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1
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The Class of Estimators of Finite Population Mean Using Incomplete Multi-Auxiliary Information

100%
Srivastava M., Garg N.
Statistics in Transition new series
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2013
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vol. 14
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issue 2
201-216
EN
In this paper, a class of estimators is considered for estimating the mean of the finite population utilizing available incomplete multi-auxiliary information. Some special cases of this class of estimators are considered. The approximate expressions for bias and mean square error of the suggested estimators have also been derived and theoretical results are numerically supported.
2
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Generalized exponential estimators for the finite population mean

100%
Zaman T.
Statistics in Transition new series
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2020
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vol. 21
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issue 1
159-168
EN
This study proposes a new class of exponential-type estimators in simple random sampling for the estimation of the population mean of the study variable using information of the population proportion possessing certain attributes. Theoretically, mean squared error (MSE) equations of the suggested ratio exponential estimators are obtained and compared with the Naik and Gupta (1996) ratio and product estimators, the ratio and product exponential estimator presented in Singh et al. (2007) and the ratio exponential estimators presented in Zaman and Kadilar (2019a). As a result of these comparisons, it is observed that the proposed estimators always produce more efficient results than the others. In addition, these theoretical results are supported by the application of original datasets.
3
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Estimating population coefficient of variation using a single auxiliary variable in simple random sampling

100%
Singh R., Mishra M.
Statistics in Transition new series
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2019
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vol. 20
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issue 4
89-111
EN
This paper proposes an improved estimation method for the population coefficient of variation, which uses information on a single auxiliary variable. The authors derived the expressions for the mean squared error of the proposed estimators up to the first order of approximation. It was demonstrated that the estimators proposed by the authors are more efficient than the existing ones. The results of the study were validated by both empirical and simulation studies.
4
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On the properties of some predictor in time series analysis

100%
Czogała M., Department od Statistics U. o. E.
Acta Universitatis Lodziensis. Folia Oeconomica
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2008
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vol. 216
EN
Cieślak (1993) and Kohler and College (1988) considered a predictor being an arithmetic mean of a set of k-latest observations in time series, where k was constant. In this paper a modified predictor is presented and its properties are discussed. For each t-th observation the hypothesis that there is no change in the level of the time series is tested. When the hypothesis isn’t rejected the predictor is an arithmetic mean of a set of t-latest observations otherwise the predictor is equal to the value o f the last observation in the time series. The mean square error is used for assessing the error of prediction.
PL
W swoich pracach Cieślak (1993) oraz Kohler i College (1988) rozważali predyktor będący średnią arytmetyczną k-ostatnich obserwacji szeregu czasowego, gdzie k jest stale. W pracy przedstawiona jest modyfikacja wspomnianego predyktora oraz omówione są jego własności. Zaproponowany predyktor jest średnią arytmetyczną k-ostatnich obserwacji szeregu czasowego, przy czym k nie jest wielkością stałą. Dla każdej t-kolejnej obserwacji szeregu czasowego weryfikowana jest hipoteza, twierdząca, że w poziomie szeregu czasowego nie nastąpiła zmiana. Gdy hipoteza zerowa nie jest odrzucona predyktor jest wyznaczany jako średnia arytmetyczna z wszystkich t-ostatnich obserwacji, w przypadku przeciwnym predyktor jest równy ostatniej obserwacji tego szeregu czasowego. Do oceny błędów predykcji wykorzystany jest błąd średniokwadratowy.
5
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A Class of Product-Type Exponential Estimators of the Population Mean in Simple Random Sampling Scheme

100%
Onyeka A. C.
Statistics in Transition new series
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2013
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vol. 14
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issue 2
189-200
EN
The present study proposes a class of product-type exponential estimators for estimating the population mean of the study variable, using known values of some population parameters of an auxiliary character, under the simple random sampling without replacement (SRSWOR) scheme. Furthermore, the study also proposes a modified exponential estimator based on both the ratio-type and the product-type exponential estimators. Properties of the proposed estimators, under the SRSWOR scheme, are obtained up to first order approximation. The modified exponential estimator under optimum conditions is shown to be more efficient than the simple sample mean and the ratio-type and product-type exponential estimators. The theoretical results are supported by an empirical illustration.
6
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Some Effective Estimation Procedures Under Non- Esponse in Two-Phase Successive Sampling

100%
Singh G. N., Khetan M., Maurya S.
Statistics in Transition new series
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2016
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vol. 17
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issue 2
163-182
EN
This work is designed to assess the effect of non-response in estimation of the current population mean in two-phase successive sampling on two occasions. Sub-sampling technique of non-respondents has been used and exponential methods of estimation under two-phase successive sampling arrangement have been proposed. Properties of the proposed estimation procedures have been examined. Empirical studies are carried out to justify the suggested estimation procedures and suitable recommendations have been made to the survey practitioners.
7
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Estimation of product of two population means by multiauxiliary characters under double sampling the non-respondents

