Abstract: An omnibus test for normality with an adjustment for symmetric alternatives is developed using the empirical likelihood ratio technique. We first transform the raw data via a jackknife transformation technique by deleting one observation at a time. The probability integral transformation was then applied on the transformed data, and under the null hypothesis, the transformed data have a limiting uniform distribution, reducing testing for normality to testing for uniformity. Employing the empirical likelihood technique, we show that the test statistic has a chi-square limiting distribution. We also demonstrated that, under the established symmetric settings, the CUSUM-type and Shiryaev–Roberts test statistics gave comparable properties and power. The proposed test has good control of type I error. Monte Carlo simulations revealed that the proposed test outperformed studied classical existing tests under symmetric short-tailed alternatives. Findings from a real data study further revealed the robustness and applicability of the proposed test in practice. PubDate: Wed, 03 Mar 2021 13:50:02 +000
Abstract: A compounded method—exploiting the searching capabilities of an operation research algorithm and the power of bootstrap techniques—is presented. The resulting algorithm has been successfully tested to predict the turning point reached by the epidemic curve followed by the COVID-19 virus in Italy. Future lines of research, which include the generalization of the method to a broad set of distribution, will be finally given. PubDate: Thu, 11 Feb 2021 18:20:00 +000
Abstract: This paper provides a model-based method for the forecast of the total number of currently COVID-19 positive individuals and of the occupancy of the available intensive care units in Italy. The predictions obtained—for a time horizon of 10 days starting from March 29th—will be provided at a national as well as at a more disaggregated level, following a criterion based on the magnitude of the phenomenon. While those regions hit the most by the pandemic have been kept separated, those less affected regions have been aggregated into homogeneous macroareas. Results show that—within the forecast period considered (March 29th–April 7th)—all of the Italian regions will show a decreasing number of COVID-19 positive people. The same will be observed for the number of people who will need to be hospitalized in an intensive care unit. These estimates are valid under constancy of the government’s current containment policies. In this scenario, northern regions will remain the most affected ones, whereas no significant outbreaks are foreseen in the southern regions. PubDate: Sat, 16 Jan 2021 18:20:01 +000
Abstract: Due to its impact on health and quality of life, Thailand’s ozone pollution has become a major concern among public health investigators. Saraburi Province is one of the areas with high air pollution levels in Thailand as it is an important industrialized area in the country. Unfortunately, the August 2018 Pollution Control Department (PCD) report contained some missing values of the ozone concentrations in Saraburi Province. Missing data can significantly affect the data analysis process. We need to deal with missing data in a proper way before analysis using standard statistical techniques. In the presence of missing data, we focus on estimating ozone mean using an improved compromised imputation method that utilizes chain ratio exponential technique. Expressions for bias and mean square error (MSE) of an estimator obtained from the proposed imputation method are derived by Taylor series method. Theoretical finding is studied to compare the performance of the proposed estimator with existing estimators on the basis of MSE’s estimators. In this case study, the results in terms of the percent relative efficiencies indicate that the proposed estimator is the best under certain conditions, and it is then applied to the ozone mean estimation for Saraburi Province in August 2018. PubDate: Sat, 05 Dec 2020 13:50:00 +000
Abstract: A higher-order likelihood-based asymptotic method to obtain inference for the difference between two KS Sharpe ratios when gross returns of an investment are assumed to be lognormally distributed is proposed. Theoretically, our proposed method has distributional accuracy, whereas conventional methods for inference have distributional accuracy. Using an example, we show how discordant confidence interval results can be depending on the methodology used. We are able to demonstrate the accuracy of our proposed method through simulation studies. PubDate: Sat, 10 Oct 2020 15:50:01 +000
Abstract: In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators. PubDate: Sat, 26 Sep 2020 12:35:01 +000
Abstract: This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa. PubDate: Tue, 22 Sep 2020 14:35:08 +000
Abstract: One of the easiest and fastest ways of building a healthy financial future is investing in the global market. However, the prices of the global market are highly volatile due to the impact of economic crises. Therefore, future prediction and comparison lead traders to make the low-risk decisions with price. The present study is based on time series modelling to forecast the daily close price values of financial instruments in the global market. The forecasting models were tested with two sample sizes, namely, 5-year close price values for correlation analysis and 3-year close price values for model building from 2013 January to 2018 January. The forecasting capabilities were compared for both ARIMA and GARCH class models, namely, TGARCH, APARCH, and EGARCH. The best-fitting model was selected based on the minimum value of the Akaike information criterion (AIC) and Bayesian information criteria (BIC). Finally, the comparison was carried out between ARIMA and GARCH class models using the measurement of forecast errors, based on the Root Mean Square Deviation (RMSE), Mean Absolute Error (MAE), and Mean absolute percentage error (MAPE). The GARCH model was the best-fitted model for Australian Dollar, Feeder cattle, and Coffee. The APARCH model provides the best out-of-sample performance for Corn and Crude Oil. EGARCH and TGARCH were the better-fitted models for Gold and Treasury bond, respectively. GARCH class models were selected as the better models for forecasting than the ARIMA model for daily close price values in global financial market instruments. PubDate: Mon, 14 Sep 2020 13:50:04 +000
