Presence Of Extreme Observations Research Articles

Dual-type quantile regression approach for mean estimation incorporating sampled and non-sampled data

Drawing inspiration from recent advancements in robust mean estimation within finite sampling theory, we introduce a novel dual-type class of mean estimators in a design-based framework. The dual-type class is based on quantile regression and is specifically designed to be effective in the presence of extreme observations. Significantly, it integrates the averages of both sampled observations and non-sampled observations of auxiliary variable. In the initial discussion of this class, it is presumed that the target variable is non-sensitive, signifying its relevance to subjects that respondents do not consider embarrassing when queried directly. In this standard setting, we present specific estimators within the class and determine their theoretical properties. The class's scope broadens to include scenarios where the target variable incorporates sensitive topics, giving rise to nonresponse rates and inaccurate reporting. To alleviate these errors, one can promote respondent cooperation by employing scrambled response methods that obscure the actual value of the sensitive variable. Accordingly, the article delves into discussions on additive methods. Subsequently, a numerical study is conducted using asymmetric data to evaluate the effectiveness of the dual-type class by comparing it with several existing estimators, both in the absence and presence of scrambled responses.

Oil Price Shocks to Foreign Assets and Liabilities in Saudi Arabia under Pegged Exchange Rate

The Saudi economy ought to maintain a significant amount of foreign exchange reserves due to the pegged exchange rate regime. As a hydrocarbon economy, we measure the dynamic response of external assets and liabilities of banks to the international oil price in Saudi Arabia. In the presence of extreme observations, we apply sophisticated frameworks, including cross-quantilograms, quantile-on-quantile and TVP-VAR approaches, to analyze weekly time-series data from 1993 to 2021. Our results from the cross-quantilogram and quantile-on-quantile frameworks demonstrate that foreign assets and liabilities responded asymmetrically to the volatilities of international oil prices under the bullish and bearish states of the market over different memories. The TVP-VAR results indicate that, during the COVID-19 pandemic, the Saudi economy encountered negative net foreign assets, which occurred mainly as a significant plague of international oil prices. Our findings are robust under different estimators.

Compromised imputation based mean estimators using robust quantile regression

Missing information is a typical issue in sampling surveys. The analysts have perceived that statistical inference possibly ruined due to occurrence of non-response. Ratio type regression estimators under simple random sampling (SRS) scheme for estimating the population mean are commonly used when some of the data suffered with the issue of missingness. It is worth noting that this class is based on ordinary least square regression coefficient which is not suitable when extreme values present in the data set. In this research, primarily a modified class of estimators is presented by adapting the idea of Zaman and Bulut. Later on, a class of quantile regression type estimators is defined which is an effective technique in presence of extreme observations. The utilization of quantile regression in the idea of Zaman and Bulut’s work empowered the proposed class of estimators for the estimation of population mean especially for missingness in the data. For mean square error (MSE), the hypothetical equations are also formulated for adapted and proposed estimators, on the basis of three possible cases of missingness. To justify the proposed work these hypothetical innovations are illustrated by the numerical demonstrations.

Complex Survival System Modeling for Risk Assessment of Infant Mortality Using a Parametric Approach.

Pakistan is still one of the five countries contributing to half of the child deaths worldwide and holds a low ratio of infant survival. A high rate of poverty, low level of education, limited health facilities, rural-urban inequalities, and political uncertainty are the main reasons for this condition. Survival models that evaluate the performance of models over simulated and real data set may serve as an effective technique to determine accurate complex systems. The present study proposed an efficient extension of the recent parametric technique for risk assessment of infant mortality to address complex survival systems in the presence of extreme observations. This extended method integrated four distributions with the basic algorithm using a real data set of infant survival without extreme observations. The proposed models are compared with the standard partial least squares-Cox regression (PLS-CoxR), and higher efficiency of these proposed algorithms is observed for handling complex survival time systems for risk assessment. The algorithm is also used to analyze simulated data set for further verification of results. The optimal model revealed that the mother's age, type of residence, wealth index, permission to go to a medical facility, distance to a health facility, and awareness about tuberculosis significantly affected the survival time of infants. The flexibility and continuity of extended parametric methods support the implementation of public health surveillance data effectively for data-oriented evaluation. The findings may support projecting targeted interventions, producing awareness, and implementing policies planned to reduce infant mortality.

