Browsing by Author "Piyush Kant Rai"

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A comparative study of a class of direct estimators for domain mean with a direct ratio estimator for domain mean using auxiliary character
(Glowny Urzad Statystyczny, 2021) Brij Behari Khare; Ashutosh; Piyush Kant Rai
Estimation techniques for a domain parameter play a very significant role in the theory of sample surveys. In the recent years many advanced methodologies have been developed for domain estimation. In particular, direct and synthetic estimators are applied for the estimation of domain mean in the government and private sectors under certain assumptions as to the size of the samples relating to particular domains. The findings demonstrate that the direct estimator fails to perform more efficiently as compared to the synthetic estimator when reliable units are not directly accessible in the studied domains. Moreover, due to the fact that small units belong to the sample of the studied domain, the direct estimator produces an unacceptably large standard error. In contrast, if a sufficient number of units are available in the studied domain, the direct estimator produces effective results. This paper presents the theoretical aspects of the proposed class of direct estimators for domain mean with the use of a single auxiliary character, compared with an existing direct ratio estimator for domain mean (given in section 3.2). In addition, an empirical study has been provided to support the validity of the proposed estimators. The findings prove that the proposed estimators outperform the direct ratio estimator for domain mean using a single auxiliary character in the case of two studied populations and their analysed domains considered from Sarndal et al. (1992). © 2021 Glowny Urzad Statystyczny. All rights reserved.
A Comparative Study on Calibration Approach Based Estimators for Domain Estimation Utilizing Power Function: Revisited
(Springer Science and Business Media Deutschland GmbH, 2023) Ashutosh; Piyush Kant Rai; Ajeet Kumar Singh
The calibration approach based estimators of the domain mean have growing demand during past couple of decades. Estimation of domains is another challenging task for surveyors and several efforts have been made to produce the reliable estimators for this purpose. Prominently the power function based estimators in the sample surveys are having dual advantages for the selection and their application to produce an improved estimation at any stage in the terms of efficiency without much complexity. In the domain estimation utilization of the power function in the development of calibration based estimators are also very promising and provide considerable results. A simulation study has examined for the comparison of several calibration estimators along with the proposed estimator in terms of the absolute relative bias and simulated relative standard error. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
A Dual Problem of Calibration Ratio-Type Estimator under Stratified Systematic Sampling Scheme
(Iranian Statistical Society, 2024) Alka; Piyush Kant Rai; Muhammad Qasim
This article introduces a dual problem of widely used calibration ratio-type estimators for estimating population mean of the study variable considering auxiliary information under dual constraints using stratified systematic sampling design. Under large sample approximations, the expression for bias and variance of the proposed estimator are derived. In addition, the optimality condition for the proposed estimator and hence optimum variance expression is also obtained for the same. Moreover, a study based on real-life data is carried out to judge the performance of the proposed calibration estimator in terms of minimum relative bias and relative root mean squared error criterion. The study reveals that the calibration ratio-type estimator under dual constraints may be preferred in practice as it provides consistent and more precise parameter estimates. © (2024), (Iranian Statistical Society). All Rights Reserved.
A Joint Calibration Estimator of Population Total Under Minimum Entropy Distance Function Based on Dual Frame Surveys
(Springer, 2020) Piyush Kant Rai; G.C. Tikkiwal; Alka
The concept of dual frame-based estimators has been already developed in sample surveys. These dual frame estimators are theoretically optimal in some cases but difficult to apply in practice, while the others are generally applicable but may have larger variances. In this chapter, we propose Joint Calibration Estimator (JCE) under minimum entropy distance function for the dual frame surveys. The proposed estimator has smaller bias and considerable decrement in variance under Lahiri–Midzuno design as compared to Simple Random Sampling Without Replacement when sample size increases. In addition, we obtain the optimal weights along with its sensitive weighing interval for the combined JCE under non-overlapping frames for which it is more efficient than individual frame-based estimator. © Springer Nature Singapore Pte Ltd 2020.
Alternative approach to moments of order statistics from one-parameter Weibull distribution
(Glowny Urzad Statystyczny, 2020) Piyush Kant Rai; Anu Sirohi
The Weibull distribution is used to describe various observed failures of phenomena and widely used in survival analysis and reliability theory. Sometimes it is very difficult to compute moments of such distributions due to various reasons for e.g. analytical issues, multi parameter cases etc. This study presents the computation of the moments and the expected value of the product of order statistics in the sample from the one-parameter Weibull distribution. An alternative approach in connection to survival function is used to obtain these moments and expected values. In addition the characteristic function of the above distribution is also obtained in the form of gamma functions. Further an illustration is shown to find the first two moments and expected value of the product of order statistics by using this approach. © 2020 Glowny Urzad Statystyczny. All rights reserved.
