Journal Of Statistics Research Articles

Robust precision matrix estimation via weighted median regression with regularization

AbstractA precision matrix is an important parameter of interests because its elements describe useful association information among multiple variables, which has a wide variety of applications. For example, it is used for inferring gene regulation networks in genomic studies and stock association networks in financial studies. However, in many cases, the precision matrix needs to be robustly estimated due to the presence of outliers. We propose estimating a sparse scaled precision matrix via weighted median regression with regularization. Our weighted median regression approach is consistent under various distributional assumptions including multivariate t‐ or contaminated Gaussian distributions. This fact is illustrated with simulation studies and a real data analysis with monthly stock return data. The Canadian Journal of Statistics 46: 265–278; 2018 © 2018 Statistical Society of Canada

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Goodness‐of‐fit tests for Lévy‐driven Ornstein‐Uhlenbeck processes

AbstractLévy‐Driven Ornstein‐Uhlenbeck (or CAR(1)) processes have been introduced in the literature as a model for stochastic volatility. A general formula to recover the unobserved driving process from a continuously observed CAR(1) was developed. When the CAR(1) process is observed at discrete times, the driving process must be approximated. Approximated increments of the driving process are used to test the hypothesis that the CAR(1) belongs to a specified class of Lévy processes. Two goodness‐of‐fit tests are proposed. The performance of the tests is illustrated through simulation. The Canadian Journal of Statistics 46: 355–376; 2018 © 2018 Statistical Society of Canada

A Command for Fitting Mixture Regression Models for Bounded Dependent Variables Using the Beta Distribution

In this article, we describe the betamix command, which fits mixture regression models for dependent variables bounded in an interval. The model is a generalization of the truncated inflated beta regression model introduced in Pereira, Botter, and Sandoval (2012, Communications in Statistics—Theory and Methods 41: 907–919) and the mixture beta regression model in Verkuilen and Smithson (2012, Journal of Educational and Behavioral Statistics 37: 82–113) for variables with truncated supports at either the top or the bottom of the distribution. betamix accepts dependent variables defined in any range that are then transformed to the interval (0, 1) before estimation.

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 7, No. 2

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 2 Bibi Abdelouahab, University Mentouri Constantine, AlgeriaCarolyn Huston, Commonwealth Scientific and Industrial Research Organization (CSIRO), AustraliaLuiz Ricardo Nakamura, University of Sao Paulo, BrazilMohieddine Rahmouni, University of Tunis, TunisiaPablo José Moya Fernández, Universidad de Granada, SpainPhilip Westgate, University of Kentucky, USASajid Ali, Quaid-i-Azam University, PakistanShatrunjai Pratap Singh, John Hancock Financial Services, USASubhradev Sen, Alliance University, IndiaTomás R. Cotos-Yáñez, University of Vigo, SpainVyacheslav Abramov, Swinburne University of Technology, Australia Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education

On the minimum coverage probability of model averaged tail area confidence intervals

AbstractFrequentist model averaging has been proposed as a method for incorporating “model uncertainty” into confidence interval construction. Such proposals have been of particular interest in the environmental and ecological statistics communities. A promising method of this type is the model averaged tail area (MATA) confidence interval put forward by Turek & Fletcher (2012). The performance of this interval depends greatly on the data‐based model weights. A computationally convenient formula for the coverage probability of this interval was provided by Kabaila, Welsh, & Abeysekera (2016), in the simple scenario of two nested linear regression models. We consider more complicated scenarios with a large number of linear regression models. For each of a given set of components of the regression parameter vector, we either set the component to zero or let it vary freely. We provide an easily computed upper bound on the minimum coverage probability of the MATA confidence interval. This upper bound provides evidence against the use of a model weight based on the Bayesian Information Criterion (BIC). The Canadian Journal of Statistics 46: 279–297; 2018 © 2018 Statistical Society of Canada

Change detection via affine and quadratic detectors

The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, Hypothesis testing via affine detectors, Electronic Journal of Statistics 10:2204--2242, 2016. Namely, we consider the Change Detection problem as follows: given an evolving in time noisy observations of outputs of a discrete-time linear dynamical system, we intend to decide, in a sequential fashion, on the null hypothesis stating that the input to the system is a nuisance, vs. the alternative stating that the input is a signal, with both the nuisances and the nontrivial signals modeled as inputs belonging to finite unions of some given convex sets. Assuming the observation noises zero mean sub-Gaussian, we develop computation-friendly sequential decision rules and demonstrate that in our context these rules are provably near-optimal.

