A sufficient condition for the MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated in a misspecified linear regression model

In this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family of shrinkage estimators for each individual regression coefficient. It is shown analytically that when our concern is to estimate each individual regression coefficient, the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators under some conditions even when the relevant regressors are omitted. Also, by numerical evaluations, we showed the effects of our theorem for several specific cases. It is shown that the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators for wide region of parameter space even when there exist omitted variables in the specified model.     

Comparison of point estimators of normal percentiles

There are available several point estimators of the percentiles of a normal distribution with both mean and variance unknown. Consequently, it would seem appropriate to make a comparison among the estimators through some “closeness to the true value” criteria. Along these lines, the concept of Pitman-closeness efficiency is introduced. Essentially, when comparing two estimators, the Pit-man-closeness efficiency gives the “odds” in favor of one of the estimators being closer to the true value than is the other in a given situation. Through the use of Pitman-closeness efficiency, this paper compares (a) the maximum likelihood estimator, (b) the minimum variance unbiased estimator, (c) the best invariant estimator, and (d) the median unbiased estimator within a class of estimators which includes (a), (b), and (c). Mean squared efficiency is also discussed.     

Ban Estimation for Chi-Square Test Criteria in Categorical Data

This expository paper describes some recent work that further develops the theory of BAN estimators and the related chi-scuare test statistics.The extensions are in several directions: (a) the class of regular estimators is broadened by permitting extraneous random elements; (b) more general models are permitted under the constraint equations specification; and (c) BAN estimators are defined for general models combining features of two types of specification.In particular, WLS estimators are shown to be BAN.     

关于均匀分布统计分析的一些思考

对于均匀分布给出了在全样本场合下参数的区间估计,在定数截尾场合下参数的点估计和区间估计,并通过大量Monte-Carlo模拟从均方差的角度比较各种点估计的优劣,考察各种区间估计方法的精度,通过实例说明这些点估计和区间估计方法的应用。     

Comparisons of the alternative biased estimators for the distributed lag models

The finite distributed lag models include highly correlated variables as well as lagged and unlagged values of the same variables. Some problems are faced for this model when applying the ordinary least squares (OLS) method or econometric models such as Almon and Koyck models. The primary aim of this study is to compare performances of alternative estimators to the OLS estimator defined by combining the Almon estimator with some estimators using Almon (1965) data. A simulation study with different model parameters is performed and the estimators are compared according to the root mean square error (RMSE) and prediction mean square error (PMSE).     

Restricted minimum bias linear estimation in regression

In this article a class of restricted minimum bias linear estimators of the vector of unknown regression coefficients when multicollinearity among the columns of the design matrix exists, is obtained. The ordinary ridge regression, principal components and shrinkage estimators are members of this class. Moreover, our ap-proach can be used to improve, in some sense, certain classes of generalized ridge and shrinkage estimators of the vector of un-known parameters in linear models.     

Generalized preliminary test stochastic restricted estimator in the linear regression model

ABSTRACT

In this paper, we propose three generalized estimators, namely, generalized unrestricted estimator (GURE), generalized stochastic restricted estimator (GSRE), and generalized preliminary test stochastic restricted estimator (GPTSRE). The GURE can be used to represent the ridge estimator, almost unbiased ridge estimator (AURE), Liu estimator, and almost unbiased Liu estimator. When stochastic restrictions are available in addition to the sample information, the GSRE can be used to represent stochastic mixed ridge estimator, stochastic restricted Liu estimator, stochastic restricted almost unbiased ridge estimator, and stochastic restricted almost unbiased Liu estimator. The GPTSRE can be used to represent the preliminary test estimators based on mixed estimator. Using the GPTSRE, the properties of three other preliminary test estimators, namely preliminary test stochastic mixed ridge estimator, preliminary test stochastic restricted almost unbiased Liu estimator, and preliminary test stochastic restricted almost unbiased ridge estimator can also be discussed. The mean square error matrix criterion is used to obtain the superiority conditions to compare the estimators based on GPTSRE with some biased estimators for the two cases for which the stochastic restrictions are correct, and are not correct. Finally, a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings of the proposed estimators.     

Non-minimaxity of linear combinations of restricted location estimators and related problems

The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. Although the corresponding linear combination of the unbiased estimators is minimax under the restricted problem, it has a drawback of taking values outside the restricted parameter space. Thus, it is reasonable to use the linear combination of the restricted estimators such as maximum likelihood or truncated estimators. In this paper, a necessary and sufficient condition for such restricted estimators to be minimax is derived, and it is shown that the restricted estimators are not minimax when the number of the location parameters is large. The condition for minimaxity is examined for some specific distributions. Finally, similar problems of estimating the product and sum of the restricted scale parameters are studied, and it is shown that analogous non-dominance properties appear when the number of the scale parameters is large.     

Time varying long memory parameter estimation for locally stationary long memory processes

The semiparametric estimators of time varying long memory parameter are investigated for locally stationary long memory processes. The GPH estimator and the local Whittle estimator are considered. Under some mild regularity assumptions, the weak consistency and the asymptotic normality of the estimators are obtained. The finite sample performance of the estimators is discussed through a small simulation study.     

Preliminary test estimators in double sampling with two auxiliary variables

An attempt has been mads to suggest some estimators for population mean in double sampling with two auxiliary variables., alternative to the usual regression estimator. When the experimenter has partial Information about the mean of the auxiliary variable or variables, preliminary test estimators can be used. The bias, mean square error, relative efficiency and optimum allocation of sample sizes are obtained for the suggested estimators.     

