Improving on two-stage estimators for scale families

Summary Consider the problem of finding an estimator for a scale parameter such that its risk function is bounded by a preassigned constant. As a solution of the problem, two-stage estimators based on only the second sample have been proposed. The paper shows that these estimators can be improved by combining the first and the second sample.     

Partially generalized least squares and two-stage least squares estimators

A class of partially generalized least squares estimators and a class of partially generalized two-stage least squares estimators in regression models with heteroscedastic errors are proposed. By using these estimators a researcher can attain higher efficiency than that attained by the least squares or the two-stage least squares estimators without explicitly estimating each component of the heteroscedastic variances. However, the efficiency is not as high as that of the generalized least squares or the generalized two-stage least squares estimator calculated using the knowledge of the true variances. Hence the use of the term partial.     

The nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator

Several limited-information type estimators of the nonlinear simultaneous equation model are considered and their asymptotic covariance matrices are compared. Amemiya (1974) proposed the general class of nonlinear two-stage least-squares estimators. In this paper, its two specific members are considered and, in addition, the nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator are proposed. Both are shown to be asymptotically more efficient than the nonlinear two-stage least-squares estimator, and the second has the advantage of being computationally simple.     

A simplified approach to M-estimation with application to two-stage estimators

This paper presents a simple version of the theory of M-estimation. It is argued that the theory is immediately applicable to almost all estimation schemes employed by econometricians. It is further argued that the great overlooked benefit of the theory is that is provides almost automatic asymptotic results, e.g., probability limits and asymptotic covariances. Thus one need not be a theoretical econometrician to invent and use specially tailored estimators. To illustrate its use the theory is applied to a variety of theoretical and applied problems. Particular attention is paid to two-stage estimators.     

Regular estimators for subclasses of linear estimators

Summary The concept of regular estimator is due toRoy/Chakravarti. For its application they confined to the most general class of linear estimators. The present paper considers some subclasses of linear estimators.     

Some large-concentration-parameter asymptotics for the k-class estimators

A sufficient condition is derived in this paper for the consistency and asymptotic normality of the k-class estimators (k-stochastic or nonstochastic) as the concentration parameter increases indefinitely, with the sample size either staying fixed or also increasing. It is further shown that the limited-information maximum likelihood estimator satisfies this condition. Since large sample size implies a large concentration parameter, but not vice versa, the usual conditions for consistency and asymptotic normality of the k-class estimators as the sample size increases can be inferred from the results given in this paper. But more importantly, the results in this paper shed further light on the small-sample properties of the stochastic k-class estimators and can serve as a starting point for the derivation of asymptotic approximations for these estimators as the concentration parameter goes to infinity, while the sample size either stays fixed or also goes to infinity.     

Dominating estimators for minimum-variance portfolios

In this paper, we derive two shrinkage estimators for minimum-variance portfolios that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of assets d≥4$d\ge 4$ and number of observations n≥d+2$n\ge d+2$. The small-sample properties of the shrinkage estimators as well as their large-sample properties for fixed d$d$ but n→∞$n\to \infty$ and n,d→∞$n,d\to \infty$ but n/d→q≤∞$n/d\to q\le \infty$ are investigated. Furthermore, we present a small-sample test for the question of whether it is better to completely ignore time series information in favor of naive diversification.     

Model averaging estimators for the stochastic frontier model

Journal of Productivity Analysis - Model uncertainty is a prominent feature in many applied settings. This is certainty true in the efficiency analysis realm where concerns over the proper...     

Robust estimators for estimating discontinuous functions

We study the asymptotic behavior of a wide class of kernel estimators for estimating an unknown regression function. In particular we derive the asymptotic behavior at discontinuity points of the regression function. It turns out that some kernel estimators based on outlier robust estimators are consistent at jumps.     

Approximations for densities of sufficient estimators

A simple method of obtaining asymptotic expansions for the densities of sufficient estimators is described. It is an extension of the one developed by O. Barndorff-Nielsen and D.R. Cox (1979) for exponential families. A series expansion in powers of n^?1 is derived of which the first term has an error of order n^?1 which can effectively be reduced to $\text{n}{}^{\mathrm{<mtext>-</mtext><mtext>?3</mtext><mtext>2</mtext>}}$ by renormalization. The results obtained are similar to those given by H.E. Daniels's (1954) saddlepoint method but the derivations are simpler. A brief treatment of approximations to conditional densities is given. Theorems are proved which extend the validity of the multivariate Edgeworth expansion to parametric families of densities of statistics which need not be standardized sums of independent and identically distributed vectors. These extensions permit the treatment of problems arising in time series analysis. The technique is used by J. Durbin (1980) to obtain approximations to the densities of partial serial correlation coefficients.     

