Journal of Advanced Statistics

9

Authors: Jian Wu, Junhua Zhang, Gaorong Li

This paper studies the problems of variable selection and estimation in the additive models with missing response at random. Based on the centered spline basis function approximation, we propose two new imputed estimating equation methods to implement the variable selection for the additive models with missing response at random by using the smooth-threshold estimating equation. Two new imputed methods can select the significant variables and estimate the unknown functions simultaneously. The proposed methods not only avoid the problem of solving a convex optimization, but also reduce the burden of computation. With the proper choices of the regularization parameter, we show that the resulting estimators enjoy the oracle property. The data driven method is used to choose the tuning parameter. A numerical study is analyzed to confirm the performance of the proposed methods

9

Authors: Brijesh P. Singh, Shweta Dixit

The cesarean delivery is a common practice in present scenario in most of the developed as well as many developing countries including India. Cesarean birth has increased noticeably over the last years especially in countries with high or middle income. The present study is based on analysis of data from National Family Health Survey third round in India, which investigate the role of age at marriage and age at first delivery on cesarean cases of first birth. Finding suggests that proposed distribution is appropriate for the age at marriage and first birth of the women, whose first birth is cesarean. Maximum likelihood estimates obtained for the parameters of the distribution. The model suggests the modal age at marriage and first birth in case of first cesarean birth in Uttar Pradesh is 18.41 and 20.56 years.

10

Authors: Piyali Kundu

This paper deals with the estimation of the reliability function R3 = Pr(Y3 > max(Y1, Y2)), when the random variables Y1, Y2 and Y3 are independent exponential with respective unknown location parameters µ1, µ2 and µ3. Here we have derived several estimators of R3 which includes uniformly minimum variance unbiased estimator (UMVUE), Bayes estimator (BE) and generalized Bayes estimator(GBE). Moreover, we have compared these estimators based on their risks under different loss functions.

8

Authors: Md. Moyazzem Hossain, Faruq Abdulla

Bangladesh is recognized as a rice-eating nation; nevertheless, large quantities of potatoes are produced and consumed each year. In Bangladesh, potato has gradually gained popularity. Potato is used as food crop as well as vegetable by both the poor and rich people. Recently, the government has been trying to diversify food habits and encourage potato consumption to reduce pressure on rice. In this regard, potato can play an important role as an alternative and a multipurpose food crop of Bangladesh. This study considered the published secondary data of yearly potato production in Bangladesh over the period 1971 to 2013. The best selected Box-Jenkins ARIMA model for forecasting the potato production for whole Bangladesh is ARIMA(0,2,1). The comparison between the original series and forecasted series shows that the fitted model behaved statistically well and is suitable to forecast the potato productions in Bangladesh.

13

Authors: Mehdi Razzaghi, Dong Zhang

To determine the genes that are differentially expressed between samples in microarray experiments, traditionally the expression levels were assessed by taking the intensity levels at a spot on the array and flagging the gene if the magnitude of the fold change exceeded a threshold. Recently, however, there has been much effort to improve the methodology by incorporating the variability of the intensity ratios. While the Student’s t-test and several of its variants have been proposed by several authors, a methodology that has found widespread popularity is the application of the mixture model in a hierarchical approach whereby the mean of the distribution of the normalized log ratios is assumed to be a random variable having a mixture of two components. One component is a point mass distribution concentrated at zero to represent the non-differentially expressed genes and another component is a suitable distribution with zero mean to represent the differentially expressed genes. The normal and the Laplace distributions have been previously suggested for the differentially expressed genes component of the mixture. But, once again, the symmetry assumption can make these distributions unsuitable. Here, we take a more general approach and apply the beta-normal model to describe the distribution of the mean of the differentially expressed genes. The advantage of this approach is that we no longer assume symmetry for the distribution and let the data determine its shape. We show that our approach includes the earlier results based on normality assumption as a special case. Simulation results demonstrate that there are advantages in using the more general beta-normal distribution. An example with a microarray experimental data is utilized to provide further illustration.

10

Authors: R.U. Khan, M.A. Khan

In this paper, simple explicit expressions and some recurrence relations satisfied by single and product moments of generalized order statistics from exponential-Weibull lifetime distribution have been obtained. These relations are deduced for moments of order statistics and upper record values. Further, conditional moments and a recurrence relation for single moments of the generalized order statistics are used to characterize this distribution and some computational works are also carried out.

