weighted least square
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Propagated electromagnetic signal over the cellular radio communication channels and interfaces are usually highly stochastic and complex with unequal noise variation pattern. This is due to multipath nature of the propagation channels and diverse radio propagation mechanisms that impact the signal strength at the receiver en-route the transmitter, and verse versa. This also makes measurement, predictive modeling and estimation based analysis of such signal very challenging and complex as well. One important and popular parametric modelling and estimation technique in mathematics and engineering science, especially for signal processing applications is the least square regression (LSR). The dominance use and popularity of the LSR approach may be attributed to its simplified supporting theory, relatively fast application procedure and ubiquitous application packages. However, LSR is known to be very sensitive to outliers and unusual stochastic signal data. In this work, we propose the application of weighted least square regression method for enhanced propagation practical field strength estimation modelling over cellular radio communication networks interface. The signal data was collected from a commercial LTE networks service provider. Also, we provide statistical computational analyses to compare the resultant estimation outcome of the weighted least square and the standard least approach. From the result, it is found that the WLSR approach is reliably better the most popular standard least square method. The significance and academic of value of this paper is that our proposed and implemented WLSR method can used as replacement of the standard LSR approach for robust mobile signal processing of future communication system networks.

Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable’s relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation.

Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.