Hermite series estimators for probability densities

Summary For Hermite series density estimators assertions about rates of convergence of MSE, MISE and about asymptotic normality are given. Moreover, we study the behaviour of these estimators if the density is not continuous. Hermite series estimators with random length are also considered. Convergence in probability and a.s. of these estimators is proved.     

On the admissibility of estimators for the finite population variance

Summary With each unti of a finite population is associated an unknown variate value. We are interested in the variance of these values and consider (1) simple random sampling without replacement. (2) quadratic loss and (3) a one parameter class of estimators. We determine all admissible elements of the class. The usual unbiased estimator for the variance which is an element of the class considered turns out to be inadmissible.     

Riesz estimators

We consider properties of estimators that can be written as vector lattice (Riesz space) operations. Using techniques widely used in economic theory and functional analysis, we study the approximation properties of these estimators paying special attention to additive models. We also provide two algorithms RIESZVAR(i-ii) for the consistent parametric estimation of continuous multivariate piecewise linear functions.     

Minimax estimators for a bounded location parameter

Summary Recently, Bischoff and Fieger (1992) considered the classical problem of estimating a bounded normal mean when the loss is thep-th power of the error. They proved that forp>-2 a two point prior is least favourable in case the parameter interval is small enough. In the present paper it is shown that this result remains valid forp>1. Moreover, the normal family is generalized to location parameter families. Finally, it is proved that no two point prior is least favourable for absolute error loss, i.e., forp=1.     

On minimum distance estimators for unimodal densities

It is shown that minimum distance estimators for families of unimodal densities are always consistent; the rate of convergence is indicated. An algorithm is proposed for computing the minimum distance estimator for the family of all unimodal densities. References are given to the maximum likelihood method and the kernel method.     

Stable Asymptotics for M‐estimators

We review some first‐order and higher‐order asymptotic techniques for M‐estimators, and we study their stability in the presence of data contaminations. We show that the estimating function (ψ) and its derivative with respect to the parameter play a central role. We discuss in detail the first‐order Gaussian density approximation, saddlepoint density approximation, saddlepoint test, tail area approximation via the Lugannani–Rice formula and empirical saddlepoint density approximation (a technique related to the empirical likelihood method). For all these asymptotics, we show that a bounded ψ (in the Euclidean norm) and a bounded (e.g. in the Frobenius norm) yield stable inference in the presence of data contamination. We motivate and illustrate our findings by theoretical and numerical examples about the benchmark case of one‐dimensional location model.     

Quantile models and estimators for data analysis

Quantile regression is used to estimate the cross sectional relationship between high school characteristics and student achievement as measured by ACT scores. The importance of school characteristics on student achievement has been traditionally framed in terms of the effect on the expected value. With quantile regression the impact of school characteristics is allowed to be different at the mean and quantiles of the conditional distribution. Like robust estimation, the quantile approach detects relationships missed by traditional data analysis. Robust estimates detect the influence of the bulk of the data, whereas quantile estimates detect the influence of co-variates on alternate parts of the conditional distribution. Since our design consists of multiple responses (individual student ACT scores) at fixed explanatory variables (school characteristics) the quantile model can be estimated by the usual regression quantiles, but additionally by a regression on the empirical quantile at each school. This is similar to least squares where the estimate based on the entire data is identical to weighted least squares on the school averages. Unlike least squares however, the regression through the quantiles produces a different estimate than the regression quantiles.     

Practical estimators for sampling on successive occasions

In een steekproefschema dat zich uitstrekt over enige tijd kan de steekproefomvang varieren van periode tot periode. Een aantal schattingsmethoden worden voorgesteld die zoveel mogelijk informatie benutten uit de voorafgaande waarnemingen. Ze worden vergeleken met de regressieschatting die theoretisch optimaal is. Bij net waarnemen echter van een zeer groot aantal kenmerken is de regressie-schatting niet langer bruikbaar als gevolg van de grote aantallen berekeningen.
De voorgestelde schatters verliezen aan precisie maar veroorzaken geen reken-technische problemen.