88%
Khare B. B., Sinha R. R.
Statistics in Transition new series
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2019
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vol. 20
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issue 3
81-95
EN
This paper considers the problem of estimating the product of two population means using the information on multi-auxiliary characters with double sampling the non-respondents. Classes of estimators are proposed for estimating P under two different situations [discussed by Rao (1986, 90)] using known population mean of multi-auxiliary characters. Further, this problem has been extended to the case when population means of the auxiliary characters are unknown and they are estimated on the basis of a larger first phase sample. In this situation, a class of two phase sampling estimators for estimating P is suggested using multi-auxiliary characters with unknown population means in the presence of non-response. The expressions of bias and mean square error of all the proposed estimators are derived and their properties are studied. An empirical study using real data sets is given to justify the theoretical considerations.
8
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Some classes of modified ratio type estimators in sample surveys

88%
Swain A. K. P. C., Das M.
Statistics in Transition new series
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2015
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vol. 16
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issue 1
37–52
EN
In this paper some classes of modified ratio type estimators with additive and multiplicative adjustments made to the simple mean per unit estimator and classical ratio estimator are suggested to obtain more efficient ratio type estimators compared to the classical one. Their biases and mean square errors are obtained and compared with first order approximations.
9
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Ratio estimation of two population means in two-phase stratified random sampling under a scrambled response situation

88%
Das P., Singh G. N., Bandyopadhyay A.
Statistics in Transition new series
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2023
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vol. 24
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issue 5
45-61
EN
In this paper, we have described the development of an effective two-phase stratified random sampling estimation procedure in a scrambled response situation. Two different exponential, regression-type estimators were formed separately for different structures of two-phase stratified sampling schemes. We have studied the properties of the suggested strategy. The performance of the proposed strategy has been demonstrated through numerical evidence based on a data set of a natural population and a population generated through simulation studies. Taking into consideration the encouraging findings, suitable recommendations for survey statisticians are prepared for the application of the proposed strategy in real-life conditions.
10
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Some Rotation Patterns in Two-Phase Sampling

75%
Singh G. N., Prasad S.
Statistics in Transition new series
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2011
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vol. 12
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issue 1
25-44
EN
A problem related to the estimation of population mean on the current occasion using two-phase successive (rotation) sampling on two occasions has been considered. Two-phase ratio, regression and chain-type estimators for estimating the population mean on current (second) occasion have been proposed. Properties of the proposed estimators have been studied and their respective optimum replacement policies are discussed. Estimators are compared with the sample mean estimator, when there is no matching and the natural optimum estimator, which is a linear combination of the means of the matched and unmatched portions of the sample on the current occasion. Results are demonstrated through empirical means of comparison and suitable recommendations are made.
11
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Interval shrinkage estimation of the parameter of exponential distribution in the presence of outliers under loss functions

75%
Nasiri P.
Statistics in Transition new series
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2022
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vol. 23
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issue 3
65-78
EN
In this paper, we studied estimators based on an interval shrinkage with equal weights point shrinkage estimators for all individual target points θ¯ ∈ (θ0, θ1) for exponentially distributed observations in the presence of outliers drawn from a uniform distribution. Estimators obtained from both shrinkage and interval shrinkage were compared, showing that the estimators obtained via the interval shrinkage method perform better. Symmetric and asymmetric loss functions were also used to calculate the estimators. Finally, a numerical study and illustrative examples were provided to describe the results.
12
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Chain Ratio Estimator for the Population Mean in the Presence of Non-Response

75%
Khare B. B., Srivastava U., Kumar K.
Statistics in Transition new series
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2012
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vol. 13
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issue 3
495-518
EN
In this paper we have proposed two chain ratio type estimators for population mean using two auxiliary variables in the presence of non-response. The proposed estimators have been found to be more efficient than the relevant estimators for the fixed values of preliminary sample of size n′and subsample of size n(
13
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Ratio-To-Regression Estimator In Successive Sampling Using One Auxiliary Variable

75%
Ralte Z., Das G.
Statistics in Transition new series
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2015
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vol. 16
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issue 2
183-202
EN
The problem of estimation of finite population mean on the current occasion based on the samples selected over two occasions has been considered. In this paper, first a chain ratio-to-regression estimator was proposed to estimate the population mean on the current occasion in two-occasion successive (rotation) sampling using only the matched part and one auxiliary variable, which is available in both the occasions. The bias and mean square error of the proposed estimator is obtained. We proposed another estimator, which is a linear combination of the means of the matched and unmatched portion of the sample on the second occasion. The bias and mean square error of this combined estimator is also obtained. The optimum mean square error of this combined estimator was compared with (i) the optimum mean square error of the estimator proposed by Singh (2005) (ii) mean per unit estimator and (iii) combined estimator suggested by Cochran (1977) when no auxiliary information is used on any occasion. Comparisons are made both analytically as well as empirically by using real life data.
14
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ROBUSTNESS OF TWEEDIE MODEL OF RESERVES WITH RESPECT TO DISTRIBUTION OF SEVERITY OF CLAIMS

