Browsing by Author "Rai, Piyush Kant"

Now showing 1 - 7 of 7
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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) Khare, Brij Behari; Ashutosh; Rai, Piyush Kant
    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.
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    A Comparative Study on Calibration Approach Based Estimators for Domain Estimation Utilizing Power Function: Revisited
    (Springer Science and Business Media Deutschland GmbH, 2023) Ashutosh; Rai, Piyush Kant; Singh, Ajeet Kumar
    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.
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    CALIBRATION ESTIMATOR OF POPULATION MEAN UNDER STRATIFIED SYSTEMATIC SAMPLING DESIGN
    (DAV College, 2021) Alka; Ekpenyong, Emmanuel John; Rai, Piyush Kant; Tiwari, Shiwani
    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.
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    Parametric Frailty Analysis in Presence of Collinearity: An Application to Assessment of Infant Mortality
    (MDPI, 2022) Albalawi, Olayan; Sirohi, Anu; Rai, Piyush Kant; Alanzi, Ayed R. A.
    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.
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    Simulation study of small domain with calibration approach
    (John Wiley and Sons Ltd, 2022) Ashutosh, Ashutosh; Shahzad, Usman; Al-Noor, Nadia H.; Rai, Piyush Kant
    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.
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    Some r�k class proportional hazard regression models in the presence of collinearity: an evidence from Indian infant mortality
    (Taylor and Francis Ltd., 2023) Sirohi, Anu; Rai, Piyush Kant
    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.
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    Two-Step Calibration Estimator with Double Use of Auxiliary Variable: Method and Application
    (Iranian Statistical Society, 2022) Singh, Alka; Rai, Piyush Kant; Qasim, Muhammad
    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.