Robust test for means when population variances are unequal

We consider the problem of testing the equality of two population means when the population variances are not necessarily equal. We propose a Welch-type statistic, say T^* _c, based on Tiku!s ‘1967, 1980’ modified maximum likelihood estimators, and show that this statistic is robust to symmetric and moderately skew distributions. We investigate the power properties of the statistic T^* _c; T^* _c clearly seems to be more powerful than Yuen's ‘1974’ Welch-type robust statistic based on the trimmed sample means and the matching sample variances. We show that the analogous statistics based on the ‘adaptive’ robust estimators give misleading Type I errors. We generalize the results to testing linear contrasts among k population means     

A time series model with random coefficients

There are many time series applications where an experi­menter observes the simultaneous responses of several sub­systems over time. In these instances one is often not interested in the parameters of individual subsystems, but rather in an overall characterization of the system in question. Under the assumption that subsystems are independent and first order autoregressive, the present paper presents two methods for estimating the distribution of the subsystem coefficients.     

Local Power Analyses of Goodness-of-fit Tests for Copulas

Abstract.  The asymptotic behaviour of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cramér–von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made by considering their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Cramér–von Mises test and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods.     

Estimation of regression models with equi-correlated responses when some observations on the response variable are missing

The present article deals with the problem of estimation of parameters in a linear regression model when some data on response variable is missing and the responses are equi-correlated. The ordinary least squares and optimal homogeneous predictors are employed to find the imputed values of missing observations. Their efficiency properties are analyzed using the small disturbances asymptotic theory. The estimation of regression coefficients using these imputed values is also considered and a comparison of estimators is presented.     

Provincial Conditional Income Convergence in China, 1953-1997: A Panel Data Approach

This paper examines the tendency towards income convergence among China's main provinces during the two periods: the pre-reform period 1953-1977 and the reform period 1978-1997 using the framework of the Solow growth model. The panel data method accounts for not only province-specific initial technology level but also the heterogeneity of the technological progress rate between the fast-growing coastal and interior provinces. Estimation problems of weak instruments and endogeneity are addressed by the use of a system generalized method of moments (GMM) estimator. The main empirical finding is that there is a system-wide income divergence during the reform period because the coastal provinces do not share a common technology progress rate with the interior provinces.     

Improved estimators for the selected location parameters

_i , i = 1, 2, ..., k be k independent exponential populations with different unknown location parameters θ _i , i = 1, 2, ..., k and common known scale parameter σ. Let Y _i denote the smallest observation based on a random sample of size n from the i-th population. Suppose a subset of the given k population is selected using the subset selection procedure according to which the population π _i is selected iff Y _i ≥Y ₍₁₎−d, where Y ₍₁₎ is the largest of the Y _i 's and d is some suitable constant. The estimation of the location parameters associated with the selected populations is considered for the squared error loss. It is observed that the natural estimator dominates the unbiased estimator. It is also shown that the natural estimator itself is inadmissible and a class of improved estimators that dominate the natural estimator is obtained. The improved estimators are consistent and their risks are shown to be O(kn ⁻²). As a special case, we obtain the coresponding results for the estimation of θ₍₁₎, the parameter associated with Y ₍₁₎. Received: January 6, 1998; revised version: July 11, 2000     

Best monotone M‐estimators

The author shows how to find M‐estimators of location whose generating function is monotone and which are optimal or close to optimal. It is easy to identify a consistent sequence of estimators in this class. In addition, it contains simple and efficient approximations in cases where the likelihood function is difficult to obtain. In some neighbourhoods of the normal distribution, the loss of efficiency due to the approximation is quite small. Optimal monotone M‐estimators can also be determined in cases when the underlying distribution is known only up to a certain neighbourhood. The author considers the e‐contamination model and an extension thereof that allows the distributions to be arbitrary outside compact intervals. His results also have implications for distributions with monotone score functions. The author illustrates his methodology using Student and stable distributions.     

NONPARAMETRIC QUANTILE ESTIMATION FROM RECORD-BREAKING DATA

Sometimes, in industrial quality control experiments and destructive stress testing, only values smaller than all previous ones are observed. Here we consider nonparametric quantile estimation, both the ‘sample quantile function’ and kernel-type estimators, from such record-breaking data. For a single record-breaking sample, consistent estimation is not possible except in the extreme tails of the distribution. Hence replication is required, and for m. such independent record-breaking samples the quantile estimators are shown to be strongly consistent and asymptotically normal as m-→∞. Also, for small m, the mean-squared errors, biases and smoothing parameters (for the smoothed estimators) are investigated through computer simulations.     

Comparing robust generalized variances and comments on efficiency

Numerous papers have considered the problem of comparing univariate measures of dispersion corresponding to two independent groups. This paper considers a multivariate generalization of this problem where the goal is to compare robust generalized variances. For reasons given in the paper, attention is focused on a particular W-estimator where multivariate outliers are downweighted via a projection-type outlier detection method. Included are results on the small-sample efficiency of several estimators plus comments on using the usual generalized variance.     

The asymptotic equivalence between the iterated improved 2sls estimator and the 3sls estimator

In this paper we show that the 3SLS estimator of a system of equations is asymptotically equivalent to an iterative 2SLS estimator applied to each equation, augmented with the residuals from the other equations. This result is a natural extension of Telser (1964).