63%
Boratyńska A., Juszczak D.
Metody Ilościowe w Badaniach Ekonomicznych
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2015
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vol. 16
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issue 1
53-74
EN
The aim of the work is to discuss the robustness of estimation procedures and robustness of prediction in Tweedie's compound Poisson model. This model is applied to the claim reserving problem. The quality of parameter estimators and predictors is studied when the distribution of severity of claims is disturbed. The ε-contamination class of distributions is considered. The example, where errors of estimators are large is presented. The simulation methods, using the R programming environment, are applied.
15
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On the smoothed parametric estimation of mixing proportion under fixed design regression model

63%
Ramakrishnaiah Y. S., Trivedi M., Satish K.
Statistics in Transition new series
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2019
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vol. 20
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issue 1
87-102
EN
The present paper revisits an estimator proposed by Boes (1966) - James (1978), herein called BJ estimator, which was constructed for estimating mixing proportion in a mixed model based on independent and identically distributed (i.i.d.) random samples, and also proposes a completely new (smoothed) estimator for mixing proportion based on independent and not identically distributed (non-i.i.d.) random samples. The proposed estimator is nonparametric in true sense based on known “kernel function” as described in the introduction. We investigated the following results of the smoothed estimator under the non-i.i.d. set-up such as (a) its small sample behaviour is compared with the unsmoothed version (BJ estimator) based on their mean square errors by using Monte-Carlo simulation, and established the percentage gain in precision of smoothed estimator over its unsmoothed version measured in terms of their mean square error, (b) its large sample properties such as almost surely (a.s.) convergence and asymptotic normality of these estimators are established in the present work. These results are completely new in the literature not only under the case of i.i.d., but also generalises to non-i.i.d. set-up.
16

Using Bayesian Statistics in Enterprise Demography

51%
Kotlebová E., Láska I.
Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie
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2015
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issue 11(947)
67-81
EN
Knowledge of the number of different kinds of enterprises that will be created in a coming year is essential information. It can be used in macroeconomic analyses and as a constituent of the background for economic policy. From a demographics point of view, we consider the creation (birth) of some enterprise as a basic indicator. It can also be approached from the point of view of inference, as the creation of enterprise is influenced by a wide variety of inputs. Enterprise creation may therefore be thought of as a random process. The analytic tools Bayesian statistics provide make it possible involve more kinds of information into statistical analysis and gradually update the parameter estimations. We used the conjugate family Poisson / gamma to estimate the number of enterprises to be created in a coming year. The considerations were concerned with the mean square error, which was used as the main criterion of the point estimation quality. We solved two kinds of problems: to find a Bayesian point estimation that has a smaller mean square error than the classical one in a predetermined interval, and, along with it, to model prior information in a very simple way. In finding some connection among the variables contained in the conjugate family Poisson / gamma, we solved both presented problems and also developed a simple algorithm for optimal point estimation of the Poisson distribution parameter. This algorithm was used to estimate the number of enterprises created.
PL
Znajomość liczby przedsiębiorstw różnego typu, których utworzenie jest planowane w najbliższym roku, stanowi istotną informację, która może zostać wykorzystana w aspekcie makroekonomicznym, a także może stanowić podstawę do kreowania polityki ekonomicznej. Z demograficznego punktu widzenia podstawowym przedmiotem rozważań jest powstanie przedsiębiorstwa. Możliwe jest również podejście nawiązujące do zasad wnioskowania statystycznego, gdyż na tworzenie przedsiębiorstw oddziałują liczne i zróżnicowane czynniki, co daje podstawy do postrzegania tego procesu jako losowego. Metody analityczne statystyki bayesowskiej dają możliwość uwzględnienia w procesie badania większej ilości informacji oraz stopniowej korekty oszacowania danego parametru. Do oszacowania liczby planowanych do utworzenia przedsiębiorstw wykorzystano rodzinę rozkładów sprzężonych Poisson-gamma. Niezbędne rozważania oparte zostały na błędzie średniokwadratowym, przyjętym jako główne kryterium oceny jakości dokonanej estymacji punktowej. W artykule przedstawiono rozwiązania dwóch problemów badawczych: poszukiwania takiego estymatora bayesowskiego, który ma mniejszy błąd średniokwadratowy w porównaniu z ujęciem klasycznym dla z góry określonego przedziału, oraz przejrzystego sposobu modelowania rozkładów a priori. Dzięki zidentyfikowaniu pewnych powiązań pomiędzy zmiennymi opisywanymi mieszankami rozkładów z rodziny Poisson-gamma możliwe stało się rozwiązanie obu wyżej sformułowanych problemów oraz zbudowanie prostego algorytmu optymalnej estymacji punktowej parametru rozkładu Poissona. Algorytm ten został wykorzystany do oszacowania liczby nowo tworzonych przedsiębiorstw.
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