Fuzzy approach to semi-parametric of a sample selection model

The sample selection model has been studied in the context of semi-parametric methods. With the deficiencies of the parametric model, such as inconsistent estimators, semi-parametric estimation methods provide better alternatives. This article focuses on the context of fuzzy concepts as a hybrid to the semiparametric sample selection model. The better approach when confronted with uncertainty and ambiguity is to use the tools provided by the theory of fuzzy sets, which are appropriate for modeling vague concepts. A fuzzy membership function for solving uncertainty data of a semi-parametric sample selection model is introduced as a solution to the problem.

The sample selection model is a combination of the regression and probit models. The models are usually estimated by Heckman’s two-step estimator. However, Heckman’s two-step estimator often performs poorly. In the context of the parametric method, Monte Carlo simulations are studied. The goal is to simulate and test as early as possible so that we can anticipate the problem of the accuracy of a model. The best approach is to take advantage of the tools provided by the theory of fuzzy sets. It appears very suitable for modeling vague concepts. It is difficult to determine some of the criteria and arrive at a quantitative value. Fuzzy sets theory and its properties through the concept of fuzzy number. The fuzzy function used for solving uncertain of a parametric sample selection model. Estimates from the fuzzy are used to calculate some of equation of the sample selection model. Finally, estimates of the Mean, Root Mean Square Error (RMSE) and the other estimators can be obtained by Heckman two-step estimator through iteration from some parameters and some of values.

Geometric modeling involving uncertainty of data is the major problem in CAGD. By using the theory of fuzzy set and its properties, the issues of uncertainty can be solved through the concept of fuzzy numbers. We apply fuzzy numbers as uncertainty data and defined a new kind of fuzzy control points. With this type of points we then introduced a fuzzy Bezier curve and fuzzy B-spline. By these definitions, we construct a curve of such fuzzy spline and given an example of fuzzy Bezier curve and fuzzy B-spline in the context of CAGD at the end of this concept papers.

It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. The additional structure can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one‐dimensional line segment in the parameter space, and we demonstrate that this line segment can be short in practice. We show that the identified set is sharp when the model is correct and empty when there exist no parameter values that make the sample selection model consistent with the data. We also provide non‐sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.

Summary In sample selection models, a treatment can influence the observed outcome in two ways: by affecting the binary selection or participation decision and by affecting the latent outcome. The former is called the ‘extensive margin effect’, and the latter is called the ‘intensive margin effect’. Despite the popularity of these effects, however, the intensive margin effect does not have the traditional causal parameter interpretation because it is conditioned on the selecting or participating decision, which is a post-treatment variable possibly affected by the treatment. The paper presents a causal framework for sample selection models and introduces various subpopulation effects. It is difficult to separate such effects in general; however, in certain popular models (nearly parametric sample selection models, semiparametric ‘independence models’, semiparametric zero-censored models and ‘polynomial approximation’ models) with linear latent equations, they are separately identified and easily estimable with probit and least squares estimators. An empirical analysis is provided to illustrate these causal effects in sample selection models.

It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. We find that the additional structure in the classical sample selection model can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one-dimensional line-segment in the parameter space, and we demonstrate that this line segment can be short in principle as well as in practice. We show that the identified set is sharp when the model is correct and empty when model is not correct. We also provide non-sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.

In our real-life problems, there are situations with the uncertain data that may not be successfully modelled by the classical mathematics. There are some mathematical tools for dealing with uncertainties—they are fuzzy set theory introduced by Zadeh [10], rough set theory introduced by Pawlak [7], and soft set theory initiated by Molodtsov [5]. In this chapter, we recall some basic notions relevant to our Chaps. 2– 10, such as fuzzy sets, intuitionistic fuzzy sets, interval fuzzy sets, soft set, fuzzy soft sets, rough sets, fuzzy rough sets, fuzzy rough soft set, and others.

