Tuning parameter selection in penalized generalized linear models for discrete data

In recent years, we have seen an increased interest in the penalized likelihood methodology, which can be efficiently used for shrinkage and selection purposes. This strategy can also result in unbiased, sparse, and continuous estimators. However, the performance of the penalized likelihood approach depends on the proper choice of the regularization parameter. Therefore, it is important to select it appropriately. To this end, the generalized cross‐validation method is commonly used. In this article, we firstly propose new estimates of the norm of the error in the generalized linear models framework, through the use of Kantorovich inequalities. Then these estimates are used in order to derive a tuning parameter selector in penalized generalized linear models. The proposed method does not depend on resampling as the standard methods and therefore results in a considerable gain in computational time while producing improved results. A thorough simulation study is conducted to support theoretical findings; and a comparison of the penalized methods with the L₁, the hard thresholding, and the smoothly clipped absolute deviation penalty functions is performed, for the cases of penalized Logistic regression and penalized Poisson regression. A real data example is being analyzed, and a discussion follows. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.     

Gradient-based smoothing parameter selection for nonparametric regression estimation

Estimating gradients is of crucial importance across a broad range of applied economic domains. Here we consider data-driven bandwidth selection based on the gradient of an unknown regression function. This is a difficult problem given that direct observation of the value of the gradient is typically not observed. The procedure developed here delivers bandwidths which behave asymptotically as though they were selected knowing the true gradient. Simulated examples showcase the finite sample attraction of this new mechanism and confirm the theoretical predictions.     

Bayesian approach to LR assessment in case of rare type match

The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses, and for its assessment, Bayesian methods are widespread in the forensic field. However, the Bayesian ‘recipe’ for the LR presented in most of the literature consists of plugging‐in Bayesian estimates of the involved nuisance parameters into a frequentist‐defined LR: frequentist and Bayesian methods are thus mixed, giving rise to solutions obtained by hybrid reasoning. This paper provides the derivation of a proper Bayesian approach to assess LRs for the ‘rare type match problem’, the situation in which the expert wants to evaluate a match between the DNA profile of a suspect and that of a trace from the crime scene, and this profile has never been observed before in the database of reference. LR assessment using the two most popular Bayesian models (beta‐binomial and Dirichlet‐multinomial) is discussed and compared with corresponding plug‐in versions.     

Methods for Default and Robust Bayesian Model Comparison: the Fractional Bayes Factor Approach

In the Bayesian approach to model selection and hypothesis testing, the Bayes factor plays a central role. However, the Bayes factor is very sensitive to prior distributions of parameters. This is a problem especially in the presence of weak prior information on the parameters of the models. The most radical consequence of this fact is that the Bayes factor is undetermined when improper priors are used. Nonetheless, extending the non-informative approach of Bayesian analysis to model selection/testing procedures is important both from a theoretical and an applied viewpoint. The need to develop automatic and robust methods for model comparison has led to the introduction of several alternative Bayes factors. In this paper we review one of these methods: the fractional Bayes factor (O'Hagan, 1995). We discuss general properties of the method, such as consistency and coherence. Furthermore, in addition to the original, essentially asymptotic justifications of the fractional Bayes factor, we provide further finite-sample motivations for its use. Connections and comparisons to other automatic methods are discussed and several issues of robustness with respect to priors and data are considered. Finally, we focus on some open problems in the fractional Bayes factor approach, and outline some possible answers and directions for future research.     

基于二叉树模型的战略柔性价值研究

将战略投资价值分为内在价值和战略柔性价值,结合战略投资特点对传统二叉树模型进行修正,结合实例分析了推迟柔性和放弃柔性的价值;并从模型参数设定、成本波动率、竞争因素、策略次优执行以及企业对战略投资的内部管理程序等方面分析了影响战略柔性价值的因素,并得出结论:修正的二叉树模型是企业管理战略投资和战略柔性价值的有用工具。     

A Review and Comparison of Bandwidth Selection Methods for Kernel Regression

Over the last decades, several methods for selecting the bandwidth have been introduced in kernel regression. They differ quite a bit, and although there already exist more selection methods than for any other regression smoother, one can still observe coming up new ones. Given the need of automatic data‐driven bandwidth selectors for applied statistics, this review is intended to explain and, above all, compare these methods. About 20 different selection methods have been revised, implemented and compared in an extensive simulation study.     

