On the efficiency of ratio estimator over the regression estimator

It is well known that the ratio and product estimators have the limitation of having efficiency not exceeding that of the linear regression estimator. This paper develops a new approach to ratio estimation that produces a more precise and efficient ratio estimator that is superior to the regression estimator both in efficiency and biasedness. An empirical study is given.     

On the best linear unbiased estimator and the linear sufficiency of a general growth curve model

Growth curve models are used to analyze repeated measures data (longitudinal data), which are functions of time. In this paper, some necessary and sufficient conditions for linear function B₁YB₂ to be the best linear unbiased estimator (BLUE) of estimable functions X₁ΘX₂ (or K₁ΘK₂) under the general growth curve model were established. In addition, the representations of BLUE(K₁ΘK₂) (or BLUE(X₁ΘX₂)) were derived when the conditions are satisfied. Two special notions of linear sufficiency with respect to the general growth curve model are given in the end. The findings of this paper enrich some known results in the literature.     

On the maximum-likelihood estimator for the location parameter of a cauchy distribution

In the literature of point estimation, the Cauchy distribution with location parameter is often cited as an example for the failure of maximum-likelihood method and hence the failure of the likelihood principle in general. Contrary to the above notion, we prove that even in this case the likelihood equation has multiple roots and that the maximum-likelihood estimator (the global maximum) remains as an asymptotically optimal estimator in the Bahadur sense.     

On asymptotic properties of the parameter estimator for a type of SPDE

In this paper, we study a random field _U?(t,x)$U_{?}(t,x)$ governed by some type of stochastic partial differential equations with an unknown parameter θ$\theta$ and a small noise ?$?$. We construct an estimator of θ$\theta$ based on the continuous observation of N   Fourier coefficients of _U?(t,x)$U_{?}(t,x)$, and prove the strong convergence and asymptotic normality of the estimator when the noise ?$?$ tends to zero.     

On the inadmssibelity of ridge estimator in a linear model

The necessary and sufficient conditions for the inadmissibility of the ridge regression is discussed under two different criteria, namely, average loss and Pitman nearness. Although the two criteria are very different, same conclusions are obtained. The loss functions considered in this article are th likelihood loss function and the Mahalanobis loss function. The two loss functions are motivated from the point of view of classification of two normal populations. Under the Mahalanobis loss it is demonstrated that the ridge regression is always inadmissible as long as the errors are assumed to be symmetrically distributed about the origin.     

On the efficiency of a testimator for the weibull shape parameter

In estimating the shape parameter of a two-parameter Weibull distribution from a failure-censored sample, a recently popular procedure is to employ a testimator which is a shrinkage estimator based on a preliminary hypothesis test for a guessed value of the parameter. Such an adaptive testimator is a linear compound of the guessed value and a statistic. A new compounding coefficient is numerically shown to yield higher efficiency in many situations compared to some of the existing ones.     

On the least-squares model averaging interval estimator

In many applications of linear regression models, randomness due to model selection is commonly ignored in post-model selection inference. In order to account for the model selection uncertainty, least-squares frequentist model averaging has been proposed recently. We show that the confidence interval from model averaging is asymptotically equivalent to the confidence interval from the full model. The finite-sample confidence intervals based on approximations to the asymptotic distributions are also equivalent if the parameter of interest is a linear function of the regression coefficients. Furthermore, we demonstrate that this equivalence also holds for prediction intervals constructed in the same fashion.     

On optimality of the horvitz-thompson estimator under a markov process model

For any varying probability sampling design the Horvitz-Thompson (1952) estimator is shown to be optimal within the class of all unbiased estimators of a finite population total under a Markov process model     

Immaculating the inconsistent estimator of slope parameter in measurement error model with replicated data

ABSTRACT

The measurement error model with replicated data on study as well as explanatory variables is considered. The measurement error variance associated with the explanatory variable is estimated using the complete data and the grouped data which is used for the construction of the consistent estimators of regression coefficient. These estimators are further used in constructing an almost unbiased estimator of regression coefficient. The large sample properties of these estimators are derived without assuming any distributional form of the measurement errors and the random error component under the setup of an ultrastructural model.     