Nutritional Status and the Associated Factors in Under Five Years Children of Lamjung, Gorkha and Tanahun Districts of Nepal

Background: The nutritional status of children is important as it determines their health, physical growth as well as development, productive life and academic performance. The national figures for stunting, underweight and wasting in under five years children in Nepal stands at 41%, 29% and 11%, respectively according to NDHS 2011. However, the magnitude of this problem in hilly areas of Nepal is not well understood.Objectives: The objective of this study was to find the nutritional status of 6 to 59 months of children and its associated factors.Materials and Methods: A cross-sectional, population-based study design has been used for this study. The study population was 6 to 59 months children who were permanent or temporary residents of the study area. The respondent was the mother of the under 5 year child. A total 10% (n=1353) study participants were selected from each of the 4 VDCs of Lamjung and Gorkha, and each of the 5 VDCs of Tanahun during April-May, 2014 by applying systematic random sampling. A semi-structured questionnaire was administered to mothers by face to face interview method. The anthropometric measurements (weight and height) were also recorded. Binary logistic regression was applied to identify the factors associated to the nutritional status.Results: In the study, 56.3% were boys and 43.7% were girls. The prevalence of wasting, stunting and underweight was 10.6% (95% C.I: 9.0-12.2), 53.9% (95% C.I: 51.2-56.6) and 20.8% (95% C.I: 18.6-23.0), respectively. The wasting, stunting and underweight were higher in boys than in girls. The factors were duration of breast feeding, occupation of mothers, family size, site of delivery, height of mothers and age of mother during the delivery.Conclusion: Stunting was more prevalent than wasting in the study districts and implies that there is a problem of chronic malnutrition. The factors highlighted in this study should be adequately addressed by concerned authorities to address malnutrition in these hilly districts of Nepal.Nepalese Journal of Statistics, 2017, Vol. 1, 15-28

Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling

Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

Study on Associated Risk Factors of Hypertension at Sipaghat of Sindhupalchowk District, Nepal

Background: Hypertension is a progressive cardiovascular syndrome arising from complex and interrelated etiologies. Males have slightly higher prevalence than female in most of countries of Southeast-Asian region.Objective: The objective of study is to find out prevalence and the risk factors of hypertension at Sipaghat, Sindhulchowk, Nepal.Materials and Methods: A cross-sectional study was conducted at Sipaghat of Sindhupalchowk district in May 2016 and 260 persons were selected randomly. Results: The prevalence of hypertension was higher in male (25.4%) than female (17.4%). Mean age of study population was 42.08 years with standard deviation, 15.95 years. Variables namely age group, smoking, alcohol consumption and family history of hypertension were found to be significant at 5 percent level of significance. Alcohol consumption and smokers have more than two times higher chance of getting hypertension compared to alcohol non-consumer and nonsmoker with 95% confidence intervals were 1.08-4.80 and 1.21-6.10, respectively. Persons with family history of hypertension have 3.8 times more chance of getting hypertension compared to no family history of hypertension with 1.89-7.61 of 95% confidence interval.Conclusion: Lifestyle modification reduces blood pressure which prevents or delays the incidence of hypertension. Hypertension can be controlled and prevented by modifying the lifestyle. People should be advised to avoid modifiable risk factors of hypertension like smoking, consumption of alcohol and physical inactivity through health education programs.Nepalese Journal of Statistics, 2017, Vol. 1, 73-82

Factors Associated with the Level of Depression among Elderly Women Residing in Old Age home of Devghat, Tanahu