Ratio and product estimators in stratified random sampling

Khoshnevisan et al. [2007. A general family of estimators for estimating population mean using known value of some population parameter(s). Far East Journal of Theoretical Statistics 22, 181–191] have introduced a family of estimators using auxiliary information in simple random sampling. They have showed that these estimators are more efficient than the classical ratio estimator and that the minimum value of the mean square error (MSE) of this family is equal to the value of MSE of regression estimator. In this article, we adapt the estimators in this family to the stratified random sampling and motivated by the estimator in Searls [1964. Utilization of known coefficient of kurtosis in the estimation procedure of variance. Journal of the American Statistical Association 59, 1225–1226], we also propose a new family of estimators for the stratified random sampling. The expressions of bias and MSE of the adapted and proposed families are derived in a general form. Besides, considering the minimum cases of these MSE equations, the efficient conditions between the adapted and proposed families are obtained. Moreover, these theoretical findings are supported by a numerical example with original data.     

Estimation of Measures in M/M/1 Queue

Maximum likelihood and uniform minimum variance unbiased estimators of steady-state probability distribution of system size, probability of at least ? customers in the system in steady state, and certain steady-state measures of effectiveness in the M/M/1 queue are obtained/derived based on observations on X, the number of customer arrivals during a service time. The estimators are compared using Asympotic Expected Deficiency (AED) criterion leading to recommendation of uniform minimum variance unbiased estimators over maximum likelihood estimators for some measures.     

Improved versions of greenwood estimators under koziol-green model

ABSTRACT

It is well known that the Greenwood estimators underestimate the variances of the Nelson-Aalen estimator and the Kaplan-Meier estimator. In this article, we reveal some “improved” versions of the Greenwood estimators under the Koziol-Green model.     

Some simple estimators for the two-parameter gamma distribution

ABSTRACT

In this paper, we propose two new simple estimation methods for the two-parameter gamma distribution. The first one is a modified version of the method of moments, whereas the second one makes use of some key properties of the distribution. We then derive the asymptotic distributions of these estimators. Also, bias-reduction methods are suggested to reduce the bias of these estimators. The performance of the estimators are evaluated through a Monte Carlo simulation study. The probability coverages of confidence intervals are also discussed. Finally, two examples are used to illustrate the proposed methods.     

MSE performance of the weighted average estimators consisting of shrinkage estimators

In this paper, we consider a regression model and propose estimators which are the weighted averages of two estimators among three estimators; the Stein-rule (SR), the minimum mean squared error (MMSE), and the adjusted minimum mean-squared error (AMMSE) estimators. It is shown that one of the proposed estimators has smaller mean-squared error (MSE) than the positive-part Stein-rule (PSR) estimator over a moderate region of parameter space when the number of the regression coefficients is small (i.e., 3), and its MSE performance is comparable to the PSR estimator even when the number of the regression coefficients is not so small.     

A REGRESSION APPROACH TO THE ESTIMATION OF THE FINITE POPULATION MEAN IN THE PRESENCE OF NON‐RESPONSE

This paper presents various estimators for estimating the population mean of the study variable y using information on the auxiliary variable x in the presence of non‐response. Properties of the suggested estimators are studied and compared with those of existing estimators. It is shown that the estimators suggested in this paper are among the best of all the estimators considered. An empirical study is carried out to demonstrate the performance of the suggested estimators and of others, and it is found that the empirical results support the theoretical study.     

A two-step robust estimation of the process mean using M-estimator

Parameter estimation is the first step in constructing control charts. One of these parameters is the process mean. The classical estimators of the process mean are sensitive to the presence of outlying data and subgroups which contaminate the whole data. In existing robust estimators for the process mean, the effects of the presence of the individual outliers are being considered, while, in this paper, a robust estimator is being proposed to reduce the effect of outlying subgroups as well as the individual outliers within a subgroup. The proposed estimator was compared with some classical and robust estimators of the process mean. Although, its relative efficiency is fourth among the estimators tested, its robustness and efficiency are large when the outlying subgroups are present. Evaluation of the results indicated that the proposed estimator is less sensitive to the presence of outliers and the process mean performs well when there are no individual outliers or outlying subgroups.     

Mean Squared Error Matrix Comparisons of Some Restricted Almost Unbiased Estimators

In this article, we introduce two almost unbiased estimators for the vector of unknown parameters in a linear regression model when additional linear restrictions on the parameter vector are assumed to hold. Superiority of the two estimators under the mean squared error matrix (MSEM) is discussed. Furthermore, a numerical example and simulation study are given to illustrate some of the theoretical results.     

Admissible estimation in an one parameter nonregular family of absolutely continuous distributions

Consider the problem of estimating under squared error loss an arbitrarily positive, strictly increasing or decreasing parametric function based on a sample of size n in an one parameter nonregular family of absolutly continuous distributions with both endpoints of the support depending on a single parameter. We first provide sufficient conditions for the admissibility of generalized Bayes estimators with respect to some specific priors and then treat several examples which illustrate the admissibility of best invariant estimators in some location or scale parameter problems.     

A note on comparison and improvement of estimators based on likelihood

The problem of estimation of a parameter of interest in the presence of a nuisance parameter, which is either location or scale, is considered. Three estimators are taken into account: usual maximum likelihood (ML) estimator, maximum integrated likelihood estimator and the bias-corrected ML estimator. General results on comparison of these estimators w.r.t. the second-order risk based on the mean-squared error are obtained. Possible improvements of basic estimators via the notion of admissibility and methodology given in Ghosh and Sinha [A necessary and sufficient condition for second order admissibility with applications to Berkson's bioassay problem. Ann Stat. 1981;9(6):1334–1338] are considered. In the recent paper by Tanaka et al. [On improved estimation of a gamma shape parameter. Statistics. 2014; doi:10.1080/02331888.2014.915842], this problem was considered for estimating the shape parameter of gamma distribution. Here, we perform more accurate comparison of estimators for this case as well as for some other cases.