Analyzing Variety of Birth Intervals: A Stochastic Approach
(Elsevier B.V., 2019) Ram Chandra Yadava; Piyush Kant Rai
Usually, while studying human fertility through stochastic approach, mainly two dimensions of fertility are considered, viz., (i) how frequently females give births in a given interval of time and (ii) how the births are spaced. The second approach is normally called as study of fertility through birth intervals. The present chapter mainly focuses its attention on the study of birth intervals. It is known that birth intervals are very much affected by sampling frame and are also affected by truncation of observations. Consequently, there are variety of birth intervals where intervals are ascertained under different conditions. This article attempts to derive probability distributions of different types of birth intervals, their uses, and limitations. It also discusses the problems of drawing valid inferences when population of females is heterogeneous with respect to fertility parameters. © 2019 Elsevier B.V.
Bayesian estimation for logarithmic transformed exponential distribution under different loss functions
(Natural Sciences Publishing, 2020) Teena Goyal; Piyush Kant Rai; Sandeep Kumar Maurya
The aim of the present article is to find the better estimator for the parameter of logarithmic transformed exponential distribution using informative and non-informative prior under squared error, linex and general entropy loss functions. The performances of these proposed estimators have been compared based on their simulated risk. © 2020 NSP.
Calibration approach-based estimator of population total under successive sampling design
(Taylor and Francis Ltd., 2024) Piyush Kant Rai; Shiwani Tiwari; Alka
The present article deals with the estimation of the finite population total on two occasions using a calibration approach. The estimators from different approaches on two successive occasions using calibration technique are obtained. Some of the properties of proposed estimators are also provided, including optimum composite weights and their sensitivity interval. An empirical study has been carried out using real data for numerical illustration to show the efficiency of the proposed calibrated estimator. In addition, a simulation study is also performed where proposed estimators are found to be more efficient than the other existing traditional estimators for different choices of tuning weights and composite weights under various sample proportions. © 2024 Taylor & Francis Group, LLC.
Calibration approach-based estimator of population total under successive sampling design
(Taylor and Francis Ltd., 2025) Piyush Kant Rai; Shiwani Tiwari; Alka
The present article deals with the estimation of the finite population total on two occasions using a calibration approach. The estimators from different approaches on two successive occasions using calibration technique are obtained. Some of the properties of proposed estimators are also provided, including optimum composite weights and their sensitivity interval. An empirical study has been carried out using real data for numerical illustration to show the efficiency of the proposed calibrated estimator. In addition, a simulation study is also performed where proposed estimators are found to be more efficient than the other existing traditional estimators for different choices of tuning weights and composite weights under various sample proportions. © 2024 Taylor & Francis Group, LLC.
Calibration based chain ratio-type estimator of population total under successive sampling
(Springer, 2024) Shiwani Tiwari; Alka; Piyush Kant Rai
This article suggests a chain ratio-type estimator of population total based on calibration that takes into account auxiliary variables present on both occasions, and information on the study variable is not available on the first occasion. The optimal composite weights to choose, together with their performance range, are presented along with the bias expression. An empirical and simulation-based study is used to evaluate the effectiveness of the suggested estimator. The studies demonstrate that the proposed estimator outperforms the other estimators for various composite weight selections with varying matched and unmatched sample sizes. © The Author(s) under exclusive licence to The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2024.
CALIBRATION ESTIMATOR OF POPULATION MEAN UNDER STRATIFIED SYSTEMATIC SAMPLING DESIGN
(DAV College, 2021) Alka; Emmanuel John Ekpenyong; Piyush Kant Rai; Shiwani Tiwari
The calibration estimation technique is widely used in survey sampling for improving the precision of population parameter estimates. In this paper, a calibrated mean estimator using stratified systematic sampling design is proposed and the expressions for theoretical bias and theoretical variance are derived. A simulation study along with real-life application based analysis is conducted where the percent relative efficiency (PRE) is considered as a performance criterion. Based on the results, the proposed estimator is found to be more efficient than the usual mean estimators and the calibrated mean estimator developed by Tracy et al. (2003). © 2021 DAV College. All rights reserved.
