Journal Of Statistics Research Articles

Estimation of total electricity consumption curves by sampling in a finite population when some trajectories are partially unobserved

AbstractMillions of smart meters that are able to collect individual load curves, that is, electricity consumption time series, of residential and business customers at fine scale time grids are now deployed by electricity companies all around the world. It may be complex and costly to transmit and exploit such a large quantity of information, therefore it can be relevant to use survey sampling techniques to estimate mean load curves of specific groups of customers. Data collection, like every mass process, may undergo technical problems at every point of the metering and collection chain resulting in missing values. We consider imputation approaches (linear interpolation, kernel smoothing, nearest neighbours, principal analysis by conditional estimation) that take advantage of the specificities of the data, that is to say the strong relation between the consumption at different instants of time. The performances of these techniques are compared on a real example of Irish electricity load curves under various scenarios of missing data. A general variance approximation of total estimators is also given which encompasses nearest neighbours, kernel smoothers imputation and linear imputation methods. The Canadian Journal of Statistics 47: 65–89; 2019 © 2018 Statistical Society of Canada

On the estimation of extropy

ABSTRACTRecently, Lad, Sanfilippo, and Agro [(2015), ‘Extropy: Complementary Dual of Entropy’, Statistical Science, 30, 40–58.] showed the measure of entropy has a complementary dual, which is termed extropy. The present article introduces some estimators of the extropy of a continuous random variable. Properties of the proposed estimators are stated, and comparisons are made with Qiu and Jia’s estimators [(2018a), ‘Extropy Estimators with Applications in Testing uniformity’, Journal of Nonparametric Statistics, 30, 182–196]. The results indicate that the proposed estimators have a smaller mean squared error than competing estimators. A real example is presented and analysed.

A Comparative Study of Exclusive Breastfeeding Practices Among Working and Non-Working Women in Bharatpur-Tandi, Chitwan, Nepal

Background: Breastfeeding has been accepted as the most vital intervention for reducing infant mortality, ensuring optimal growth and development of children. Twenty-two percent of newborn deaths can be prevented through breastfeeding in the first hour of birth.Objective: The objective is to find the proportion of exclusive breastfeeding practices among working and non-working women and significant factors associated with exclusive breastfeeding practices. Exclusive breastfeeding means a baby receives only breast milk without any additional food or drinks, including water until 6 months of age.Materials and Methods: Semi-structured schedule was adopted to take the information from the respondents. The sample size of the study was 140 of which 70 working and 70 non-working women were selected purposively. Results: The percentage of exclusive breastfeeding practices among working women was 67.10% and 81.4% among non-working women. More than 90% of the women knew the importance of breastfeeding. Similarly, 68.9% of working and 67.7 % of the non-working women had initiated breastfeeding within one hour of birth. Type of family, number of children, working hour were statistically significant to exclusive breastfeeding practices.Conclusion: Exclusive breastfeeding practices were quite higher among non-working women compared to working women. In order to improve breastfeeding practices the concerned authority should formulate the provision of child health care center at working places.Nepalese Journal of Statistics, Vol. 2, 1-10

Factors Associated with Intimate Partner Violence: Logistic Regression Approach

Background: Intimate Partner Violence is a major health and human rights problem. Globally, intimate partner violence includes physical act of violence together with sexual coercion, physical threats, psychological abuse and controlling actions by the intimate partner.Objective: This study aims to identify the factors influencing intimate partner violence of married women in Pokhara, Lekhnath Metropolitan City ward number 27, Kaski, Nepal.Materials and Methods: This study is entirely based on the primary data. The sample contains 303 married women of 15-49 years selected by systematic sampling. Data was collected using structured questionnaire and face to face interview. The questionnaire used is modified version of the questionnaire designed and recommended by World Health Organization (WHO) and Program for Appropriate Technology in Health ‘PATH’ (2005). Data was analyzed using descriptive and inferential statistical methods. To determine the significant factors, Logistic regression model was used for establishing linkage between intimate partner violence and several explanatory variables.Results: Fitted model showed the variables, affair with other women and alcohol consumption habit were highly significant predictors for the intimate partner violence. Occupation of husband was significant predictor for physical violence and occupation of respondent was significant for sexual violence. Goodness of fit tests (Hosmer-Lemeshow chi-square statistic, Negelkerke R2) showed that all three models fit well to the proposed Logistic regression model.Conclusion: Although violence is a multidimensional concept, this study has attempted to capture three types of violence namely psychological, physical and sexual called IPV. The IPV was collapsed to create a dichotomous variable on the basis of whether the woman has IPV or not. A number of independent variables are taken into account based on scientific literature review.Nepalese Journal of Statistics, Vol. 2, 37-52

