semiparametric approach
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Regression modeling with a semiparametric approach is a combination of two approaches, namely the parametric regression approach and the nonparametric regression approach. The semiparametric regression model can be used if the response variable has a known relationship pattern with one or more of the predictor variables used, but with the other predictor variables the relationship pattern cannot be known with certainty. The purpose of this research is to examine the estimation form of the semiparametric spline truncated regression model. Suppose that random error is assumed to be independent, identical, and normally distributed with zero mean and variance , then using this assumption, we can estimate the semiparametric spline truncated regression model using the Maximum Likelihood Estimation (MLE) method.  Based on the results, the estimation results of the semiparametric spline truncated regression model were obtained  p=(inv(M'M)) M'y 

Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi- and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.

Informality is a common problem in Colombia, with almost 50 percent of the workers employed in this sector. This may be a solution for unemployment, but it is a lose/lose game unless the individuals have a comparative advantage in the informal sector. This article uses information from the Colombian Great Integrated Household Survey (GIHS) to analyze the wage gap between formal and informal urban sectors in two different periods, 2008:4 and 2017:4, using a semiparametric approach. Kernel density functions by groups are estimated; counterfactuals are generated by weighting wages of informal sector workers by their probability of working in the formal sector, to estimate how much an informal sector worker could make if treated as formal, according to his characteristics. The results indicate that only some groups (self-employed and some entrepreneurs) are better off if formalized.

This paper proposes a new approach to examine the relationship between CO2 emissions and economic developing. In particular, we propose to test the Environmental Kuznets Curve (EKC) hypothesis for a panel of 24 OECD countries and 32 non-OECD countries by developing a more flexible estimation technique which enables to account for functional form misspecification, cross-sectional dependence, and heterogeneous relationships among variables, simultaneously. We propose a new nonparametric estimator that extends the well-known Common Correlated Effect (CCE) approach from a fully parametric framework to a semiparametric panel data model. Our results corroborates that the nature and validity of the income–pollution relationship based on the EKC hypothesis depends on the model assumptions about the functional form specification. For all the countries analyzed, the proposed semiparametric estimator leads to non-monotonically increasing or decreasing relationships for CO2 emissions, depending on the level of economic development of the country.

This paper is the first to study a comparatively new Environmental Kuznets Curve which traces empirically the relationship between environmental abatement and real GDP. Our model is a partial linear semi parametric model that allows for two way fixed effects to eliminate the bias arising from two sources. We use data for recycling and real GDP, for fifty states of the United States for the years between 1988 and 2017. We find evidence that this relationship is characterized by an increasing curve which confirms the existence of a J curve, a finding that agrees with the predictions from recent theoretical models.