Abstract: This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed. PubDate: Mon, 07 Sep 2020 17:35:01 +000
Abstract: This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples. PubDate: Mon, 07 Sep 2020 14:50:02 +000
Abstract: Multivariate noises in the learning process are most of the time supposed to follow a standard multivariate normal distribution. This hypothesis does not often hold in many real-world situations. In this paper, we consider an approach based on multivariate skew-normal distribution. It allows for a multiple continuous variation from normality to nonnormality. We give an extension of the generalized least squares error function in a context of multivariate nonlinear regression to learn imprecise data. The simulation study and application case on real datasets conducted and based on multilayer perceptron neural networks (MLP) with bivariate continuous response and asymmetric revealed a significant gain in precision using the new quadratic error function for these types of data rather than using a classical generalized least squares error function having any covariance matrix. PubDate: Wed, 29 Jul 2020 07:20:19 +000
Abstract: In this paper, a new definition of the number of observations near the th order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions . Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations. PubDate: Wed, 15 Jul 2020 10:50:02 +000
Abstract: In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on -record values. Following the method used by Drees et al. (2004) and Zhou (2009), we prove that the likelihood equations, in terms of -record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies. PubDate: Wed, 24 Jun 2020 12:20:05 +000
Abstract: In this paper, we propose a copula approach in measuring the dependency between inflation and exchange rate. In unveiling this dependency, we first estimated the best GARCH model for the two variables. Then, we derived the marginal distributions of the standardised residuals from the GARCH. The Laplace and generalised t distributions best modelled the residuals of the GARCH(1,1) models, respectively, for inflation and exchange rate. These marginals were then used to transform the standardised residuals into uniform random variables on a unit interval [0, 1] for estimating the copulas. Our results show that the dependency between inflation and exchange rate in Ghana is approximately 7%. PubDate: Wed, 17 Jun 2020 03:35:04 +000
Abstract: Like most commodities, the price of silver is driven by supply and demand speculation, which makes the price of silver notoriously volatile due to the smaller market, lower market liquidity, and fluctuations in demand between industrial and store value use. The concern of this article was to model and forecast the silver price volatility dynamics on the Ethiopian market using GARCH family models using data from January 1998 to January 2014. The price return series of silver shows the characteristics of financial time series such as leptokurtic distributions and thus can suitably be modeled using GARCH family models. An empirical investigation was conducted to model price volatility using GARCH family models. Among the GARCH family models considered in this study, ARMA (1, 3)-EGARCH (3, 2) model with the normal distributional assumption of residuals was found to be a better fit for price volatility of silver. Among the exogenous variables considered in this study, saving interest rate and general inflation rate have a statistically significant effect on monthly silver price volatility. In the EGARCH (3, 2) volatility model, the asymmetric term was found to be positive and significant. This is an indication that the unanticipated price increase had a greater impact on price volatility than the unanticipated price decrease in silver. Then, concerned stockholders such as portfolio managers, planners, bankers, and investors should intervene and pay due attention to these factors in the formulation of financial and related market policy. PubDate: Mon, 25 May 2020 06:20:04 +000
Abstract: In this paper, we derive the cumulative distribution functions (CDF) and probability density functions (PDF) of the ratio and product of two independent Weibull and Lindley random variables. The moment generating functions (MGF) and the k-moment are driven from the ratio and product cases. In these derivations, we use some special functions, for instance, generalized hypergeometric functions, confluent hypergeometric functions, and the parabolic cylinder functions. Finally, we draw the PDF and CDF in many values of the parameters. PubDate: Fri, 01 May 2020 01:20:09 +000
Abstract: Recently, different distributions have been generalized using the -R {Y} framework but the possibility of using Dagum distribution has not been assessed. The -R {Y} combines three distributions, with one as a baseline distribution, with the strength of each distribution combined to produce greater effect on the new generated distribution. The new generated distributions would have more parameters but would have high flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution. This paper therefore generalized the Dagum distribution using the quantile function of Lomax distribution. A member of -Dagum class of distribution called exponentiated-exponential-Dagum {Lomax} (EEDL) distribution was proposed. The distribution will be useful in survival analysis and reliability studies. Different characterizations of the distribution are derived, such as the asymptotes, stochastic ordering, stress-strength analysis, moment, Shannon entropy, and quantile function. Simulated and real data are used and compared favourably with existing distributions in the literature. PubDate: Fri, 24 Apr 2020 13:05:08 +000
