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The central idea of this paper is to compare mean responses of several subjects in the presence of censoring and subject-specific variation. We develop a semiparametric mixed model for fitting subject-specific hazard curves to a set of censored failure times. A spline-based model and a mixed effects framework for smoothing are used. Efficient estimators of fixed parameters and predictors of the random components are derived and their asymptotic properties studied. This is a generalization of the method proposed by [Cai, T., Hyndman, R. J., & Wand, M. P. (2002). Mixed model-based hazard estimation. Journal of Computational and Graphical Statistics, 11(4), 784–798. https://doi.org/10.1198/106186002862] to incorporate additional subject-specific variation of the hazard function. The results are illustrated using two motivating examples.

Complex weather conditions—in particular clouds—leads to uncertainty in photovoltaic (PV) systems, which makes solar energy prediction very difficult. Currently, in the renewable energy domain, deep-learning-based sequence models have reported better results compared to state-of-the-art machine-learning models. There are quite a few choices of deep-learning architectures, among which Bidirectional Gated Recurrent Unit (BGRU) has apparently not been used earlier in the solar energy domain. In this paper, BGRU was used with a new augmented and bidirectional feature representation. The used BGRU network is more generalized as it can handle unequal lengths of forward and backward context. The proposed model produced 59.21%, 37.47%, and 76.80% better prediction accuracy compared to traditional sequence-based, bidirectional models, and some of the established states-of-the-art models. The testbed considered for evaluation of the model is far more comprehensive and reliable considering the variability in the climatic zones and seasons, as compared to some of the recent studies in India.

Presence of social network among the respondents in a survey may have an influence on the patterns of response. Latent class analysis identifies hidden subgroups in the respondents in a survey and ...

Child Labour has been one of the persistent problems that has affected development. In spite of the efforts at both the national and international levels by government, social organisations and international bodies, child labour is widely prevalent in most developing and underdeveloped countries. However, except for a few summary measures, there is no detailed measurement of the impact and severity of child labour. In this paper we address some of these measurement issues in the light of data collected by the National Sample Survey Office of India.

Long short-term memory (LSTM) models based on specialized deep neural network-based architecture have emerged as an important model for forecasting time-series. However, the literature does not provide clear guidelines for design choices, which affect forecasting performance. Such choices include the need for pre-processing techniques such as deseasonalization, ordering of the input data, network size, batch size, and forecasting horizon. We detail this in the context of short-term forecasting of global horizontal irradiance, an accepted proxy for solar energy. Particularly, short-term forecasting is critical because the cloud conditions change at a sub-hourly having large impacts on incident solar radiation. We conduct an empirical investigation based on data from three solar stations from two climatic zones of India over two seasons. From an application perspective, it may be noted that despite the thrust given to solar energy generation in India, the literature contains few instances of robust studies across climatic zones and seasons. The model thus obtained subsequently outperformed three recent benchmark methods based on random forest, recurrent neural network, and LSTM, respectively, in terms of forecasting accuracy. Our findings underscore the importance of considering the temporal order of the data, lack of any discernible benefit from data pre-processing, the effect of making the LSTM model stateful. It is also found that the number of nodes in an LSTM network, as well as batch size, is influenced by the variability of the input data.

A precise understanding of solar energy generation is important for many reasons like storage, delivery, and integration. Global Horizontal Irradiance (GHI) is the strongest predictor of actual generation. Hence, the solar energy prediction problem can be attempted by predicting GHI. Auto-Regressive Integrated Moving Average (ARIMA) is one of the fundamental models for time series prediction. India is a country with significant solar energy possibilities and with extremely high weather variability across climatic zones. However, rigorous study over different climatic zones seems to be lacking from the literature study. In this paper, 90 solar stations have been considered from the 5 different climatic zones of India and an ARIMA model has been used for prediction for the month of August, the month with most variability in GHI. The prediction of the models has also been analyzed in terms of Root Mean Square Error. The components of the AR models have also been investigated critically for all climatic zones. In this study, some issues were observed for the ARIMA model where the model is not being able to predict the seasonality that is present in the data. Hence, a Seasonal ARIMA (SARIMA) model has also been used as it is more capable in case of seasonal data and the GHI data exhibits a strong seasonality pattern due to its availability only in the day time. Lastly, a comparison has also been done between the two models in terms of RMSE and 7 days Ahead Prediction.