Efficiency of an adaptive estimator of a log-zero-poisson parameter

An estimator, λ is proposed for the parameter λ of the log-zero-Poisson distribution. While it is not a consistent estimator of λ in the usual statistical sense, it is shown to be quite close to the maximum likelihood estimates for many of the 35 sets of data on which it is tried. Since obtaining maximum likelihood estimates is extremely difficult for this and other contagious distributions, this estimate will act at least as an initial estimate in solving the likelihood equations iteratively. A lesson learned from this experience is that in the area of contagious distributions, variability is so large that attention should be focused directly on the mean squared error and not on consistency or unbiasedness, whether for small samples or for the asymptotic case. Sample sizes for some of the data considered in the paper are in hundreds. The fact that the estimator which is not a consistent estimator of λ is closer to the maximum likeli-hood estimator than the consistent moment estimator shows that the variability is large enough to not permit consistency to materialize even for such large sample sizes usually available in actual practice.     

Asymptotic properties of the tumor growth curve estimator

The estimator of growth curve of tumors (based on a single observation per tumor, viz. its size at detection), proposed earlier is analyzed. The results concern its asymptotic bias and MSE as well as the limiting behavior of the estimator treated as a stochastic process.     

On the performance of the Jackknifed Liu-type estimator in linear regression model

In this paper, we are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the Liu-type estimator (LTE) and the jackknifed Liu-type estimator (JLTE). We will also present the necessary and sufficient conditions for superiority of the MJLTE over the LTE and JLTE, in terms of mean square error matrix criterion. Finally, a real data example and a Monte Carlo simulation are also given to illustrate theoretical results.     

Tuning parameter selection for a penalized estimator of species richness

Our goal is to estimate the true number of classes in a population, called the species richness. We consider the case where multiple frequency count tables have been collected from a homogeneous population and investigate a penalized maximum likelihood estimator under a negative binomial model. Because high probabilities of unobserved classes increase the variance of species richness estimates, our method penalizes the probability of a class being unobserved. Tuning the penalization parameter is challenging because the true species richness is never known, and so we propose and validate four novel methods for tuning the penalization parameter. We illustrate and contrast the performance of the proposed methods by estimating the strain-level microbial diversity of Lake Champlain over three consecutive years, and global human host-associated species-level microbial richness.     

On the restricted almost unbiased two-parameter estimator in linear regression model

Özkale and Kaçiranlar introduced the restricted two-parameter estimator (RTPE) to deal with the well-known multicollinearity problem in linear regression model. In this paper, the restricted almost unbiased two-parameter estimator (RAUTPE) based on the RTPE is presented. The quadratic bias and mean-squared error of the proposed estimator is discussed and compared with the corresponding competitors in literatures. Furthermore, a numerical example and a Monte Carlo simulation study are given to explain some of the theoretical results.     

Consistency of least-squares estimator and its jackknife variance estimator in nonlinear models

The purpose of this paper is twofold: (1) We establish the consistency of the least-squares estimator in a nonlinear modely_i = f(x_i,θ) +σ_ie_i where the range of the parameter θ is noncompact, the regression function is unbounded, and the σ_i,'s are not necessarily equal. This extends the results in Jennrich (1969) and Wu (1981). (2) Under the same model, the jackknife estimator of the asymptotic covariance matrix of the least-squares estimator is shown to be consistent, which provides a theoretical justification of the empirical results in Duncan (1978) and the use of the jackknife method in large-sample inferences.     

On the restricted almost unbiased Liu estimator in the logistic regression model

It is known that when the multicollinearity exists in the logistic regression model, variance of maximum likelihood estimator is unstable. As a remedy, in the context of biased shrinkage Liu estimation, Chang introduced an almost unbiased Liu estimator in the logistic regression model. Making use of his approach, when some prior knowledge in the form of linear restrictions are also available, we introduce a restricted almost unbiased Liu estimator in the logistic regression model. Statistical properties of this newly defined estimator are derived and some comparison results are also provided in the form of theorems. A Monte Carlo simulation study along with a real data example are given to investigate the performance of this estimator.     

Asymptotic properties of the ols and grls estimator for the replicated functional relationship model

For the simple linear functional relationship model with replication, the asymptotic properties of the ordinary (OLS) and grouping least squares (GRLS) estimator of the slope are investi- gated under the assumption of normally distributed errors with unknown covariance matrix. The relative performance of the OLS and GRLS estimator is compared in terms of the asymptotic mean square error, and a set of critical parameters are identified for determining the dominance of one estimator over the other. It is also shown that the GRLS estimator is asymptoticallyequivalent to the maximum likelihood (ML) estimator under the given assumptions.