13

Authors: Yangxin Huang, Jiaqing Chen, Xiaosun Lu

In longitudinal studies, measurements of the same individuals are taken repeatedly through time, but it often happens that some collected data are observed with the following issues. (i) Often, the primary goal is to characterize the change in response over time. Compared with conventional mean regression, quantile regression (QR) can characterize the entire conditional distribution of the outcome variable, and may be more robust to outliers and mis-specification of error distribution. (ii) longitudinal outcomes may suffer from a serious departure of normality in which normality assumption may cause lack of robustness and subsequently lead to invalid inference; and (iii) the response observations may be subject to left-censoring due to a limit of detection. Inferential procedures will become very complicated when one analyzes data with these features together. In this article, Bayesian modeling approach to nonlinear mixed-effects quantile regression models for longitudinal data is developed to study simultaneous impact of multiple data features (non-normality, left-censoring, non-linearity, outliers and heavy-tails). Simulation studies are conducted to assess the performance of the proposed models and methods. A real data example is analyzed to demonstrate the proposed methodology through comparing potential models with different distribution specifications of random-effects.

15

Authors: Bander Al-Zahrani, Samerah Basloom

The paper deals with the problem of estimating the reliability of a single and multicomponent stress-strength based on a three-parameter Dagum distribution. The maximum likelihood estimators and the Bayes estimators of R = P(Y < X) when X and Y are two independent random variables follow Dagum distribution and their asymptotic distributions are obtained. Also, the reliability of a multicomponent stress-strength model is estimated using the maximum likelihood. Consequently, the asymptotic confidence intervals of the reliability of a single and multicomponent stress-strength model are constructed. Gibbs and Metropolis sampling were used to provide sample-based estimates of the reliability and its associated credible intervals. Finally, Monte Carlo simulations are carried out for illustrative purposes.

7

Authors: Kalovwe Sebastian Kaweto, Mwaniki Ivivi Joseph

This paper seeks to model daily, weekly and monthly stock indices returns using GARCH (1,1) model which is expected to reproduce most of the stylized facts of financial time series data which, in most cases, are found in different types of market. In addition, the distributional behavior of returns as the data changes from daily through to monthly returns is investigated by performing the JB and K-S tests. The results indicate evidence of volatility clustering, leverage effects, Gaussianity and leptokurtic distribution in the stock returns. A key observation is that the monthly returns of the three indices follow a Gaussian distribution (i.e. as the data changes from daily through to monthly returns it follows a normal distribution).

10

Authors: Cleto Corposanto, Beba Molinari

This paper aims to explore the new opportunities offered by the web 2.0, with particular emphasis on the level of intrusiveness concerning web surveys and their different methods of administration. Particular attention will be drawn to the Apps and the way they intervene in the research design to give the researchers the opportunity to learn about the preferences and the consultations which are mostly relevant to the users, thanks to the analysis carried out by data mining and web survey.

15

Authors: Jin-Ting Zhang, Bu Zhou, Jia Guo, Xuefeng Liu

A two-way multivariate analysis of variance (MANOVA) aims to compare the effects of several levels of two factors in a factorial experiment with two-way layout. It is widely used in experimental sciences, e.g., biology, psychology, physics, among others. When the cell covariance matrices are the same, it can be solved using the well-known Wilks likelihood ratio, Lawley-Hotelling trace, Bartlett-Nanda-Pillai trace and Roy’s largest root tests ([1]). However, when the homogeneous assumption is violated, these tests may become seriously biased. To overcome this problem, several authors have proposed and studied different approximation solutions. In this paper, we propose and study a Modified Bartlett (MB) test using a Wald-type statistic and the modified Bartlett correction ([2]) for heteroscedastic two-way MANOVA problems. The MB test can be easily implemented using the usual χ 2 -distribution with known degrees of freedom. We show that it admits several invariant properties. Simulation studies show that the MB test generally outperforms the classical LawleyHotelling trace (LHT) test and a modified LHT test of [3] under various parameter configurations in terms of size controlling and power. A real data example illustrates our method and the effect of heteroscedasticity.

7

Authors: Carlos. N. Bouza

We consider the estimation of a proportion when there are non-responses. They may be motivated by the fact that a “yes”, as a response, identifies belonging to a sensitive group. We suggest taking a sample among the non-respondents and using a randomized response technique in the second interview. This approach motivates sampling models which are developed in this paper. The performance of the proposed model is evaluated using real world data.

14

Authors: Rashmi Aggarwal, Suresh Kumar Sharma, Kanchan Jain

The purpose of survival analysis is to model the underlying distribution of the failure time variable and to assess the dependence of the failure time variable on independent variables. In this paper, we explored PHREG procedure for different models using Bayesian approach. PHREG procedure not only fits COX model but also allows us to fit a piecewise exponential model. The Bayesian analysis treats model parameters as random variables and the inference about these parameters is based on posterior distribution of the parameters. A posterior distribution is a weighted likelihood function of the data with a prior distribution of the parameters using the Bayes’ theorem. Generally, for model regression coefficients, normal or uniform prior distributions are used in PHREG procedure. In addition to this, one may specify gamma or improper prior distribution for the scale or variance parameters as well as for hazard parameters in piecewise exponential model. PHREG procedure have been demonstrated with application to real life dataset. Bayesian analysis with PHREG procedure and piecewise constant Bayesian hazard model is also explored along with diagnostic test.