In this paper, we study the survival times of alternately occurring events. The dependence between the times to the two events is modelled through the Archimedean copula, while the dependence over the recurring cycles is modelled through a functional relationship of the distribution parameters. Taking account of appropriate censoring that may be present in the data, the model parameters are estimated using the maximum likelihood method. The standard errors of the estimators are then derived and confidence belts for the survival functions constructed. Methods for choosing the appropriate copula are also discussed. The results are illustrated through a clinical trial data on patients suffering from cystic fibrosis. A simulation study is also done to corroborate the results.

The motivation for this paper is a cystic fibrosis data which records a patient’s times to relapse and times to cure under several recurrences of the disease. The idea is to study the impact of covariates on the hazard rates of two alternately occurring events. The dependence between the times to the two events over the different cycles is modeled through an autoregressive-type setup. The partial likelihood function is then derived and the estimators obtained. The estimators are shown to be consistent and asymptotically normal. The technique is applied to study the motivating data. A simulation study is also conducted to corroborate the results.

In this article, we model alternately occurring recurrent events and study the effects of covariates on each of the survival times. This is done through the accelerated failure time models, where we use lagged event times to capture the dependence over both the cycles and the two events. However, since the errors of the two regression models are likely to be correlated, we assume a bivariate error distribution. Since most event time distributions do not readily extend to bivariate forms, we take recourse to copula functions to build up the bivariate distributions from the marginals. The model parameters are then estimated using the maximum likelihood method and the properties of the estimators studied. A data on respiratory disease is used to illustrate the technique. A simulation study is also conducted to check for consistency.

In this paper we have looked into the problems of measuring visible underemployment. Some measures to gauge the intensity of visible underemployment have been suggested and their properties studied. Measures based on given time-norms for work are also suggested. The results are illustrated through examples.

Often two recurrent events of equal importance can occur alternately. The life-time patterns of the two events can then be of considerable interest. In this paper, we consider two such events, the inclusion and exclusion of players in a team sport, and study whether there is any inherent pattern in the time-lengths between these events. The life-time distributions are modelled and methods of estimating the model parameters suggested taking into account any relationship in the pattern of recurrence. The results are then applied to the inclusion and exclusion of players in the Indian national cricket team. As further illustration, a simulation study is made. Broad application areas are identified both in the introduction and conclusion.

There is a growing discussion about the possibility of arsenic mitigation measures in Bengal and similar areas leading to undesirable substitution of water-borne-pathogen attributable risks pathogens for risks attributable to arsenic, in part because of uncertainties in relative pathogen concentrations in supplied and end-use water. We try to resolve this discussion, by assessing the relative contributions of water supply and end-user practices to water-borne-pathogen-attributable risks for arsenic mitigation options in a groundwater arsenic impacted area of West Bengal. Paired supplied arsenic-mitigated water and end-use drinking water samples from 102 households were collected and analyzed for arsenic and thermally tolerant coliforms [TTC], used as a proxy for microbiological water quality, We then estimated the DALYs related to key sequelae, diarrheal diseases and cancers, arising from water-borne pathogens and arsenic respectively. We found [TTC] in end-use drinking water to depend only weakly on [TTC] in source-water. End-user practices far outweighed the microbiological quality of supplied water in determining diarrheal disease burden. [TTC] in source water was calculated to contribute &lt, 1% of total diarrheal disease burden. No substantial demonstrable pathogen-for-arsenic risk substitution attributable to specific arsenic mitigation of supplied waters was observed, illustrating the benefits of arsenic mitigation measures in the area studied.

Abtsrcat Participants of a refresher course sponsored by the University Grants Commission (UGC) of India were asked to rank six possible reasons for attending the course. They were later also asked to rate the reasons on a five point preference scale. In this paper, our objective is to characterise and quantify the preference for these six reasons. Standard methods for the analysis of contingency tables are not appropriate for ranked preference data so we develop a variant of the y measure of association for ordinal data to examine excess preference in pairwise comparisons. The bootstrap is used to derive p-values and condence intervals for the proposed statistic. Finally, we fit a Bradley-Terry regression model to the rankings and estimate the preference for each reason in terms of ‘worth’ parameters. We repeat this analysis on the ratings data and estimate the worth parameters as functions of covariates. The model is further extended to include dependencies between the ratings. Salient results indicate that career advancement has the highest preference across all covariate classes while the preference for service to society is by far the lowest. However, the magnitude of the preferences is influenced by the number of years for which a participant has taught and whether or not he holds a doctoral degree. There are some differences in conclusions from the analysis of the ratings and rankings datasets.

