Different distance measures for fuzzy linear regression with Monte Carlo methods

The aim of this study was to determine the best distance measure for estimating the fuzzy linear regression model parameters with Monte Carlo (MC) methods. It is pointed out that only one distance measure is used for fuzzy linear regression with MC methods within the literature. Therefore, three different definitions of distance measure between two fuzzy numbers are introduced. Estimation accuracies of existing and proposed distance measures are explored with the simulation study. Distance measures are compared to each other in terms of estimation accuracy; hence this study demonstrates that the best distance measures to estimate fuzzy linear regression model parameters with MC methods are the distance measures defined by Kaufmann and Gupta (Introduction to fuzzy arithmetic theory and applications. Van Nostrand Reinhold, New York, 1991), Heilpern-2 (Fuzzy Sets Syst 91(2):259–268, 1997) and Chen and Hsieh (Aust J Intell Inf Process Syst 6(4):217–229, 2000). One the other hand, the worst distance measure is the distance measure used by Abdalla and Buckley (Soft Comput 11:991–996, 2007; Soft Comput 12:463–468, 2008). These results would be useful to enrich the studies that have already focused on fuzzy linear regression models

Alternative approaches to evaluation in empirical microeconomics

This paper reviews a range of the most popular policy evaluation methods in empirical microeconomics: social experiments, natural experiments, matching methods, instrumental variables, discontinuity design and control functions. It discusses the identification of both the traditionally used average parameters and more complex distributional parameters. In each case, the necessary assumptions and the data requirements are considered. The adequacy of each approach is discussed drawing on the empirical evidence from the education and labor market policy evaluation literature. We also develop an education evaluation model which we use to carry through the discussion of each alternative approach. A full set of STATA datasets are provided free online which contain Monte-Carlo replications of the various specifications of the education evaluation model. There are also a full set of STATA .do files for each of the estimation approaches described in the paper. The .do-files can be used together with the datasets to reproduce all the results in the paper.

Alternative Approaches to Evaluation in Empirical Microeconomics

This paper reviews some of the most popular policy evaluation methods in empirical microeconomics: social experiments, natural experiments, matching, instrumental variables, discontinuity design, and control functions. It discusses identification of traditionally used average parameters and more complex distributional parameters. The adequacy, assumptions, and data requirements of each approach are discussed drawing on empirical evidence from the education and employment policy evaluation literature. A workhorse simulation model of education returns is used throughout the paper to discuss and illustrate each approach. The full set of STATA datasets and do-files are available free online and can be used to reproduce all estimation and simulation results.evaluation methods

Alternative Approaches to Evaluation in Empirical Microeconomics

This paper reviews a range of the most popular policy evaluation methods in empirical microeconomics: social experiments, natural experiments, matching methods, instrumental variables, discontinuity design and control functions. It discusses the identification of both the traditionally used average parameters and more complex distributional parameters. In each case, the necessary assumptions and the data requirements are considered. The adequacy of each approach is discussed drawing on the empirical evidence from the education and labor market policy evaluation literature. We also develop an education evaluation model which we use to carry through the discussion of each alternative approach. A full set of STATA datasets are provided free online which contain Monte-Carlo replications of the various specifications of the education evaluation model. There are also a full set of STATA .do files for each of the estimation approaches described in the paper. The .do-files can be used together with the datasets to reproduce all the results in the paper.Evaluation methods, policy evaluation, matching methods, instrumental variables, social experiments, natural experiments, difference-in-differences, discontinuity design, control function.

Assessing the Number of Components in Mixture Models: a Review.

Despite the widespread application of finite mixture models, the decision of how many classes are required to adequately represent the data is, according to many authors, an important, but unsolved issue. This work aims to review, describe and organize the available approaches designed to help the selection of the adequate number of mixture components (including Monte Carlo test procedures, information criteria and classification-based criteria); we also provide some published simulation results about their relative performance, with the purpose of identifying the scenarios where each criterion is more effective (adequate).Finite mixture; number of mixture components; information criteria; simulation studies.

Small area estimation of general parameters with application to poverty indicators: A hierarchical Bayes approach

Poverty maps are used to aid important political decisions such as allocation of development funds by governments and international organizations. Those decisions should be based on the most accurate poverty figures. However, often reliable poverty figures are not available at fine geographical levels or for particular risk population subgroups due to the sample size limitation of current national surveys. These surveys cannot cover adequately all the desired areas or population subgroups and, therefore, models relating the different areas are needed to 'borrow strength" from area to area. In particular, the Spanish Survey on Income and Living Conditions (SILC) produces national poverty estimates but cannot provide poverty estimates by Spanish provinces due to the poor precision of direct estimates, which use only the province specific data. It also raises the ethical question of whether poverty is more severe for women than for men in a given province. We develop a hierarchical Bayes (HB) approach for poverty mapping in Spanish provinces by gender that overcomes the small province sample size problem of the SILC. The proposed approach has a wide scope of application because it can be used to estimate general nonlinear parameters. We use a Bayesian version of the nested error regression model in which Markov chain Monte Carlo procedures and the convergence monitoring therein are avoided. A simulation study reveals good frequentist properties of the HB approach. The resulting poverty maps indicate that poverty, both in frequency and intensity, is localized mostly in the southern and western provinces and it is more acute for women than for men in most of the provinces.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS702 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Three-structured smooth transition regression models based on CART algorithm

In the present work, a tree-based model that combines aspects of CART (Classification and Regression Trees) and STR (Smooth Transition Regression) is proposed. The main idea relies on specifying a parametric nonlinear model through a tree-growing procedure. The resulting model can be analysed either as a fuzzy regression or as a smooth transition regression with multiple regimes. Decisions about splits are entirely based on statistical tests of hypotheses and confidence intervals are constructed for the parameters within the terminal nodes as well as the final predictions. A Monte Carlo Experiment shows the estimators’ properties and the ability of the proposed algorithm to identify correctly several tree architectures. An application to the famous Boston Housing dataset shows that the proposed model provides better explanation with the same number of leaves as the one obtained with the CART algorithm.