A Generalised Poisson Mishra Distribution

Background: “Mishra distribution" of B. K. Sah (2015) has been obtained in honor of Professor A. Mishra, Department of Statistics, Patna University, Patna (Sah, 2015). A one parameter Poisson-Mishra distribution (PMD) of B. K. Sah (2017) has been obtained by compounding Poisson distribution with Mishra distribution. It has been found that this distribution gives better fit to all the discrete data sets which are negative binomial in nature used by Sankarn (1970) and others. A generalisation of PMD has been obtained by mixing the generalised Poisson distribution of Consul and Jain (1973) with the Mishra distribution.Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution.Results: Probability density function and the first four moments about origin of the proposed distribution have been obtained. The estimation of parameters of this distribution has been discussed by using the first moment about origin and the probability mass function at x = 0 . This distribution has been fitted to a number of discrete data-sets to which earlier Poisson-Lindley distribution (PLD) and PMD have been fitted.Conclusion: P-value of generalised Poisson-Mishra distribution is greater than PLD and PMD. Hence, it provides a better alternative to the PLD of Sankarn and PMD of B. K. Sah.Nepalese Journal of Statistics, Vol. 2, 27-36

Multiple Regression Model Fitted for Rice Production Forecasting in Nepal: A Case of Time Series Data

Background: Fitting a multiple regression model is always challenging and the level of difficulty varies according to the purpose for which it is fitted. Two major difficulties that arise while fitting a multiple regression model for forecasting are selecting 'potential predictors' from numerous possible variables to influence on the forecast variable and investigating the most appropriate model with a subset of the potential predictors.Objective: Purpose of this paper is to demonstrate a procedure adopted while fitting multiple regression model (with an attempt to optimize) for rice production forecasting in Nepal.Materials and Methods: This study has used fifty years (1961-2010) of time series data. A list of twenty-one predictors thought to impact on rice production was scanned based upon past literature, expert's hunches, availability of the data and the researcher's insight which left eleven possible predictors. Further, these possible predictors were subjected to family of automated stepwise methods which left five ‘potential predictors’ namely harvested area, rural population, farm harvest price, male agricultural labor force and, female agricultural labor force. Afterwards, best subset regression was performed in Minitab Version 16 which finally left three 'appropriate predictors' that best fit the model namely harvested area, rural population and farm harvest price.Results: The model fit was significant with p < .001. Also, all the three predictors were found highly significant with p < 0.001. The model was parsimonious which explained 93% variation in rice production with 54% overlapping predictive work done. Forecast error was less than 5%.Conclusion: Multiple regression model can be used in rice production forecasting in the country for the enhanced ease and efficiency.Nepalese Journal of Statistics, Vol. 2, 89-98

Cox Proportional Hazards Model for Identification of the Prognostic Factors in the Survival of Acute Liver Failure Patients in India

Background: Acute Liver Failure (ALF) is a kind of dangerous rare liver injury among all liver diseases. Different statistical methods such as Logistic regression, Kaplan-Meier estimate of survival function followed by Log-rank test and semi-parametric approaches of survival analysis has been applied in order to identify the significant risk factors of ALF patients. In most of the studies, regression models used in this setup has not been evaluated by model assumptions and their goodness of fit tests.Objective: To apply appropriate survival analysis technique to identify the prognostic factors in the survival of ALF patients, to develop prognostic index, and to predict survival probability for different scenario.Materials and Methods: The study is based on the retrospective cohort study design with altogether 1099 ALF patients taken from the liver clinic, All India Institute of Medical Sciences, New Delhi India. Cox regression has been considered as the suitable model for handling this time to event data, and the assumptions of the model, goodness of fit of the model was assessed and survival probabilities were predicted.Results: This study has identified six prognostic factors namely age, prothrombin time, cerebral edema, total serum bilirubin, serum creatinine and etiology for ALF patients. The hazards of mortality [HR: 2.38; 95% C.I.: (1.99, 2.85), p < 0.001] is the highest for cerebral edema among all these prognostic factors. Nearly 9%, 26%, 39%, 50%, 59% and 63% of ALF patients with a PI of 1, 3, 5, 7, 9 and 10 respectively die by 3 days of hospital stay.Conclusion: The developed Cox Proportional Hazards model with six prognostic factors has satisfied the model assumptions and goodness of fit tests. The risk score and the predicted survival probabilities will be immensely helpful to the hepatologists to make a quick decision regarding the likely prognosis of a patient at admission and helpful in triaging the ALF patients for liver transplant.Nepalese Journal of Statistics, Vol. 2, 53-74