Beta rectangular regression models to longitudinal data

In this paper, we propose a new approach for modeling repeated measures restricted to the interval (0,1) (or (a,b), with a<b known real numbers). More specifically, we developed Generalized Estimating Equations, considering beta rectangular marginal distributions, which is more robust than the usual beta distribution, against the presence of extreme observations. Diagnostic tools, including local influence analysis, were also developed. A simulation study was performed, indicating that our estimation algorithm is efficient, in terms of parameter recovery. The results also suggest that our methodology outperformed the usual beta model, for the most of the considered scenarios, indicating an interesting advantage on the estimation of the dispersion parameter. Furthermore, the developed methodology was illustrated through a real data analysis, concerning to an ophthalmic study.

Development of New Robust Optimal Score Function for the Weibull Distributed Error Term in Multilevel Models

A popular robust estimation technique for linear models is the rank-based method as an alternative to the ordinary least square (OLS) and restricted maximum likelihood (REML) in the presence of extreme observations. This method is applied in machine reliability analysis and quantum engineering, especially in artificial intelligence and optimization problems where outliers are commonly observed. This technique is also extended for the multilevel model, where the shape of error distribution contributes a significant role in more efficient estimation. In this study, we proposed the Weibull score function for the Weibull distributed error terms in the multilevel model. The efficiency of the proposed score function is compared with the existing Wilcoxon score function and the traditional method REML via Monte Carlo simulations after adding simulated extreme observations. For small values of shape parameter in Weibull distribution of error term showing the presence of outliers, the Weibull score function was found to be efficient as compared to the Wilcoxon and REML methods. However, for a large value of shape parameter, Wilcoxon score appeared either equally efficient than the Weibull score function. REML is observed least precise in all situations. These findings are verified through a real application on test scores data, with a small value of shape parameter, and the Weibull score function turned out the most efficient.

A Flexible and Robust Approach to Analyze Survival Systems in the Presence of Extreme Observations

Survival systems are difficult to analyze in the presence of extreme observations and multicollinearity. Finding appropriate models that provide a robust description of such survival systems and that address the smooth hazards in the context of covariates can be challenging given the sheer number of possibilities. Survival time algorithms that evaluate the efficiency of models in the presence of extreme observations over different datasets provide an effective tool to identify robust systems. However, the existing algorithms addressing the analysis of survival systems are limited in long-term evaluations. Therefore, an algorithm that can analyze survival time response on high-dimensional complex survival systems having extreme observations is developed which explores large margins dynamically. This algorithm is developed as a conjugate of flexible parametric models and partial least squares to estimate smooth, flexible, and robust functions to extrapolate the survival model in long-term evaluations in the presence of extreme observations. The algorithm is tested and validated using four distributions based on a simulated dataset generated from the Weibull distribution and compared with partial least squares-Cox regression. The comparison shows its flexibility and efficiency in handling different survival systems in the presence of extreme values. The algorithm is also used to analyze four real datasets of breast cancer survival time, each containing seven gene signatures. The coefficients of significant genes for each dataset are estimated. The flexibility in handling various distributions as parametric survival models supports the application of the algorithm to a large variety of different survival problems and represents a robust statistical framework for survival analysis in the presence of extreme observations.

On The Estimation Of The Shape Parameter Of A Symmetric Distribution

The shape parameter of a symmetric probability distribution is often more difficult to estimate accurately than the location and scale parameters. In this paper, we suggest an intuitive but innovative matching quantile estimation method for this parameter. The proposed shape parameter estimate is obtained by setting its value to a level such that the central 1/���� portion of the distribution will just cover all n observations, while the location and scale parameters are estimated using existing methods such as maximum likelihood (ML). This hybrid estimator is proved to be consistent and is illustrated by two distributions, namely Student-t and Exponential Power. Simulation studies show that the hybrid method provides reasonably accurate estimates. In the presence of extreme observations, this method provides thicker tails than the full ML method and protect inference on the location and scale parameters. This feature offered by the hybrid method is also demonstrated in the empirical study using two real data sets.

