Comparison of Some Semi-parametric Methods in Partial Linear Single-Index Model

The research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used

A Literature Review of Semi-functional Partial Linear Regression Models

Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

Research on the Calculation Method of Harmonic Contribution in the Case of Dominant System-side Harmonics

Existing methods for quantifying the responsibility of harmonic sources assume a dominant user side and use a harmonic source equivalence circuit to calculate the equivalent system impedance and background harmonic voltage, which in turn assesses the harmonic contribution of that source to the bus of concern. For users who actively participate in harmonic governance, it is very important to evaluate the responsibility of injecting harmonics into users. This paper assumes system-side is dominant, constructs a partial linear regression model and a constant impedance model, and tracks the regression error. The equivalent fundamental impedance is doubly screened to calculate the harmonic impedance for the corresponding number of times, which in turn quantifies the harmonic voltage duty. The results of simulation and the analysis of measured data show that this method has simple calculation model, small regression error (0.0037), high accuracy and practical engineering significance.

The Demand Model of App-Based Transportation Household Scale in Semarang, Indonesia

In the development of transportation systems, Application-Based Transportation is an innovation to adapt to technological advances. It offers users an alternative mode that is cheap, easy, and flexible according to their needs. The Application-based travel demands can be seen from its socio-economic and travel characteristics. In Indonesia, previous studies have concentrated on study areas on a city scale, with diverse land use classifications not only on the residential area which is the most users of app-based transportation. The modelling results in this study were obtained from spatial simulation and partial linear regression analysis with the T-test as the final stage of analysis. As a result, demand for App-Based Transportation is affected by two factors which include age and travel costs. They are inversely proportional to the frequency of travel. In this case, this mode is mostly used by the population with young age and low cost of travel. Also, this mode is only used on short-distance trips and trips during rush hour in the morning. During the afternoon rush hour, the trip is transferred to public transportation, which has a lower cost. Therefore, this study aims to determine the application-based transportation demand model for household units in Tlogosari, Semarang, Indonesia. An additional in-depth study is needed to be carried out on the degree of motorcycle safety to improve services.

INJECTIVE LINEAR TRANSFORMATIONS WITH EQUAL GAP AND DEFECT

Let V be an infinite-dimensional vector space over a field F and let $I(V)$ be the inverse semigroup of all injective partial linear transformations on V. Given $\alpha \in I(V)$ , we denote the domain and the range of $\alpha $ by ${\mathop {\textrm {dom}}}\,\alpha $ and ${\mathop {\textrm {im}}}\,\alpha $ , and we call the cardinals $g(\alpha )={\mathop {\textrm {codim}}}\,{\mathop {\textrm {dom}}}\,\alpha $ and $d(\alpha )={\mathop {\textrm {codim}}}\,{\mathop {\textrm {im}}}\,\alpha $ the ‘gap’ and the ‘defect’ of $\alpha $ . We study the semigroup $A(V)$ of all injective partial linear transformations with equal gap and defect and characterise Green’s relations and ideals in $A(V)$ . This is analogous to work by Sanwong and Sullivan [‘Injective transformations with equal gap and defect’, Bull. Aust. Math. Soc.79 (2009), 327–336] on a similarly defined semigroup for the set case, but we show that these semigroups are never isomorphic.