Negative Binomial Model in Linking Water-borne and Vector-borne Disease Hospitalizations with Climate Sensitive Variables in Nepal

Background: Several statistical models are built to associate climate sensitive variables such as temperature, rainfall, relative humidity and wind speed with selected water-borne (WB) diseases namely enteric fever, diarrhea and dysentery and vector-borne (VB) diseases namely malaria, encephalitis and leishmaniasis separately based upon daily time series data.Objective: The objective of the paper is to associate climate sensitive variables with WB and VB diseases in the context of Nepal through building statistical models.Materials and Methods: Analysis is based upon the ecological study design with five years of daily hospital inpatient data collected from 22 leading hospitals of 10 districts spread across all the three ecobelts of Nepal and corresponding meteorological data covering 16 stations of the selected districts collected from Department of Hydrology and Meteorology for the period 2009-2014. Negative binomial model is found suitable and used to account the over-dispersed count response variables.Results: Temperature is found to be consistently and positively associated with the accounted disease hospitalizations with around 3-9% (95% CI: 1.3-10.1% combined) and 2-12% (95% CI: 0.3-15.1% combined) estimated increase in WB and VB diseases per 10C increase in average temperature, respectively. However, the same type and level of consistency are not detected in the remaining meteorological variables in the presence of confounders like annual trend, holiday effect and seasonality.Conclusion: Under the climate change scenario of Nepal, WB and VB diseases that can be attributed to rise in temperature is expected to increase in future with substantial attributable burden of diseases. Consequently, Nepal needs to face the challenges of climate change by improving health facilities, reducing poverty among Nepalese people, implementing suitable adaptation and vulnerability related plans and policies, widespread use of eco-friendly energy and technology, etc. along with achieving the targeted sustainable development goals in years to come. Nepalese Journal of Statistics, Vol. 2, 11-26

A Probabilistic Approach for Assessment of Future Drought in Bagmati River Basin, Nepal

Background: The Bagmati River is the rain-fed river in the basin of Nepal. The climate change in rainfall patterns may lead to drought or flashflood in this basin. Drought is a silent and pervasive hazard due to the deficit of water availability. It may have adverse impact on society leading to impact on environment, culture, political and other functions of the region.Objective: This study aims to assess the future drought in the Bagmati River Basin, Nepal.Materials and Methods: Providing Regional Climates for Impact Studies precipitation data was obtained from Department of Hydrology and Meteorology, Kathmandu. The Generalized Extreme Distribution was fitted to respective total precipitations in 3 time-scales using EasyFit software. Standardized Precipitation Index (SPI) method was used to derive SPI for winter drought, SPI for summer drought and SPI for long-term (annual) drought.Results: The results of data analysis showed that winter moderate drought episodes may occur in years 2035, 2042, 2048, 2049, 2051 and 2053. Likewise, summer severe drought episode may occur in 2046. The year 2046 also indicated long-term extreme drought. Moreover, 2030, 2031, 2035, 3040 and 2053 may be long-term moderate drought episodes years in future.Conclusion: There may be winter moderate drought, summer severe drought and a long-term extreme as well as moderate drought during the future period 2030-2060.Nepalese Journal of Statistics, Vol. 2, 75-88