A Statistical Model to Investigate the Reproducibility Rate Based on Replication Experiments

The reproducibility crisis, that is, the fact that many scientific results are difficult to replicate, pointing to their unreliability or falsehood, is a hot topic in the recent scientific literature, and statistical methodologies, testing procedures and p‐values, in particular, are at the centre of the debate. Assessment of the extent of the problem–the reproducibility rate or the false discovery rate–and the role of contributing factors are still an open problem. Replication experiments, that is, systematic replications of existing results, may offer relevant information on these issues. We propose a statistical model to deal with such information, in particular to estimate the reproducibility rate and the effect of some study characteristics on its reliability. We analyse data from a recent replication experiment in psychology finding a reproducibility rate broadly coherent with other assessments from the same experiment. Our results also confirm the expected role of some contributing factor (unexpectedness of the result and room for bias) while they suggest that the similarity between original study and the replica is not so relevant, thus mitigating some criticism directed to replication experiments.     

风险投资决策的多阶段混合式期权定价模型及其分析

从风险投资的投资时间多阶段性和投资决策不确定性出发,运用实物期权的二叉树模型和扩展后的三叉树模型,建立了一个符合风险投资实际的多阶段混合式期权定价模型,以期开拓对风险投资决策的新思路。     

A School-Level Gravity Model of Student Migration Flows to Higher Education Institutions

This paper presents a gravity model of student migration flows to higher education institutions (HEIs) in Ireland. The analysis is performed on a novel dataset containing detailed information on a range of ‘push’ and ‘pull’ factors, allowing one to estimate the effects of a number of important school-level characteristics on these flows. This is achieved by estimating and comparing a fixed-effects Poisson model and two conditional fixed-effects negative binomial models and selecting the best model on the basis of the Akaike information criterion (AIC). The preferred negative binomial model accounts for over-dispersion in the student flow data and allows for estimation of the parameter coefficients of the HEI-invariant characteristics. The analysis suggests that while geography plays a very important role in explaining student flows, so too do a range of school-level characteristics. Furthermore, it is found that distance has a differential impact across HEIs and HEI types with important implications for policy-makers and HEI managers.     

Objective Bayes Factors for Inequality Constrained Hypotheses

This paper will present a Bayes factor for the comparison of an inequality constrained hypothesis with its complement or an unconstrained hypothesis. Equivalent sets of hypotheses form the basis for the quantification of the complexity of an inequality constrained hypothesis. It will be shown that the prior distribution can be chosen such that one of the terms in the Bayes factor is the quantification of the complexity of the hypothesis of interest. The other term in the Bayes factor represents a measure of the fit of the hypothesis. Using a vague prior distribution this fit value is essentially determined by the data. The result is an objective Bayes factor.     

某公司材料供应商绩效评估模型

对某公司材料供应商绩效评估模型进行了介绍,在满足公司质量第一,确保供应的前提下,详述了供应商绩效指标的设置,指标计算时所用基础数据的来源,指标重要性的确定,以及如何建立简单计算模型来整合指标数据。通过该评估模型的建立,某公司对供应商业绩的考核有了统一的考核方法和计算公式,同时对供应商业绩较为主观的评价也有客观的表现。     

On the natural selection rule in general linear models

We consider a problem of selecting the best treatment in a general linear model. We look at the properties of the natural selection rule. It is shown that the natural selection rule is minimax under to “0–1” loss function and it is a Bayes rule under a monotone permutation invariant loss function with respect to a permutation invariant prior for every variance balanced design. Some other condition on the design matrix is given so that a Bayes rule with respect to a normal prior will be of simple structure.     