Background: There has been considerable increase in elderly population all over the world and this population is thought to be at a greater risk of depression which is a major health problem. Comparatively, depression is found to be at a higher rate among women compared to men.Objective: This study aims to identify the factors influencing the level of depression among elderly women residing in old age home of Devghat, Tanahu.Materials and Methods: This study is entirely based on primary data taking a total population (116) of elderly women from face to face interview using the short version of Geriatric Depression Scale (GDS), Instrumental Activities of Daily Living Scale (IADL) and socio-demographic interview schedule. To gather information, mobile data collection tool i.e. GIS Cloud was used. Data was analyzed using descriptive and inferential statistical methods. To determine the significant factors influencing depression among the respondents, multinomial logistic regression model was used.Results: The mean score obtained from GDS was 7.52 ranging from 2 to 14. About 24% of the respondents had mild depression and 47% of them had severe depression. More than 66% of them were from rural area. About 50% of respondents had no financial support; about 53% of them were found with feeling of loneliness. Regression analysis showed that the factors like age at marriage, type of place of previous residence, financial support, satisfaction of living condition, feeling of loneliness, and IADL score were found to be significantly associated with level of depression.Conclusion: The result of the study indicates that most of the elderly women living in the old age home were suffering from depression. Some actions like raising fund through charity approach, counseling, promoting social volunteers or family members to visit old age home and supporting them, etc. should be addressed from the concerned authorities so that depression can be reduced which will support to the well-being and superior life of elderly women.Nepalese Journal of Statistics, 2017, Vol. 1, 29-40

Factors Affecting Maternal Health Care Services Utilization in Nepal: Insight from the Nepal Demographic Health Survey 2006 and 2011

Background: In this study, a maternal health care service is analyzed under the components of place of delivery (POD). POD is highlighted as ‘home delivery’ and ‘institutional delivery’.Objective: The objective of this study is to analyze factors associated with the utilization of health institute as delivery and estimate the probabilities of institutional delivery using some selected independent variables.Materials and Methods: Data used were extracted from individual recode of a data file of Nepal Demography Health Survey (NDHS) 2006 and 2011. The unit of analysis for this study is Ever Married Women (EMW) who had at least one live birth in the five years preceding the survey. Sample of this study consists of 4182 EMW for 2006 NDHS and 4079 EMW for 2011 NDHS. The dependent variable is place of delivery. The independent variables are mixture of categorical and continuous variables. For building of suitable statistical models, various types of models were explored and different measure of models adequacy test were applied. Finally, two logistic regression models were developed separately for 2006 and 2011 NDHS data.Results: Fitted model showed several variables: education level, wealth index, birth order, residence and ANC by provider were highly significant predictors for the selection of place of delivery for 2006 NDHS but in 2011 NDHS age was also highly significant. Goodness of fit tests (Hosmer-Lemeshow chi-square statistic), multicollinearity diagnostics, residual analysis and outliers (leverage value) showed that both models fit well to the proposed logistic regression model.Conclusion: A Comparative assessment of model coefficients between 2006 and 2011 NDHS, it is found that the values are only slightly different for most of the predictors under consideration demonstrating consistency of associations found in the two surveys.Nepalese Journal of Statistics, 2017, Vol. 1, 55-72

Variance Estimator Using Tri-mean and Inter Quartile Range of Auxiliary Variable

Background: Whenever the population is large and it is very time taking and costly to take observation on each unit of the population then sampling is the only way to get the appropriate estimate of the population parameter under consideration. Many authors have given many estimators for estimating population variance with greater efficiency.Objective: The objective of the study is to search for more efficient estimator than the competing estimators of population variance of study variable.Materials and Methods: The estimator utilizing information on tri-mean and inter quartile range of auxiliary variable has been is developed. The expressions for the bias and mean squared error (MSE) of the proposed estimator have been derived up to the first order of approximation. A theoretical comparison of the proposed estimator has been made with the competing estimators of population variance.Results: The theoretical findings have been justified with the help of numerical example from some natural populations. It has been found that the proposed estimator is best among the competing estimators of population variance as it has least mean squared error among them.Conclusion: Since the proposed estimator is best among the competing estimator of the population variance, therefore it must be used for the improved estimation of population variance.Nepalese Journal of Statistics, 2017, Vol. 1, 83-91