Class of composite estimators of population total using calibration estimation based on matched and unmatched sample under successive sampling
(Taylor and Francis Ltd., 2025) Alka; Shiwani Tiwari; Piyush Kant Rai; Emmanuel John Ekpenyong
This paper develops a class of composite estimators for the finite population total in successive occasions using calibration technique. Empirical studies were carried out using real and simulated data to show the efficiency of the proposed calibrated estimators using various criteria. The proposed estimators were found to be more efficient than the other existing traditional estimator for different choices of tuning weights and composite weights under various sample proportions. © 2025 Informa UK Limited, trading as Taylor & Francis Group.
Composite estimators for domain estimation and sensitivity performance interval of their weights
(Polskie Towarzystwo Semiotyczne, 2024) Piyush Kant Rai; Sweta Singh
Some composite estimators based on various combinations of two different existing estimators are obtained for domain estimation. The estimation of weights and thus obtaining optimum weights to combine two or more different existing direct and indirect estimators to form composite estimators are not an easy task for practitioners due to many reasons. To account for the absence of optimum weights, we obtained the sensitivity performance intervals for weights with respect to the proposed composite estimator. Subsequently, we determined the sensible values of the involved weights. The aim of this procedure was to confine the superiority for different composite combinations i.e., simple direct vs. direct ratio, simple direct vs. synthetic ratio and direct ratio vs. synthetic ratio composite estimators as compared to the existing estimators. © Piyush Kant Rai, Sweta Singh.
On the structure of infant mortality using accelerated failure time (AFT) model: A comparative study based on national family health survey (NFHS) data in India
(Institute of Medico-Legal Publications, 2019) Anu Sirohi; Piyush Kant Rai
This paper analyzes the effect of socioeconomic and demographic factors on infant mortality in India. The Paper also examines reasonable comparison of the three National Family Health Survey (NFHS), the largest sample survey of India from the 1993-1994, 1998-1999 and 2005-06 with respect to different determinants of infant mortality. Accelerated Failure Time (AFT) model is used to measure the direct effect of the above factors on the survival of infants. On the basis of Akaikes Information Criterion (AIC), the Weibull AFT model fits better to other selected models. In all the three NFHS, Weibull AFT model shows the significant effect of the factors on infant survival. © 2019, Indian Journal of Public Health Research and Development. All rights reserved.
Parametric Frailty Analysis in Presence of Collinearity: An Application to Assessment of Infant Mortality
(MDPI, 2022) Olayan Albalawi; Anu Sirohi; Piyush Kant Rai; Ayed R. A. Alanzi
This paper analyzes the time to event data in the presence of collinearity. To address collinearity, the ridge regression estimator was applied in multiple and logistic regression as an alternative to the maximum likelihood estimator (MLE), among others. It has a smaller mean square error (MSE) and is therefore more precise. This paper generalizes the approach to address collinearity in the frailty model, which is a random effect model for the time variable. A simulation study is conducted to evaluate its performance. Furthermore, the proposed method is applied on real life data taken from the largest sample survey of India, i.e., national family health survey (2005–2006) data to evaluate the association of different determinants on infant mortality in India. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
Simulation analysis of non-respondent information in context of small domain
(Elsevier Ltd, 2024) Ashutosh Ashutosh; Marius Stefan; Piyush Kant Rai; Walid Emam; Soofia Iftikhar; Malik Muhammad Anas
In the real-world, there are various situations when all units are not accessible of the respondent called unit non-response. The effect of unit non-response is a tricky matter for estimating the total number of unit. The present work highlights the interest about subpopulations (domains) in two affairs: i. if domains total of the supportive information is accessible ii. if domains total of the supportive variable does not access. The government needs to be introducing the actual facilities in these small domains. The supportive information is used to find out the estimate of the non respondent information and to apply this information for desired domains. Sometimes, it has been found that the accessible auxiliary variable for the domains might be positive shape. Therefore, it develops an appropriate model that has positive skewness. The present context highlighted the indirect method using a power-based estimation with calibration approach. By combining power based estimation and calibration technique, it is possible to obtain more accurate estimates for intended small domains. Even the supportive information is positively biased. This approach helps us in mitigating the effect of non-respondent and improving the overall reliability of the estimators. The simulation was conducted for different sizes 70 and 90 when nonresponse variable in the study variable. The results show that investigated power-based estimate provides better option over relevant exponential, ratio, and generalized regression estimators for intended domains. © 2024 The Authors