基于二叉树期权定价模型的房地产投资决策分析研究

将实物期权理论引入房地产投资决策过程中,分析了传统DCF法存在的缺陷和房地产投资的期权特性,建立了房地产投资项目的二叉树期权定价模型,并对该模型在实际投资中进行了案例分析。     

Model selection in stochastic frontier analysis with an application to maize production in Kenya

This paper shows how to compute the standard errors for partial effects of exogenous firm characteristics influencing firm inefficiency under a range of popular stochastic frontier model specifications. We also develop an R²-type measure to summarize the overall explanatory power of the exogenous factors on firm inefficiency. The paper also applies a recently developed model selection procedure to choose among alternative stochastic frontier specifications using data from household maize production in Kenya. The magnitude of estimated partial effects of exogenous household characteristics on inefficiency turns out to be very sensitive to model specification, and the model selection procedure leads to an unambiguous choice of best model. We propose a bootstrapping procedure to evaluate the size and power of the model selection procedure. The empirical application also provides further evidence on how household characteristics influence technical inefficiency in maize production in developing countries.

Model selection in random effects models for directed graphs using approximated Bayes factors

With the development of an MCMC algorithm, Bayesian model selection for the p ₂ model for directed graphs has become possible. This paper presents an empirical exploration in using approximate Bayes factors for model selection. For a social network of Dutch secondary school pupils from different ethnic backgrounds it is investigated whether pupils report that they receive more emotional support from within their own ethnic group. Approximated Bayes factors seem to work, but considerable margins of error have to be reckoned with.     

SCARA机器人小臂有限元模型设计

本文讲述了用ANSYS软件设计SCARA机器人小臂有限元模型的方法,这对初学者正确使用ANSYS很有帮助。     

Extrapolation‐based Bandwidth Selectors: A Review and Comparative Study with Discussion on Bivariate Applications

Cross‐validation is a widely used tool in selecting the smoothing parameter in a non‐parametric procedure. However, it suffers from large sampling variation and tends to overfit the data set. Many attempts have been made to reduce the variance of cross‐validation. This paper focuses on two recent proposals of extrapolation‐based cross‐validation bandwidth selectors: indirect cross‐validation and subsampling‐extrapolation technique. In univariate case, we notice that using a fixed value parameter surrogate for indirect cross‐validation works poorly when the true density is hard to estimate, while the subsampling‐extrapolation technique is more robust to non‐normality. We investigate whether a hybrid bandwidth selector could benefit from the advantages of both approaches and compare the performance of different extrapolation‐based bandwidth selectors through simulation studies, real data analyses and large sample theory. A discussion on their extension to bivariate case is also presented.     

The Spatial Durbin Model and the Common Factor Tests

Abstract

The spatial Durbin model occupies an interesting position in the field of spatial econometrics. It is the reduced form of a model with cross-sectional dependence in the errors and it may be used as the nesting equation in a more general approach of model selection. Specifically, in this equation we obtain the common factor tests (of which the likelihood ratio is the best known) whose objective is to discriminate between substantive and residual dependence in an apparently misspecified equation. Our paper tries to delve deeper into the role of the spatial Durbin model in the problem of specifying a spatial econometric model. We include a Monte Carlo study related to the performance of the common factor tests presented in the paper in small sample sizes.     

Estimating the Kullback–Liebler risk based on multifold cross‐validation

This paper concerns a class of model selection criteria based on cross‐validation techniques and estimative predictive densities. Both the simple or leave‐one‐out and the multifold or leave‐m‐out cross‐validation procedures are considered. These cross‐validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.     

Inferential Implications of Over‐Parametrization: A Case Study in Incomplete Categorical Data

In the context of either Bayesian or classical sensitivity analyses of over‐parametrized models for incomplete categorical data, it is well known that prior‐dependence on posterior inferences of nonidentifiable parameters or that too parsimonious over‐parametrized models may lead to erroneous conclusions. Nevertheless, some authors either pay no attention to which parameters are nonidentifiable or do not appropriately account for possible prior‐dependence. We review the literature on this topic and consider simple examples to emphasize that in both inferential frameworks, the subjective components can influence results in nontrivial ways, irrespectively of the sample size. Specifically, we show that prior distributions commonly regarded as slightly informative or noninformative may actually be too informative for nonidentifiable parameters, and that the choice of over‐parametrized models may drastically impact the results, suggesting that a careful examination of their effects should be considered before drawing conclusions.