J. Royal Stat. Soc. B 44:98–130. [Google Scholar]) information principle. Kenward’s (1987 Kenward, M.G. (1987). A method for comparing profiles of repeated measurements. Appl. Stat. 36:296–308.[Crossref], [Web of Science ®] , [Google Scholar]) cattle data sets are analyzed for illustration,and comparison to the literature work is made through simulation studies. Our numerical analysis confirms the superiority of the proposed method to existing approaches in terms of Akaike information criterion.     

Estimation on semi-functional linear errors-in-variables models

Abstract

Semi-functional linear regression models are important in practice. In this paper, their estimation is discussed when function-valued and real-valued random variables are all measured with additive error. By means of functional principal component analysis and kernel smoothing techniques, the estimators of the slope function and the non parametric component are obtained. To account for errors in variables, deconvolution is involved in the construction of a new class of kernel estimators. The convergence rates of the estimators of the unknown slope function and non parametric component are established under suitable norm and conditions. Simulation studies are conducted to illustrate the finite sample performance of our method.     

Sequential order statistics from dependent random variables

Abstract

This paper provides an extension for “sequential order statistics” (SOS) introduced by Kamps. It is called “developed sequential order statistics” (DSOS) and is useful for describing lifetimes of engineering systems when component lifetimes are dependent. Explicit expressions for the joint density function, the marginal distributions and the means of DSOS are derived. Under the well known “conditional proportional hazard rate” (CPHR) model and the Gumbel families of copulas for dependency among component lifetimes, some findings are reported. For example, it is proved that the joint density functions of DSOS and SOS have the same structure. Various illustrative examples are also given.     

Forecasting the Incidence of Cancer in Regional Victoria,Australia

Loddon Mallee Integrated Cancer Service plays a key role in planning the delivery of cancer services in the Loddon Mallee Region of Victoria, Australia. Forecasting the incidence of cancer is an important part of planning for these services. This article is written from an industry perspective. We describe the context of our work, review the literature on forecasting the incidence of cancer, discuss contemporary approaches, describe our experience with forecasting models, and list issues associated with applying these models. An extensive bibliography illustrates the world-wide interest in this forecasting problem. We hope that it is useful to researchers.     

A Compressive Sensing Based Analysis of Anomalies in Generalized Linear Models

In this article, we present a compressive sensing based framework for generalized linear model regression that employs a two-component noise model and convex optimization techniques to simultaneously detect outliers and determine optimally sparse representations of noisy data from arbitrary sets of basis functions. We then extend our model to include model order reduction capabilities that can uncover inherent sparsity in regression coefficients and achieve simple, superior fits. Second, we use the mixed ?₂/?₁ norm to develop another model that can efficiently uncover block-sparsity in regression coefficients. By performing model order reduction over all independent variables and basis functions, our algorithms successfully deemphasize the effect of independent variables that become uncorrelated with dependent variables. This desirable property has various applications in real-time anomaly detection, such as faulty sensor detection and sensor jamming in wireless sensor networks. After developing our framework and inheriting a stable recovery theorem from compressive sensing theory, we present two simulation studies on sparse or block-sparse problems that demonstrate the superior performance of our algorithms with respect to (1) classic outlier-invariant regression techniques like least absolute value and iteratively reweighted least-squares and (2) classic sparse-regularized regression techniques like LASSO.     

Empirical Analysis of Interval-Censored Failure Time Data with Linear Transformation Models

Interval-censored data naturally arise in many studies. For their regression analysis, many approaches have been proposed under various models and for most of them, the inference is carried out based on the asymptotic normality. In particular, Zhang et al. (2005) discussed the procedure under the linear transformation model. It is well-known that the symmetric property implied by the normal distribution may not be appropriate sometimes. Also the method could underestimate the variance of estimated parameters. This paper proposes an empirical likelihood-based procedure for the problem. Simulation and the analysis of a real data set are conducted to assess the performance of the procedure.     

A-optimal designs for heteroscedastic multifactor regression models

Abstract

This paper searches for A-optimal designs for Kronecker product and additive regression models when the errors are heteroscedastic. Sufficient conditions are given so that A-optimal designs for the multifactor models can be built from A-optimal designs for their sub-models with a single factor. The results of an efficiency study carried out to check the adequacy of the products of optimal designs for uni-factor marginal models when these are used to estimate different multi-factor models are also reported.