A set consists of elements sharing the same property. This property is essential for setting set boundaries. Hence, the following question appears: Can we always unambiguously define these boundaries? The answer is, no. We can unambiguously define a set containing all municipalities belonging to the district D. Municipality either belongs to the district D (from administrative point of view), or does not belong. However, for the set expressing high distance we cannot clearly define sharp boundary to distinguish high from non-high distance. This section begins with the classical sets in order to smoothly continue to fuzzy sets. Next, relevant properties and operations of fuzzy sets are discussed. Further, the concept of fuzzy number, as a subcategory of fuzzy sets, is explained. Fuzzy sets and many-valued logics are basis for fuzzy logic. Fuzzy logic facilitates commonsense reasoning with imprecise predicates expressed as fuzzy sets. In the second part fuzzy conjunction, negation, disjunction, implication and quantifiers are examined. Mentioned concepts are used throughout the book.

The purpose of this paper is to present a performance evaluation model for forecasting production efficiency for Decision Making Units (DMUs). This model is based on the fuzzy set theory, fuzzy regression, and the DEA model. A stochastic DEA approach has been proposed and used widely to analyze the performance of the uncertain input or output data, but this approach requires large data samples and assumes probability distribution in measurement error terms. The concept of fuzzy numbers was seldom considered, although the stochastic DEA approach can be used for prediction. This paper integrates fuzzy regression and fuzzy DEA as one model. The results of this research show that the model developed in this paper is applicable to evaluate the "reform policy for passenger loading operations" currently undertaken by the Taipei City Bus Company. Based on this study, the integration of fuzzy numbers, fuzzy regression, and the DEA model can be applied to evaluate production efficiency of the city bus company for the short-term future.

Problem statement: It is well known that, the standard approach to estimating a sample selection models shows an inconsistent estimation results if the distributional assumption are incorrect. Approach: An important progress in the last decade to develop an alternative to overcome the deficiency is through the used of semi-parametric method. However, the usage of semi-parametric approach still does not cover the deficiency of the model. Results: We introduced a fuzzy membership function for solving uncertainty data of a sample selection model and employed method for sample selection models, that is, the two-step estimators to estimate a model of the so-called the self-selection decision. Fuzzy Parametric of Sample Selection Model (FPSSM) is builds as a hybrid to the conventional parametric sample selection model. Conclusion/Recommendations: The result showed that as a whole, the FPSSM give a better estimate and consistent when compared to the Parametric of Sample Selection Model (PSSM). This application demonstrate that the proposed fuzzy modeling approach was quite reasonable and provides an important and significant finding compared with conventional method especially in terms of estimation and consistency.

In 2013, B.C. Cuong and V. Kreinovich introduced the concept of picture fuzzy set [1], which is a directly generalization concept of the Zadeh's fuzzy sets and Atanassov's intuitionistic fuzzy sets. Picture Fuzzy Sets Theory and Picture Fuzzy Logic [5] was received many developments with applications in computational intelligent problems (see [5] and [9-19]). A combination of picture fuzzy sets with Molodsov's soft sets [26] are Picture Fuzzy Soft Sets was given in section 5 of [1]. Rough set was introduced by Z. Pawlak in 1982 [4], which becomes a usefully mathematical tool for data mining, especially for redundant and uncertain data. The combination of fuzzy set and rough set theories lead to various models and receive many interesting results. Recently in the NICS 2017 [9] we defined the picture fuzzy rough sets for the soft computing problems. This paper is devoted to the new sets - Picture Fuzzy Rough Soft Sets and the a concept "Picture Fuzzy Dynamic Systems", which could be important branches of picture fuzzy systems and applications.

Comparison of semiparametric and parametric methods for estimating copulas

Conditional independence in sample selection models

Tests of specification for parametric and semiparametric models

A semiparametric likelihood method is proposed for the estimation of sample selection models. The method is a two-step semiparametric scoring estimation procedure based on an index restriction and kernel estimation. Under some regularity conditions, the estimator is square-root n-consistent and asymptotically normal. The estimator is also asymptotically efficient in the sense that its asymptotic covariance matrix attains the semiparametric efficiency bound under the index restriction. For the binary choice sample selection model, it also attains the efficiency bound under the independence assumption. This method can be applied to the estimation of general sample selection models.