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 7, No. 1

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 1 Afsin Sahin, Gazi University, TurkeyAli Reza Fotouhi, University of the Fraser Valley, CanadaBibi Abdelouahab, University Mentouri Constantine, AlgeriaFelix Almendra-Arao, UPIITA del Instituto Politécnico Nacional , MéxicoLuiz Ricardo Nakamura, University of Sao Paulo, BrazilMaryam Eskandarzadeh, Persion Gulf Boshehr University, IranShatrunjai Pratap Singh, John Hancock Financial Services, USAVilda 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

Time Series Modeling on Monthly Data of Tourist Arrivals in Nepal: An Alternative Approach

Background: There are various approaches of modeling on time series data. Most of the studies conducted regarding time series data are based on annual trend whereas very few concerned with data having monthly fluctuation. The data of tourist arrivals is an example of time series data with monthly fluctuation which reveals that there is higher number of tourist arrivals in some months/seasons whereas others have less number. Starting from January, it makes a complete cycle in every 12 months with 3 bends indicating that it can be captured by biquadratic function.Objective: To provide an alternative approach of modeling i.e. combination of Autoregressive model with polynomial (biquadratic) function on time series data with monthly/seasonal fluctuation and compare its adequacy with widely used cyclic autoregressive model i.e. AR (12).Materials and Methods: This study is based on monthly data of tourist arrivals in Nepal. Firstly, usual time series model AR (12) has been adopted and an alternative approach of modeling has been attempted combining AR and biquadratic function. The first part of the model i.e. AR represents annual trend whereas biquadratic part does for monthly fluctuation.Results: The fitted cyclic autoregressive model on monthly data of tourist arrivals is Est. Ym = 3614.33 + 0.9509Ym-12, (R2=0.80); Est. Ym indicates predicted tourist arrivals for mth month and Ym-12 indicates observed tourist arrivals in (m-12)th month and the combined model of AR and biquadratic function is Est. Yt(m) = -46464.6 + 1.000Yt-1 + 52911.56m - 17177m2 + 2043.95m3 - 79.43m4, (R2=0.78); Est. Yt(m) indicates predicted tourist arrivals for mth month of tth year and Yt-1 indicates average tourist arrivals in (t-1)th year. The AR model combined with polynomial function reveals normal and homoscedastic residuals more accurately compared to first one.Conclusion: The use of polynomial function combined with autoregressive model can be useful for time series data having seasonal fluctuation. It can be an alternative approach for picking up a good model for such type of data. Nepalese Journal of Statistics, 2017, Vol. 1, 41-54

Improved local polynomial estimation in time series regression

ABSTRACTWe propose a modification of local polynomial estimation which improves the efficiency of the conventional method when the observation errors are correlated. The procedure is based on a pre-transformation of the data as a generalization of the pre-whitening procedure introduced by Xiao et al. [(2003), ‘More Efficient Local Polynomial Estimation in Nonparametric Regression with Autocorrelated Errors’, Journal of the American Statistical Association, 98, 980–992]. While these authors assumed a linear process representation for the error process, we avoid any structural assumption. We further allow the regressors and the errors to be dependent. More importantly, we show that the inclusion of both leading and lagged variables in the approximation of the error terms outperforms the best approximation based on lagged variables only. Establishing its asymptotic distribution, we show that the proposed estimator is more efficient than the standard local polynomial estimator. As a by-product we prove a suitable version of a central limit theorem which allows us to improve the asymptotic normality result for local polynomial estimators by Masry and Fan [(1997), ‘Local Polynomial Estimation of Regression Functions for Mixing Processes’, Scandinavian Journal of Statistics, 24, 165–179]. A simulation study confirms the efficiency of our estimator on finite samples. An application to climate data also shows that our new method leads to an estimator with decreased variability.

