A modified ratio-product estimator of population mean using some known parameters of the auxiliary variable

The estimation of population mean is one of the challenging aspects in sampling theory and population study and much effort has been vigorously employed to improve the precision of estimates. In this research work, a modified ratio-product estimator of population mean Y of the study variable Y using median and coefficient of variation of the auxiliary variabl X , in simple random sampling scheme is proposed. The expression of bias and MSE of the proposed estimator have been obtained under large sample approximation, asymptotically optimum estimator (AOE) is identified with its approximate MSE formula. Estimator based on “estimated optimum values” was also investigated. Theoretical and empirical comparison of proposed estimator with some other ratio and product estimators justified the performance of the proposed estimators. A minimum of 20 percent reduction in the MSE were observed from each of the existing estimators considered. It is found that the proposed estimator were uniformly better than all other modified ratio and product estimators and thus most preferred over the existing estimators for the use in practical application.Keywords: Finite population mean, bias, mean square error, auxiliary variable, optimum estimator, study variabl

Applications of Some Robust Statistics in Forestry.

All statistical procedures are based on a set of assumptions, such as normality, independence and linearity. In practical applications, these assumptions can rarely be satisfied completely. Deviation from classical parametric assumptions may result in loss of efficiency or even lead to misleading conclusions. Robust statistics that have been extensively studied in the past two decades provide alternatives to deal with such problems. This research was designed to investigate the applicability of robust estimation of population means and robust linear regression in forestry. Five robust estimators, Huber\u27s minimax estimator, Hampel\u27s three parameter redescending estimator, Andrew\u27s wave estimator, Tukey\u27s biweight estimator, and sample median were examined for their performance in estimating population means. Simulations on four families of distributions, beta, gamma, lognormal, and Weibull, suggested that the five robust estimators have a bias problem in estimating means of skewed populations. Analyses of simulated data revealed that magnitudes of robust estimator bias were closely related to a proposed robust sample skewness measure, Skew\sb{\alpha}. Regression models were developed to predict bias of the five robust estimators from Skew\sb{\alpha}. The predicted bias was then used in constructing a bias corrected robust estimator from each of the five estimators. The modified estimators were evaluated against corresponding original estimators and the sample mean on simulated data from four families of distributions and also on a forestry data set. The bias-corrected robust estimators were better than the original estimators in terms of bias and mean square error. Two robust linear regression procedures, least median of squares and least trimmed squares, were used to fit two individual tree volume equations on nine data sets and two yield models on one data set. The two robust regressions were evaluated against ordinary least squares based on prediction capabilities. For most of the data sets the robust procedures and least squares method produced similar prediction error values. For data sets that contained extreme outliers, the two robust procedures yielded smaller prediction error values than least-squares estimation

Maximum Pseudo-likelihood Estimation of Copula Models and Moments of Order Statistics

It has been shown that despite being consistent, and in some cases efficient, maximum pseudo-likelihood (MPL) estimation for copula models overestimates the level of dependence especially for small samples with low level of dependence. This is especially relevant in finance and insurance applications when data is scarce. We show that the canonical MPL method uses the mean of order statistics, and we propose to use the median or the mode instead. We show that the MPL estimators proposed are consistent and asymptotically normal. In a simulation study, we compare the finite sample performance of the proposed estimators with that of the original MPL and the inversion method estimators based on Kendall's tau and Spearman's rho. In our results the modified MPL estimators, especially the one based on the mode of the order statistics, have better finite sample performance both in terms of bias and mean square error. An application to general insurance data shows that the level of dependence estimated between different products can vary substantially with the estimation method used

Modified ratio-product estimator of population mean in the presence of median and coefficient of variation of the auxiliary variable in stratified random sampling

For the past decades, the estimation of population mean is one of the challenging aspects in sampling survey techniques and much effort has been employed to improve the precision of estimates. In this research work, we proposed a modified ratio-product estimator of population mean of the variable of interest using median and coefficient of variation of the auxiliary variable in stratified random sampling scheme. The expression of bias and MSE of the proposed estimator have been obtained under large sample approximation, asymptotically optimum estimator (AOE) is identified with its approximate MSE formula. Estimator based on “estimated optimum values” was also investigated. Theoretical and empirical comparison of proposed estimator with some other ratio and product estimator justified the performance of the proposed estimator. There is a minimum of 15 percent reduction in the MSE from each of the existing ratio and product estimators considered. Thus most preferred over the existing estimators for the use in practical application.Keywords: bias, mean square error, auxiliary variable, optimum estimator, stratified random sampling, study variabl

A nonparametric model-based estimator for the cumulative distribution function of a right censored variable in a finite population

In survey analysis, the estimation of the cumulative distribution function (cdf) is of great interest: it allows for instance to derive quantiles estimators or other non linear parameters derived from the cdf. We consider the case where the response variable is a right censored duration variable. In this framework, the classical estimator of the cdf is the Kaplan-Meier estimator. As an alternative, we propose a nonparametric model-based estimator of the cdf in a finite population. The new estimator uses auxiliary information brought by a continuous covariate and is based on nonparametric median regression adapted to the censored case. The bias and variance of the prediction error of the estimator are estimated by a bootstrap procedure adapted to censoring. The new estimator is compared by model-based simulations to the Kaplan-Meier estimator computed with the sampled individuals: a significant gain in precision is brought by the new method whatever the size of the sample and the censoring rate. Welfare duration data are used to illustrate the new methodology.Comment: 18 pages, 5 figure

Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion

The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate inferences about the data's mean in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's Inequality. We now propose growth estimators of the Negative Binomial mean. Under high dispersion, zero values are likely to be overrepresented in the data. A growth estimator constructs a Normal-style confidence interval by effectively removing a small, pre--determined number of zeros from the data. We propose growth estimators based upon multiplicative adjustments of the sample mean and direct removal of zeros from the sample. These methods do not require estimating the nuisance dispersion parameter. We will demonstrate that the growth estimators' confidence intervals provide improved coverage over a wide range of parameter values and asymptotically converge to the sample mean. Interestingly, the proposed methods succeed despite adding both bias and variance to the Normal approximation

Empirical comparison of the performance of location estimates of fuzzy number-valued data

© Springer Nature Switzerland AG 2019. Several location measures have already been proposed in the literature in order to summarize the central tendency of a random fuzzy number in a robust way. Among them, fuzzy trimmed means and fuzzy M-estimators of location extend two successful approaches from the real-valued settings. The aim of this work is to present an empirical comparison of different location estimators, including both fuzzy trimmed means and fuzzy M-estimators, to study their differences in finite sample behaviour.status: publishe