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Regression ratio mean estimators of a study variable Y are defined as the coefficients provided by the ordinary least-squares regression of Y on a given auxiliary variable X. They can be improved by using the coefficient of variation and the coefficient of kurtosis of X. The influence of outliers on the estimates of the population mean of Y is neutralized by calculating robust regression coefficients, obtained by the method of either least absolute deviations, Huber-M, Huber-MM, Hampel-M, Tukey-M, or adjusted least squares. These robust coefficients are used to estimate the population mean of Y under simple random sampling. Extension to systematic sampling—which is a probability sampling in which every element of the population has equal probability of inclusion to be drawn—using the coefficients provided by quantile regression—whose coefficients result from the minimization of the sum of absolute deviations rather than from the square deviations from the regression line—requires ratio estimators of the population mean of Y. The mean square errors of these estimators are expressed analytically. If the quantile regression coefficient is greater than the ratio of the covariance between the study and the auxiliary variables to the variance of the auxiliary variable minus a function of the mean or the coefficient of variation, skewness, or kurtosis of X and Y , then the proposed robust quantile regression mean estimator of Y is more efficient than the ratio estimators in the presence of outliers under systematic sampling. The reason is that these estimators only use regression coefficients and not the ratio between the population mean and sample means of the auxiliary variable X. The aforementioned condition occurs with the values of the case study. For empirical data of 176 forest strips, the proposed estimate of the volume of timber is over 30% more efficient than the ratio estimates based on quantile regression coefficients. [ABSTRACT FROM AUTHOR]

The presence of extreme values in a data set reduces the efficiency of variance estimators. L-moments are based on the ordered form of a random variable to estimate the variance of the population. The two variance estimators are used for calibration to a stratified random sampling design and relying on an auxiliary variable. The proposed estimators use the properties of L-moments, such as the L-mean, also called L-location, the L-standard deviation, also called L-scaling, and the L-coefficient of variation, which is a measure of variation. The use of these properties allows for providing better estimators. A simulation proves the better efficiency of these estimators. [ABSTRACT FROM AUTHOR]

Variance is one of the most vital measures of dispersion widely employed in practical aspects. A commonly used approach for variance estimation is the traditional method of moments that is strongly influenced by the presence of extreme values, and thus its results cannot be relied on. Finding momentum from Koyuncu's recent work, the present paper focuses first on proposing two classes of variance estimators based on linear moments (L-moments), and then employing them with auxiliary data under double stratified sampling to introduce a new class of calibration variance estimators using important properties of L-moments (L-location, L-cv, L-variance). Three populations are taken into account to assess the efficiency of the new estimators. The first and second populations are concerned with artificial data, and the third populations is concerned with real data. The percentage relative efficiency of the proposed estimators over existing ones is evaluated. In the presence of extreme values, our findings depict the superiority and high efficiency of the proposed classes over traditional classes. Hence, when auxiliary data is available along with extreme values, the proposed classes of estimators may be implemented in an extensive variety of sampling surveys. [ABSTRACT FROM AUTHOR]

One of the most significant topics in statistics is the issue of variance estimation. In the research literature, various variance estimators are constructed based on traditional moments that are particularly affected by the presence of extreme values. Therefore, the focus of this paper is on the adoption of L-Moments features to propose some new calibration estimators for a variance with some suitable calibration constraints under stratified random sampling. The empirical efficiency of proposed estimators is calculated through simulation based on Covid-19 pandemic data for the period January 22, 2020, up to August 23, 2020. The results indicate that the proposed estimators are superior and highly efficient compared to the existing traditional estimator when the data includes extreme values. [ABSTRACT FROM AUTHOR]

Median ranked set sampling is a sampling procedure used to estimate the population mean when the variable of interest is difficult or costly to measure. Two estimators for the population mean based on the minimum and maximum values of the auxiliary variable are built upon a successive use of ranks, second raw moments, and the linearly transformed auxiliary variable. The biases and the mean square errors of the estimators are derived. The proposed estimators under median ranked set sampling have higher efficiencies than the ratio, regression, difference-cum-ratio, and exponential estimators. [ABSTRACT FROM AUTHOR]

Variance is one of themost important measures of descriptive statistics and commonly used for statistical analysis. The traditional second-order central moment based variance estimation is a widely utilized methodology. However, traditional variance estimator is highly affected in the presence of extreme values. So this paper initially, proposes two classes of calibration estimators based on an adaptation of the estimators recently proposed by Koyuncu and then presents a new class of L-Moments based calibration variance estimators utilizing L-Moments characteristics (L-location, Lscale, L-CV) and auxiliary information. It is demonstrated that the proposed L-Moments based calibration variance estimators are more efficient than adapted ones. Artificial data is considered for assessing the performance of the proposed estimators. We also demonstrated an application related to apple fruit for purposes of the article. Using artificial and real data sets, percentage relative efficiency (PRE) of the proposed class of estimators with respect to adapted ones are calculated. The PRE results indicate to the superiority of the proposed class over adapted ones in the presence of extreme values. In this manner, the proposed class of estimators could be applied over an expansive range of survey sampling whenever auxiliary information is available in the presence of extreme values. [ABSTRACT FROM AUTHOR]

It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data. To solve the problem of typical observations when the covariates of the nonparametric component are functional, the robust estimates for the regression parameter and regression operator are introduced. The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic. We use the Nearest Neighbors procedure (kNN) to construct the kernel estimator of the proposed robust model. Under some regularity conditions, we state consistency results for kNN functional estimators, which are uniform in the number of neighbors (UINN). Furthermore, a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach. [ABSTRACT FROM AUTHOR]

This paper examines the causal relationship between oil prices and the Gross Domestic Product (GDP) in the Kingdom of Saudi Arabia. The study is carried out by a data set collected quarterly, by Saudi Arabian Monetary Authority, over a period from 1974 to 2016. We seek how a change in real crude oil price affects the GDP of KSA. Based on a new technique, we treat this data in its continuous path. Precisely, we analyze the causality between these two variables, i.e., oil prices and GDP, by using their yearly curves observed in the four quarters of each year. We discuss the causality in the sense of Granger, which requires the stationarity of the data. Thus, in the first Step, we test the stationarity by using the Monte Carlo test of a functional time series stationarity. Our main goal is treated in the second step, where we use the functional causality idea to model the co-variability between these variables. We show that the two series are not integrated; there is one causality between these two variables. All the statistical analyzes were performed using R software. [ABSTRACT FROM AUTHOR]