Robust forecasting of electricity prices: Simulations, models and the impact of renewable sources

In this paper a robust approach to modeling electricity spot prices is introduced. Differently from what has been recently done in the literature on electricity price forecasting, where the attention has been mainly drawn by the prediction of spikes, the focus of this contribution is on the robust estimation of nonlinear SETARX models (Self-Exciting Threshold Auto Regressive models with eXogenous regressors). In this way, parameter estimates are not, or very lightly, influenced by the presence of extreme observations and the large majority of prices, which are not spikes, could be better forecasted. A Monte Carlo study is carried out in order to select the best weighting function for Generalized M-estimators of SETAR processes. A robust procedure to select and estimate nonlinear processes for electricity prices is introduced, including robust tests for stationarity and nonlinearity and robust information criteria. The application of the procedure to the Italian electricity market reveals the forecasting superiority of the robust GM-estimator based on the polynomial weighting function with respect to the non-robust Least Squares estimator. Finally, the introduction of generation from renewable sources in the robust estimation of SETARX processes contributes to the improvement of the forecasting ability of the model.

The Influence of Renewables on Electricity Price Forecasting: A Robust Approach

In this paper a robust approach to modelling electricity spot prices is introduced. Differently from what has been recently done in the literature on electricity price forecasting, where the attention has been mainly drawn by the prediction of spikes, the focus of this contribution is on the robust estimation of nonlinear SETARX models (Self-Exciting Threshold Auto Regressive models with eXogenous regressors). In this way, parameters estimates are not, or very lightly, influenced by the presence of extreme observations and the large majority of prices, which are not spikes, could be better forecasted. A Monte Carlo study is carried out in order to select the best weighting function for Generalized M-estimators of SETAR processes. A robust procedure to select and estimate nonlinear processes for electricity prices is introduced, including robust tests for stationarity and nonlinearity and robust information criteria. The application of the procedure to the Italian electricity market reveals the forecasting superiority of the robust GM-estimator based on the polynomial weighting function respect to the non-robust Least Squares estimator. Finally, the introduction of external regressors in the robust estimation of SETARX processes contributes to the improvement of the forecasting ability of the model.

On the Estimation of the Shape Parameter of a Symmetric Distribution

The shape parameter of a symmetric probability distribution is often more difficult to estimate accurately than the location and scale parameters. In this paper, we suggest an intuitive but innovative matching quantile estimation method for this parameter. The proposed shape parameter estimate is obtained by setting its value to a level such that the central 1-1/n portion of the distribution will just cover all n observations, while the location and scale parameters are estimated using existing methods such as maximum likelihood (ML). This hybrid estimator is proved to be consistent and is illustrated by two distributions, namely Student-t and Exponential Power. Simulation studies show that the hybrid method provides reasonably accurate estimates. In the presence of extreme observations, this method provides thicker tails than the full ML method and protect inference on the location and scale parameters. This feature offered by the hybrid method is also demonstrated in the empirical study using two real data sets.

Robust regression in monthly business survey

There are many sample surveys of populations that contain outliers (extreme values). This is especially true in business, agricultural, household and medicine surveys. Outliers can have a large distorting influence on classical statistical methods that are optimal under the assumption of normality or linearity. As a result, the presence of extreme observations may adversely affect estimation, especially when it is carried out at a low level of aggregation. To deal with this problem, several alternative techniques of estimation, less sensitive to outliers, have been proposed in the statistical literature. In this paper we attempt to apply and assess some robust regression methods (LTS, M-estimation, S-estimation, MM-estimation) in the business survey conducted within the framework of official statistics.

Robust Regression in Monthly Business Survey

Abstract There are many sample surveys of populations that contain outliers (extreme values). This is especially true in business, agricultural, household and medicine surveys. Outliers can have a large distorting influence on classical statistical methods that are optimal under the assumption of normality or linearity. As a result, the presence of extreme observations may adversely affect estimation, especially when it is carried out at a low level of aggregation. To deal with this problem, several alternative techniques of estimation, less sensitive to outliers, have been proposed in the statistical literature. In this paper we attempt to apply and assess some robust regression methods (LTS, M-estimation, S-estimation, MM-estimation) in the business survey conducted within the framework of official statistics.