The problem of missing values problem is common in all branches of statistics and especially in regression analysis. Here we consider estimation of the regression parameters in the presence of missingness in the response. The usual method is to replace the missing value by its predicted value based on the available observations without any correction for the disturbance term. Instead we suggest a method which corrects the usual predictor with a guess of the disturbance term based on the available residuals. Comparison between the two methods shows that the latter leads to better results.

In this study we consider the estimators of the parameters of a stable ARMA(p, q) process. The autoregressive parameters are estimated by the instrumental variable technique while the moving average parameters are estimated using a derived autoregressive process. The estimators are shown to be asymptotically normal and their rate of convergence to normality is derived.

In this article, we consider a random coefficient ARMA(p, q) model with stable roots and show that the distribution of the estimators of the model parameters is asymptotically normal. The rate of convergence to normality is then derived.

Remediation aimed at reducing human exposure to groundwater arsenic in West Bengal, one of the regions most impacted by this environmental hazard, are currently largely focussed on reducing arsenic in drinking water. Rice and cooking of rice, however, have also been identified as important or potentially important exposure routes. Quantifying the relative importance of these exposure routes is critically required to inform the prioritisation and selection of remediation strategies. The aim of our study, therefore, was to determine the relative contributions of drinking water, rice and cooking of rice to human exposure in three contrasting areas of West Bengal with different overall levels of exposure to arsenic, viz. high (Bhawangola-I Block, Murshidibad District), moderate (Chakdha Block, Nadia District) and low (Khejuri-I Block, Midnapur District). Arsenic exposure from water was highly variable, median exposures being 0.02 μg/kg/d (Midnapur), 0.77 μg/kg/d (Nadia) and 2.03 μg/kg/d (Murshidabad). In contrast arsenic exposure from cooked rice was relatively uniform, with median exposures being 0.30 μg/kg/d (Midnapur), 0.50 μg/kg/d (Nadia) and 0.84 μg/kg/d (Murshidabad). Cooking rice typically resulted in arsenic exposures of lower magnitude, indeed in Midnapur, median exposure from cooking was slightly negative. Water was the dominant route of exposure in Murshidabad, both water and rice were major exposure routes in Nadia, whereas rice was the dominant exposure route in Midnapur. Notwithstanding the differences in balance of exposure routes, median excess lifetime cancer risk for all the blocks were found to exceed the USEPA regulatory threshold target cancer risk level of 10(-4)-10(-6). The difference in balance of exposure routes indicate a difference in balance of remediation approaches in the three districts.

In this paper, we consider a regression model with non-spherical covariance structure and outliers in the response. The generalized least squares estimator obtained from the full data set is generally not used in the presence of outliers and an estimator based on only the non-outlying observations is preferred. Here we propose as an estimator a convex combination of the full set and the deleted set estimators and compare its performance with the other two.

In this paper we study the diagnostics of a logistic regression model using the deletion of observation technique. The model is fitted using the maximum likelihood method and the changes in the estimates and the deviance are observed when the model is refitted after deleting an observation. Expressions are derived so that it is not necessary to re-run the regression after each deletion, thereby considerably saving the computational time.

In this paper, we consider an $\operatorname{ARMA}(p,q)$ model with stationary, $\phi$-mixing error variables having uniformly bounded fourth-order moments. Both the autoregressive and moving average components of the model involve stable and explosive roots. Estimating the autoregressive parameters using the instrumental variable technique and the moving average parameters using a derived autoregressive process, we derive the asymptotic distribution of the estimators.

In this paper we study the diagnostics of a multiresponse regression model with a first-order autoregressive error sequence. The deletion technique is used to identify the outliers taking account of the dependence structure of the errors. Besides the usual measures, some scalar measures to gauge the impact of the ouliers on the regression are suggested.