Hybrid exponential-logarithmic estimators for population mean using robust regression techniques

In survey sampling, the accurate estimation of the population mean is often challenged by the presence of outliers in the data. Traditional estimators may become inefficient or biased under such conditions. This study proposes a novel class of estimators for the population mean under simple random sampling (SRS) by incorporating robust regression methods that are less sensitive to outliers. The proposed estimators are formulated using robust regression methods, such as Hample-M, Huber-M, Tukey-M, Huber-MM, least trimmed squares (LTS), and least median of squares (LMS) to improve resistance against atypical observations while preserving efficiency under ideal conditions. The theoretical properties such as bias and mean square error (MSE) of the proposed estimators are examined. Through extensive simulation study and empirical application to real survey data, the proposed estimators demonstrate superior performance over the existing robust regression based estimators in terms of minimum relative mean square error (RMSE) and maximum relative efficiency (RE). The findings suggest that the proposed estimators provide a viable alternative for practitioners dealing with the data contaminated with outliers in sample surveys.

Applications and algorithms for least trimmed sum of absolute deviations regression

Under a semiparametric regression model, a family of robust estimates for the regression parameter is proposed. The least trimmed squares (LTS) method is a statistical technique for fitting a regression model to a set of points. Given a set of n observations and the integer trimming parameter , the LTS estimator involves computing the hyperplane that minimizes the sum of the smallest h squared residuals. The LTS estimator is closely related to the well-known least median squares (LMS) estimator in which the objective is to minimize the median squared residual. Although LTS estimator has the advantage of being statistically more efficient than LMS estimator, the computational complexity of LTS is less understood than LMS. Here, we develop an algorithm for the LTS estimator. Through a Monte Carlo approach, performance of the robust estimates is compared with the classical ones in semiparametric regression models.

This study aimed at enhancing the efficiency of Zaman estimators using exponential transformation technique. A new class of estimators was obtained using the concept of Bahl and Tuteja. The bias and mean squared error (MSE) of the new class of suggested estimators was derived up to second degree approximation. The empirical study through simulations was conducted using Normal, exponential, gamma, chi‐square and beta distributions under robust regression methods (Huber‐M, Huber‐MM, LTS (least trimmed squares) and LMS (least median of squares)) and the results revealed that proposed estimators were more efficient.

Least trimmed squares (LTS) provides a parametric family of high breakdown estimators in regression with better asymptotic properties than least median of squares (LMS) estimators. We adapt the forward search algorithm of Atkinson (1994) to LTS and provide methods for determining the amount of data to be trimmed. We examine the efficiency of different trimming proportions by simulation and demonstrate the increasing efficiency of parameter estimation as larger proportions of data are fitted using the LTS criterion. Some standard data examples are analysed. One shows that LTS provides more stable solutions than LMS.

Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood

Weak-perspective structure from motion for strongly contaminated data

It is not unusual to have outliers and multicollinearity simultaneously in censored semiparametric linear models. In this paper for dealing with multicollinearity and outliers we introduce a family of robust censored Liu and non-Liu type of estimates for the regression parameter when some non-stochastic linear restrictions are imposed. The proposed robust estimators is based on least trimmed squares (LTS) method. The efficiency of LTS estimator statistically is more than the well-known least median squares (LMS) estimator. Unfortunately the computational complexity of LTS is less well understood than that of LMS in which the objective is to minimize the median squared residual. Here, we provide the robust estimators for linear and non-linear parts of the censored model based on robust shrinkage Liu estimators. The performance of proposed estimators compared to ordinary estimators numerically is evaluated by Monte Carlo simulation studies. We further illustrate the our procedures by an application.

Using symmetry in robust model fitting

Positive-breakdown regression by minimizing nested scale estimators

This study compares the ability of different robust regression estimators to detect and classify outliers. Well-known estimators with high breakdown points were compared using simulated data. Mean success rates (MSR) were computed and used as comparison criteria. The results showed that the least median of squares (LMS) and least trimmed squares (LTS) were the most successful methods for data that included leverage points, masking and swamping effects or critical and concentrated outliers. We recommend using LMS and LTS as diagnostic tools to classify outliers, because they remain robust even when applied to models that are heavily contaminated or that have a complicated structure of outliers.

Classical regression type estimators in survey sampling often suffer from inefficiency and instability in the presence of outliers and model deviations. To address these issues, this study proposes a a new class of regression-type estimators for finite population mean using Generalized M-estimation (GM-estimation) framework within both simple random sampling without replacement (SRSWOR) and stratified double sampling designs. The proposed Mallows-GM, Schweppes-GM and SIS-GM estimators incorporate adaptive weighting schemes that jointly mitigate the effect of vertical outliers and high-leverage points. Analytical expressions for bias and mean square error (MSE) are derived under first-order approximations. Extensive Monte Carlo simulations and sensitivity analysis demonstrate that GM-type estimators achieve substantially higher efficiency and robustness than both ordinary least squares and Huber-based counterparts, with efficiency gains exceeding 150% under heavy contamination. The estimators also exhibit strong stability across varying tuning parameters and correlation structures. Overall, the proposed methodology offers a robust and efficient alternative for mean estimation in survey sampling, particularly suitable for contaminated and heterogeneous data environments.

<span lang="EN">Robust regression is a regression method used when the remainder's distribution is not reasonable, or there is an outreach to observational data that affects the model. One method for estimating regression parameters is the Least Squares Method (MKT). The method is easily affected by the presence of outliers. Therefore we need an alternative method that is robust to the presence of outliers, namely robust regression. Methods for estimating robust regression parameters include Least Trimmed Square (LTS) and Least Median Square (LMS). These methods are estimators with high breakdown points for outlier observational data and have more efficient algorithms than other estimation methods. This study aims to compare the regression models formed from the LTS and LMS methods, determine the efficiency of the model formed, and determine the factors that influence the production of community oil palm in Langkat District in 2018. The results showed that in testing, the estimated model of the regression parameters showed the same results. Compared to the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018</span>

Robust ridge estimator in restricted semiparametric regression models

Although the least median of squares (LMedS) method and the least trimmed squares (LTS) method are said to hive a high breakdown point (50%), they can break down at unexpectedly lower percentages of outliers when those outliers are clustered. In this paper, we investigate the breakdown of LMedS and the LTS when a large percentage of clustered outliers exist in the data. We introduce the concept of symmetry distance (SD) and propose an improved method, called the least trimmed symmetry distance (LTSD). The experimental results show the LTSD gives better results than the LMedS method and the LTS method particularly when there is a large percentage of clustered outliers and/or a large standard variance in the inlier population.