GAUSSIAN COPULA MARGINAL REGRESSION FOR MODELING EXTREME DATA WITH APPLICATION

Regression is commonly used to determine the relationship between the response variable and the predictor variable, where the parameters are estimated by Ordinary Least Square (OLS). This method can be used with an assumption that residuals are normally distributed (0, σ2). However, the assumption of normality of the data is often violated due to extreme observations, which are often found in the climate data. Modeling of rice harvested area with rainfall predictor variables allows extreme observations. Therefore, another approximation is necessary to be applied in order to overcome the presence of extreme observations. The method used to solve this problem is a Gaussian Copula Marginal Regression (GCMR), the regression-based Copula. As a case study, the method is applied to model rice harvested area of rice production centers in East Java, Indonesia, covering District: Banyuwangi, Lamongan, Bojonegoro, Ngawi and Jember. Copula is chosen because this method is not strict against the assumption distribution, especially the normal distribution. Moreover, this method can describe dependency on extreme point clearly. The GCMR performance will be compared with OLS and Generalized Linear Models (GLM). The identification result of the dependencies structure between the Rice Harvest per period (RH) and monthly rainfall showed a dependency in all areas of research. It is shown that the real test copula type mostly follows the Gumbel distribution. While the comparison of the model goodness for rice harvested area in the modeling showed that the method used to model the exact GCMR in five districts RH1 and RH2 in Jember district since its lowest AICc. Looking at the data distribution pattern of response variables, it can be concluded that the GCMR good for modeling the response variable that is not normally distributed and tend to have a large skew.

Outlier-Robust Evidence for the Expectation Hypothesis

We provide new evidence in favor of the expectation hypothesis (EH) as a long-run theory of the term structure of interest rates. Using nonparametric techniques, we show that the results of conventional tests that reject the EH are affected by the presence of extreme observations -- only a handful in the case of longer maturities. We use recursive estimation to provide a new method that determines statistically the number of outliers that cause a theory to fail, EH in this case. When we account for these rare peso effects, the results are very different from those previously discussed in the literature.

Recursive modelling of symmetric and asymmetric volatility in the presence of extreme observations

This paper is concerned with recursive estimation, testing and forecasting of the asymmetric volatility of daily returns in Standard and Poor’s 500 Composite Index and the Nikkei 225 Index in the presence of extreme observations, or significant spikes in the volatility of daily returns. For each of the two data sets, the empirical analysis increases the sample size up to 12 000 observations recursively to examine the effects of extreme observations on: (i) the Quasi Maximum Likelihood Estimates (QMLE) of the GARCH(1,1) and asymmetric GJR(1,1) parameters; (ii) the associated asymptotic and robust t-ratios of the QMLE; (iii) recursive statistical testing of the asymmetry parameter in GJR(1,1); (iv) the sufficient second and fourth moment conditions for consistency and asymptotic normality, respectively, of the QMLE of GARCH(1,1) and GJR(1,1); and (v) the forecast performance of the GARCH(1,1) and GJR(1,1) models for periods with significant spikes in volatility and for periods of relative calm.

Estimating smooth transition autoregressive models with GARCH errors in the presence of extreme observations and outliers

The paper investigates several empirical issues regarding quasi-maximum likelihood estimation of smooth transition autoregressive (STAR) models with GARCH errors (STAR-GARCH) and STAR models with smooth transition GARCH errors (STAR-STGARCH). Empirical evidence is provided to show that different algorithms produce substantially different estimates for the same model. Consequently, the interpretation of the model can differ according to the choice of algorithm. Convergence, the choice of different algorithms for maximizing the likelihood function, and the sensitivity of the estimates to outliers and extreme observations, are examined using daily data for S&P 500, Hang Seng and Nikkei 225 for the period January 1986 to April 2000.

Trimmed estimates in simultaneous estimation of parameters in exponential families

Let X 1,…, X p be p (≥ 3) independent random variables, where each X i has a distribution belonging to the one-parameter exponential family of distributions. The problem is to estimate the unknown parameters simultaneously in the presence of extreme observations. C. Stein ( Ann. Statist. 9 (1981), 1135–1151) proposed a method of estimating the mean vector of a multinormal distribution, based on order statistics corresponding to the | X i |'s, which permitted improvement over the usual maximum likelihood estimator, for long-tailed empirical distribution functions. In this paper, the ideas of Stein are extended to the general discrete and absolutely continuous exponential families of distributions. Adaptive versions of the estimators are also discussed.