Statistical challenges in high‐dimensional molecular and genetic epidemiology

AbstractMolecular and genetic association studies conducted in well‐characterized longitudinal cohorts offer a powerful approach to investigate factors influencing disease course or complex trait expression. As measurement technologies continue to develop and evolve, studies based on existing cohorts raise methodological challenges. Five such challenges are illustrated in two long‐term inter‐disciplinary collaborations. In one, molecular genetic prognostic factors in the natural history of node‐negative breast cancer are investigated using a combination of hypothesis‐testing and hypothesis‐generating molecular approaches. In the other, genome‐wide association methods are applied to identify genes for multiple traits in extended follow‐up data from participants of a therapeutic RCT in type 1 diabetes. The Canadian Journal of Statistics 46: 24–40; 2018 © 2017 Statistical Society of Canada

Forecasting market risk of portfolios: copula-Markov switching multifractal approach

ABSTRACTThis paper proposes a new methodology for modeling and forecasting market risks of portfolios. It is based on a combination of copula functions and Markov switching multifractal (MSM) processes. We assess the performance of the copula-MSM model by computing the value at risk of a portfolio composed of the NASDAQ composite index and the S&P 500. Using the likelihood ratio (LR) test by Christoffersen [1998. “Evaluating Interval Forecasts.” International Economic Review 39: 841–862], the GMM duration-based test by Candelon et al. [2011. “Backtesting Value at Risk: A GMM Duration-based Test.” Journal of Financial Econometrics 9: 314–343] and the superior predictive ability (SPA) test by Hansen [2005. “A Test for Superior Predictive Ability.” Journal of Business and Economic Statistics 23, 365–380] we evaluate the predictive ability of the copula-MSM model and compare it to other common approaches such as historical simulation, variance–covariance, RiskMetrics, copula-GARCH and constant conditional correlation GARCH (CCC-GARCH) models. We find that the copula-MSM model is more robust, provides the best fit and outperforms the other models in terms of forecasting accuracy and VaR prediction.

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 6, No. 6

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 6, Number 6 Afsin Sahin, Gazi University, TurkeyBibi Abdelouahab, University Mentouri Constantine, AlgeriaCarla J. Thompson, University of West Florida, USAChin-Shang Li, University of California, Davis, CA, USAGabriel A. Okyere, Kwame Nkrumah University of Science and Technology, GhanaGane Samb Lo, University Gaston Berger, SenegalHui Zhang, St. Jude Children’s Research Hospital, USAIvair R. Silva, Federal University of Ouro Preto – UFOP, BrazilMan Fung LO, Hong Kong Polytechnic University, Hong KongNahid Sanjari Farsipour, Alzahra University, IranPablo José Moya Fernández, Universidad de Granada, SpainSamir Khaled Safi, The Islamic University of Gaza, PalestineShatrunjai Pratap Singh, John Hancock Financial Services, USASohair F. Higazi, University of Tanta, EgyptSubhradev Sen, Alliance University, IndiaTaehan Bae, University of Regina, CanadaTomás R. Cotos-Yáñez, University of Vigo, SpainVilda Purutcuoglu, Middle East Technical University (METU), TurkeyVyacheslav Abramov, Swinburne University of Technology, AustraliaWojciech Gamrot, University of Economics, PolandZaixing Li, China University of Mining and Technology (Beijing), China

A two‐level directional model for dependence in circular data

AbstractWe present a likelihood‐based test for clustering among sub‐population mean directions for circular data. The test is based on a two‐level hierarchical model with von Mises distributed variation on each level. The properties of the tests are investigated and compared to the commonly applied techniques of second‐order analysis and pseudo‐pooling of directions for the situation at hand. Finally we apply the technique to some previously published data sets, to determine the presence of directional clustering among the sub‐populations. The Canadian Journal of Statistics 45: 461–478; 2017 © 2017 Statistical Society of Canada