On calibrated weights in stratified sampling

In this paper, we propose a calibration estimator of population mean in stratified sampling using the known mean and variance information from multi-auxiliary variables. The problem of determining the optimum calibrated weights is formulated as a Nonlinear Programming Problem (NLPP) that is solved using the Lagrange multiplier technique. Numerical example with real data is presented to illustrate the computational details of the proposed estimator. A comparison study is also carried out using real and simulated data to evaluate the performance and the usefulness of the proposed estimator. The study reveals that the proposed estimator with multi-auxiliary information is more efficient estimator of the population mean as it provides least estimated variance and highest gain in relative efficiency (RE). References Jean Claude Deville and Carl Erik Sarndal. Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418):376–382, 1992. doi:10.1080/01621459.1992.10475217 . Victor M Estevao and Carl Erik Sarndal. Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74(2):127–147, 2006. doi:110.1111/j.1751-5823.2006.tb00165.x Patrick J Farrell and Sarjinder Singh. Model-assisted higher-order calibration of estimators of variance. Australian and New Zealand Journal of Statistics, 47(3):375–383, 2005. doi:10.1111/j.1467-842X.2005.00402.x Wolfram Research, Inc. Mathematica, Version 11.3. Champaign, IL, 2018. Jong Min Kim, Engin A Sungur, and Tae Young Heo. Calibration approach estimators in stratified sampling. Statistics and probability letters, 77(1):99–103, 2007. doi:10.1016/j.spl.2006.05.015 Phillip S Kott. Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32(2):133, 2006. Dinesh K Rao. Mathematical programing in stratified random sampling. PhD thesis, School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Fiji, February 2017. Dinesh K. Rao, Tokaua. Tekabu, and Mohammad G M Khan. New calibration estimators in stratified sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering, pages 66–70. IEEE, 2016. Gurmindar K Singh, Dinesh K Rao, and Mohammed GM Khan. Calibration estimator of population mean in stratified random sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), pages 1–5. IEEE, 2014. Sarjindar Singh, Stephen Horn, and Frank Yu. Estimation of variance of general regression estimator: Higher level calibration approach. Survey Methodology, 24:41–50, 1998. Sarjinder Singh. Advanced Sampling Theory With Applications: How Michael Selected Amy, volume I and II. Kluwer Academic Publishers, Netherlands, 2003. Sarjinder Singh. On the calibration of design weights using a displacement function. Metrika, 75(1):85–107, 2012. doi:10.1007/s00184-010-0316-6 Sarjinder Singh, Stephen Horn, Sadeq Chowdhury, and Frank Yu. Theory and methods: Calibration of the estimators of variance. Australian and New Zealand Journal of Statistics, 41(2):199–212, 1999. doi:10.1111/1467-842X.00074 D S Tracy, S Singh, and R Arnab. Note on calibration in stratified and double sampling. Survey Methodology, 29(1):99–104, 2003. Changbao Wu and Randy R Sitter. A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96(453):185–193, 2001. doi:10.1198/016214501750333054

Robust design for the estimation of a threshold probability

AbstractWe consider the construction of robust sampling designs for the estimation of threshold probabilities in spatial studies. A threshold probability is a probability that the value of a stochastic process at a particular location exceeds a given threshold. We propose designs such that the estimation of threshold probabilities is robust to two possible model uncertainties: misspecified regression responses and covariance structures. To address these two uncertainties of this stochastic process, we average the mean squared error of the predicted values relative to the true values, over all possible covariance structures in a neighbourhood of the experimenter's nominal choice, and then maximize it over a neighbourhood of the fitted model. Finally, the maximum is minimized to obtain the robust designs. The Canadian Journal of Statistics 46: 470–481; 2018 © 2018 Statistical Society of Canada

Rank‐based inference with responses missing not at random

AbstractMissing data have become almost inevitable whenever data are collected. In this paper, interest is given to responses missing not at random in the context of regression modeling. Many of the existing methods for estimating the model parameters lack robustness or efficiency. We propose a robust and efficient approach towards estimating the true regression parameters when some responses in the regression model are missing not at random. Large sample properties of the proposed estimator are established under mild regularity conditions. Monte Carlo simulation experiments are carried out and they showed that the proposed estimator is more efficient than the least squares estimator whenever the model error distribution is heavy tailed, contaminated or when data contain gross outliers. Finally, the method is illustrated using the ACTG protocol 315 data. The Canadian Journal of Statistics 46: 501–528; 2018 © 2018 Statistical Society of Canada

Reviewer Acknowledgements

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 7, Number 5Jacek Białek, University of Lodz, PolandJingwei Meng, Indiana University, USALuiz Ricardo Nakamura, University of Sao Paulo, BrazilPablo José Moya Fernández, Universidad de Granada, SpainRebecca Bendayan, University College London, UKSajid Ali, Quaid-i-Azam University, PakistanSubhradev Sen, Alliance University, India Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education