Abstract: Nonresponse is a potential source of errors in sample surveys. It introduces bias and large variance in the estimation of finite population parameters. Regression models have been recognized as one of the techniques of reducing bias and variance due to random nonresponse using auxiliary data. In this study, it is assumed that random nonresponse occurs in the survey variable in the second stage of cluster sampling, assuming full auxiliary information is available throughout. Auxiliary information is used at the estimation stage via a regression model to address the problem of random nonresponse. In particular, auxiliary information is used via an improved Nadaraya–Watson kernel regression technique to compensate for random nonresponse. The asymptotic bias and mean squared error of the estimator proposed are derived. Besides, a simulation study conducted indicates that the proposed estimator has smaller values of the bias and smaller mean squared error values compared to existing estimators of a finite population mean. The proposed estimator is also shown to have tighter confidence interval lengths at coverage rate. The results obtained in this study are useful for instance in choosing efficient estimators of a finite population mean in demographic sample surveys. PubDate: Tue, 21 Apr 2020 14:50:05 +000
Abstract: Forecasting the covolatility of asset return series is becoming the subject of extensive research among academics, practitioners, and portfolio managers. This paper estimates a variety of multivariate GARCH models using weekly closing price (in USD/barrel) of Brent crude oil and weekly closing prices (in USD/pound) of Coffee Arabica and compares the forecasting performance of these models based on high-frequency intraday data which allows for a more precise realized volatility measurement. The study used weekly price data to explicitly model covolatility and employed high-frequency intraday data to assess model forecasting performance. The analysis points to the conclusion that the varying conditional correlation (VCC) model with Student’s t distributed innovation terms is the most accurate volatility forecasting model in the context of our empirical setting. We recommend and encourage future researchers studying the forecasting performance of MGARCH models to pay particular attention to the measurement of realized volatility and employ high-frequency data whenever feasible. PubDate: Sat, 04 Apr 2020 05:20:00 +000
Abstract: Among several variable selection methods, LASSO is the most desirable estimation procedure for handling regularization and variable selection simultaneously in the high-dimensional linear regression models when multicollinearity exists among the predictor variables. Since LASSO is unstable under high multicollinearity, the elastic-net (Enet) estimator has been used to overcome this issue. According to the literature, the estimation of regression parameters can be improved by adding prior information about regression coefficients to the model, which is available in the form of exact or stochastic linear restrictions. In this article, we proposed a stochastic restricted LASSO-type estimator (SRLASSO) by incorporating stochastic linear restrictions. Furthermore, we compared the performance of SRLASSO with LASSO and Enet in root mean square error (RMSE) criterion and mean absolute prediction error (MAPE) criterion based on a Monte Carlo simulation study. Finally, a real-world example was used to demonstrate the performance of SRLASSO. PubDate: Mon, 30 Mar 2020 07:35:09 +000
Abstract: A risk measure commonly used in financial risk management, namely, Value-at-Risk (VaR), is studied. In particular, we find a VaR forecast for heteroscedastic processes such that its (conditional) coverage probability is close to the nominal. To do so, we pay attention to the effect of estimator variability such as asymptotic bias and mean square error. Numerical analysis is carried out to illustrate this calculation for the Autoregressive Conditional Heteroscedastic (ARCH) model, an observable volatility type model. In comparison, we find VaR for the latent volatility model i.e., the Stochastic Volatility Autoregressive (SVAR) model. It is found that the effect of estimator variability is significant to obtain VaR forecast with better coverage. In addition, we may only be able to assess unconditional coverage probability for VaR forecast of the SVAR model. This is due to the fact that the volatility process of the model is unobservable. PubDate: Tue, 10 Mar 2020 07:20:05 +000
Abstract: In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. The proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. The coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based charts. PubDate: Tue, 25 Feb 2020 04:05:11 +000
Abstract: The Weibull growth model is an important model especially for describing the growth instability; therefore, in this paper, three methods, namely, generalized maximum entropy, Bayes, and maximum a posteriori, for estimating the four parameter Weibull growth model have been presented and compared. To achieve this aim, it is necessary to use a simulation technique to generate the samples and perform the required comparisons, using varying sample sizes (10, 12, 15, 20, 25, and 30) and models depending on the standard deviation (0.5). It has been shown from the computational results that the Bayes method gives the best estimates. PubDate: Tue, 14 Jan 2020 07:50:04 +000
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