The use of relevant information from auxiliary variable at the estimation stage and design stage to obtain reliable and efficient estimate is a common practice is a sample survey. But situations arise when the available auxiliary information are attribute in nature. There are some existing estimators based on auxiliary attribute in literature, however, they are less efficient when the bi-serial correlation between the study variable and auxiliary attribute is negative. Also, some depend on an unknown parameter of the study variable (Cy) which makes their applicability of the estimators in real life situations not possible unless if the value is estimated using a large sample which requires additional resources. In this work, the concept of regression base estimator was used to obtain estimators that are independent of unknown population parameter of the study variable and applicable for both negative and positive correlations. The properties (Biases and MSEs) of the modified estimators were derived up to the first order of approximation using Taylor series approach. The efficiency conditions of the proposed estimation over the existing estimator considered in the study were established. The empirical studies were conducted using both existing population parameters and stimulation to investigate the efficiency of the proposed estimators over the efficiency of the existing estimators. The results revealed that the proposed estimators have minimum MSEs and higher PREs among all the competing estimators. These imply that the proposed estimators are more efficient and can produce better estimate of the population mean compared to other existing estimators considered in the study.
The aim of this paper is to test the applicability of Co-Kriging (CK) on the study of the changing climate in Northern Nigeria. Indices were derived from climatic variables (Rainfall and Temperature) obtained from Nigerian Meteorological Agency (NIMET) and remotely sensed data covering the period from 1981 to 2010 in the form of Normalised Difference Vegetation Index (NDVI) data derived from National Oceanic Atmospheric Administration-Advanced Very High Resolution Radiometer (NOAA-AVHRR). Because of the strong relationship between NDVI and Rainfall, CK method of data interpolation was tested with R-Statistical software. A digital elevation model (DEM) of the study area at 90-meter spatial resolution was used as a supplement in an overlay procedure using the IDRISI Remote sensing and GIS software so as to derive the correct altitude values of the Met stations for comparison with the coefficient of variation of the rainfall dataset. Results from the derived CK prediction maps showed that there are high variability in NDVI and rainfall across the time-series. Furthermore, spatial average variability in the growing season rainfall was 60% with a mean temperature of 4% although coefficient of variation in rainfall for the individual climatic station's ranged from 18.15 to 60.98 per cent. While the highest coefficient of variation in temperature for the entire time series (1981-2010) was located around Katsina area, the lowest was located around Minna. From the results of this analysis it is evident that the higher prediction variance values particularly for vegetation NDVI and rainfall are located in the southern part of the study area particularly around Kaduna, Minna, and Jos as compared to the northern part of the study area falling around Maiduguri, Sokoto and Katsina which indicated relatively lower prediction values. However, further studies should also be undertaken using the raster NDVI dataset in a GIS environment to buttress our view that there were changes in the general ecosystems within the study area as result of climatic impact.
Human-assisted surveys, such as medical and social science surveys, are frequently plagued by non-response or missing observations. Several authors have devised different imputation algorithms to account for missing observations during analyses. Nonetheless, several of these imputation schemes' estimators are based on known population meanof auxiliary variable. In this paper, a new class of almost unbiased imputation method that uses as an estimate of is suggested. Using the Taylor series expansion technique, the MSE of the class of estimators presented was derived up to first order approximation. Conditions were also specified for which the new estimators were more efficient than the other estimators studied in the study. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.
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. K E Y W O R D Sefficiency, exponential type estimators, robust regression, outliers INTRODUCTIONRatio, product and regression estimators had undergone series of modification and improvement by several authors using different techniques like power transformation, exponential transformation, linear combination and so forth. Bahl and Tuteja 5 were the first to utilize exponential transformation on ratio and product estimators and thereafter several authors like Singh and Audu, 15 Audu and Singh 4 , Muili et al. 9 , Ishaq et al. 7 , Audu et al. 3 , Singh et al. 14 , Olayiwola et al. 12 , Olayiwola et al. 11 and Audu et al. 2 have used similar approach to enhance the efficiency of estimators of population parameters. Similarly, supplementary variables associated with the study variables have been identified to be helpful in improving the efficiency of ratio, product and regression estimators both at planning and estimation stages. However, the efficiency of these estimators may be affected by data which are characterized by outliers or leverages. Some of the techniques for detecting outliers include Boxplot, Stem and Leaf plot, P-P plot, Euclidean distance, Mahalanobis distance, Hosmer and Lemeshow goodness-of-fit test, Cook's 𝐷 𝑖 . 1 To address the issue of outliers' effects, authors like Kadilar and Cingi 8 , Zaman and Bulut 18 and Zaman 19 have suggested several robust ratio estimators. The current study intends to utilize exponential transformation on Zaman 19 estimators to obtain new estimators with higher efficiency.Zaman and Bulut 18 extended the work of Kadilar and Cingi 8 by inclusion of some slopes' coefficient of other robust regression estimators like Tukey-M, 16 Hampel-M, 6 LMS 13 and LAD 10 in addition to Huber-M 20 used by Kadilar and Cingi 8 and this inclusion leads to new estimators of population mean in the presence of outliers as given below:
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