Prior‐based model checking

AbstractModel checking procedures are considered based on the use of the Dirichlet process and relative belief. This combination is seen to lead to some unique advantages for this problem. Of considerable importance is the selection of the hyperparameters for the Dirichlet process. A particular choice is advocated here for the base distribution that avoids prior‐data conflict and double use of the data, while the choice of the concentration parameter is based on elicitation. Several examples are presented in which the proposed approach exhibits excellent performance. The Canadian Journal of Statistics 46: 380–398; 2018 © 2018 Statistical Society of Canada

Benchmarked small area prediction

AbstractSmall area estimation often involves constructing predictions with an estimated model followed by a benchmarking step. In the benchmarking operation, the predictions are modified so that weighted sums satisfy constraints. The most common constraint is the constraint that a weighted sum of predictions is equal to the same weighted sum of the original observations. Two benchmarking procedures for nonlinear models are proposed: a linear additive adjustment and a method based on an augmented model for the expectation function. Variance estimators for benchmarked predictors are presented and vetted through simulation studies. The benchmarking procedures are applied to county estimates of the proportion of area in cropland using data from the National Resources Inventory. The Canadian Journal of Statistics 46: 482–500; 2018 © 2018 Statistical Society of Canada

Bayesian MAP estimation using Gaussian and diffused‐gamma prior

AbstractFor sparse and high‐dimensional data analysis, a valid approximation of ‐norm has played a key role. However, there is not much study on the ‐norm approximation in the Bayesian literature. In this article, we introduce a new prior, called Gaussian and diffused‐gamma prior, which leads to a nice ‐norm approximation under the maximum a posteriori estimation. To develop a general likelihood function, we utilize a general class of divergence measures, called Bregman divergence. Due to the generality of Bregman divergence, our method can handle various types of data such as count, binary, continuous, etc. In addition, our Bayesian approach provides many theoretical and computational advantages. To demonstrate the validity and reliability, we conduct simulation studies and real data analysis. The Canadian Journal of Statistics 46: 399–415; 2018 © 2018 Statistical Society of Canada

Network-based macro fluctuations: what about an open economy?

ABSTRACTDo input–output linkages of intermediate products affect the spread of sectoral shocks at the aggregate level in Lithuania, a small and open economy? What role does openness play in the empirical exercise? We answer these questions by: (i) constructing the Lithuanian input–output transactions tables with domestic-only and domestic and imported sector-by-sector direct requirements, and (ii) applying Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehis [(2012). The network origins of aggregate fluctuations. Econometrica, 80(5), 1977–2016] network-based methodology and Gabaix and Ibragimov's [(2011). Rank-1/2: A simple way to improve the ols estimation of tail exponents. Journal of Business & Economic Statistics, 29(1), 24–39] modified log rank-log size regression. Our results indicate that the structure of input–output linkages cause aggregate economic volatility to decay at a rate lower than the established theoretical prediction. Indirect linkages play an equally important role for both domestic-only and aggregated domestic and import transactions.

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 7, No. 4

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 7, Number 4Afsin Sahin, Gazi University, TurkeyCarla J. Thompson, University of West Florida, USAEncarnación Alvarez-Verdejo, University of Granada, SpainFelix Almendra-Arao, UPIITA del Instituto Politécnico Nacional, MéxicoHui Zhang, St. Jude Children’s Research Hospital, USALuiz Ricardo Nakamura, University of Sao Paulo, BrazilMohieddine Rahmouni, University of Tunis, TunisiaPhilip Westgate, University of Kentucky, USASajid Ali, Quaid-i-Azam University, PakistanSohair F. Higazi, University of Tanta, EgyptVilda Purutcuoglu, Middle East Technical University (METU), TurkeyVyacheslav Abramov, Swinburne University of Technology, AustraliaWei Zhang, The George Washington University, USAWojciech Gamrot, University of Economics, Poland Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education

Recent Developments in Macro-Econometric Modeling: Theory and Applications

Developments in macro-econometrics have been evolving since the aftermath of the Second World War.[...]

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 7, No. 3

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 7, Number 3Abdullah A. Smadi, Yarmouk University, JordanAfsin Sahin, Gazi University, TurkeyAnna Grana', University of Palermo, ItalyGerardo Febres, Universidad Simón Bolívar, VenezuelaLuiz Ricardo Nakamura, University of Sao Paulo, BrazilPhilip Westgate, University of Kentucky, USAShatrunjai Pratap Singh, John Hancock Financial Services, USATomás R. Cotos-Yáñez, University of Vigo, SpainVilda Purutcuoglu, Middle East Technical University (METU), Turkey Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education