Simulation study of small domain with calibration approach
(John Wiley and Sons Ltd, 2022) Ashutosh Ashutosh; Usman Shahzad; Nadia H. Al-Noor; Piyush Kant Rai
Some of the flexible models are available in the statistics literature are exponential and power distribution. They are very helpful in the modeling for situations when the shape and distribution of interested variables are positively skewed. We are presenting the calibration based estimates of domain total for exponential and the power model under such prevailing circumstances. Two different situations are considered: (i) domain total of the auxiliary variable is known and (ii) domain total of the auxiliary variable is unknown. To overcome the difficulties, to get calibration weights under second situation, two phase sampling technique is utilized. The Newton–Raphson method of approximation is used to estimate the Lagrange's multiplier. In addition, the efficiency of the proposed estimator has been given with support of the proposed weights under shortest Chi-square distance function. A numerical value based on the simulation study in terms of absolute relative bias and simulated relative standard error have been given using a real data of the Sweden municipality 1984 for comparison of the estimators. Finding shows that the proposed power function based calibration estimator is more efficient than the existing calibration based estimators of the domain total in both the situations. © 2022 John Wiley & Sons, Ltd.
Some r–k class proportional hazard regression models in the presence of collinearity: an evidence from Indian infant mortality
(Taylor and Francis Ltd., 2023) Anu Sirohi; Piyush Kant Rai
Proportional hazard regression (PHR) model is used to analyze the time to event data in terms of a set of explanatory variables. The estimation and interpretation of the model parameters are unstable, when there is collinearity between explanatory variables. In order to improve the estimation of proportional hazard model with continuous covariates, the r-k class proportional hazard estimator is proposed, which combines the ridge proportional hazard regression (ridge PHR) and principal component proportional hazard regression (PCPHR). The comparisons of the r-k class PHR, ridge PHR, and PCPHR estimators to the maximum likelihood (ML) according to the asymptotic scalar mean square error (MSE) criterion are done. Simulation study is done to evaluate its performance. Furthermore, the proposed method is applied to assess the infant mortality in India. © 2021 Taylor & Francis Group, LLC.
Two-Step Calibration Estimator with Double Use of Auxiliary Variable: Method and Application
(Iranian Statistical Society, 2022) Alka Singh; Piyush Kant Rai; Muhammad Qasim
This article introduces a two-step calibration technique for the inverse relationship between study variable and auxiliary variable along with the double use of the auxiliary variable. In the first step, the calibration weights and design weights are set proportional to each other for a given sample. While in the second step, the constant of proportionality is to be obtained on the basis of some di_erent objectives of the investigation viz. bias reduction or minimum Mean Squared Error (MSE) of the proposed estimator. Many estimators based on inverse relationship between x and y have been already developed and are considered to be special cases of the proposed estimator. Properties of the proposed estimator is discussed in details. Moreover, a simulation study has also been conducted to compare the performance of the proposed estimator under Simple Random Sampling Without Replacement (SRSWOR) and Lahiri-Midzuno (L-M) sampling design in terms of percent relative bias and MSE. The benefits of two-step calibration estimator are also demonstrated using real life data. © 2023, (Iranian Statistical Society). All Rights Reserved.
Two-step calibration of design weights under two auxiliary variables in sample survey
(Taylor and Francis Ltd., 2019) Alka; Piyush Kant Rai; Muhammad Qasim
Calibration on the available auxiliary variables is widely used to increase the precision of the estimates of parameters. Singh and Sedory [Two-step calibration of design weights in survey sampling. Commun Stat Theory Methods. 2016;45(12):3510–3523.] considered the problem of calibration of design weights under two-step for single auxiliary variable. For a given sample, design weights and calibrated weights are set proportional to each other, in the first step. While, in the second step, the value of proportionality constant is determined on the basis of objectives of individual investigator/user for, for example, to get minimum mean squared error or reduction of bias. In this paper, we have suggested to use two auxiliary variables for two-step calibration of the design weights and compared the results with single auxiliary variable for different sample sizes based on simulated and real-life data set. The simulated and real-life application results show that two-auxiliary variables based two-step calibration estimator outperforms the estimator under single auxiliary variable in terms of minimum mean squared error. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.