Multivariate analysis with an autoregressive covariance model

This paper addresses the problem of testing the multivariate linear hypothesis when the errors follow an antedependence model (Gabriel, 1961, 1962). Antedependence can be formulated as a nonstationary autoregressive model of general order. Three test statistics are derived that provide analogs to three commonly used MANOVA statistics: Wilks' Lambda, the Lawley-Hotelling Trace, and Pillai's Trace. Formulas are given for each of these statistics that show how they can be obtained From any statistical computing package that calculates the usual MANOVA statistics. These antedependent statistics would be appropriate in analyzing certain multivariate data sets in which repeated measurements are taken on the same subjects over a period of time.     

The response functions for competing risks

The competing risks data consist of a pair (T,δ) where T≧0 can be interpreted as the failure time and δ as the identifier of the risk causing the failure. In many practical situations, the main interest lies in studying the inter-relationships between the probability structures of the failure time under various risks. Here, we consider two risks and propose the Junctional relationships between the probability structure of (T,δ=1) and (T,δ=2) by time-dependent scale and shape shifts. Also, a model which raptures the relative aging of a unit under the two risks is proposed. The necessary theory for confidence estimation of these shift functions is developed. These techniques are illustrated through several data sets available in the literature.     

Further Results on Zellner's Minimum Expected Loss and Full Information Maximum Likelihood Estimators for Undersized Samples

The article presents a consistent set of conditions that a prior pdf for the reduced-form parameters must satisfy if Zellner's MELO estimators for the structural coefficients of a linear structural econometric model are to exist in all normal cases where the available sample is undersized. Also, the conditions under which the full information maximum likelihood estimators of structural coefficients exist are given. Finally, the article reports application of MELO estimation to Klein's Model I.     

A new economic scheme for CCC charts with run rules based on average number of inspected items

New statistical techniques and procedures have been developed to control high-yield processes along with looking for process improvement opportunities and minimizing production cost. Cumulative count of conforming control chart is generally a technique for high-quality processes, when nonconforming items are rarely produced. The objective of this study is to design control chart based on cumulative count of conforming items and run rules that develops an economic model based on the average number of inspected items to design m-of-m CCC chart in order to facilitate minimum average cost per item produced. The optimal design parameters for different values of nonconforming fraction and different cost parameters in each scenario are determined. Finally, to analyze the behavior of optimal economic solutions, sensitivity analysis of the model parameters is performed.     

Approximating the equilibrium quantity traded and welfare in large markets

We consider the efficient outcome of a canonical economic market model involving buyers and sellers with independent and identically distributed random valuations and costs, respectively. When the number of buyers and sellers is large, we show that the joint distribution of the equilibrium quantity traded and welfare is asymptotically normal. Moreover, we bound the approximation rate. The proof proceeds by constructing, on a common probability space, a representation consisting of two independent empirical quantile processes, which in large markets can be approximated by independent Brownian bridges. The distribution of interest can then be approximated by that of a functional of a Gaussian process. This methodology applies to a variety of mechanism design problems.     

Stochastic approximation methods in linear regression models (with consideration of errors in the regressors) 1

Usually, the dependence in stationary processes is described by a set of coefficients. In this paper, a measure of dependence is proposed which can be used instead of the autocorrelation function, and another measure for the dependence between two processes instead of cross-correlation function and coherence coefficients. In the end, an improvement of extrapolation of a process is investigated which is caused by the knowledge of another related process.     

Using an approximate L1 Estimator

This note investigates the efficiency of using near-best or approximate L₁ estimators as starting values in L₁ linear programming procedures. In particular, it is shown that the total computer time can often be reduced if one first computes the least squares estimator, β, and then adjust y to y - Xβ in Barrodale and Roberts’ improved algorithm.     

On the minimum mean squared error estimators in a regression model

In this paper we analyze the properties of two estimators oroposed by Farebrother (1975) for linear regression models.     

The existence of the mean of the estimator in seemingly unrelated regressions

The purpose of this note is to spell out the conditions for the existence of the mean of the coefficient; estimator in seemingly unrelated regressions.     

Modeling statistical dependence of Markov chains via copula models

Conditional probability distributions have been commonly used in modeling Markov chains. In this paper we consider an alternative approach based on copulas to investigate Markov-type dependence structures. Based on the realization of a single Markov chain, we estimate the parameters using one- and two-stage estimation procedures. We derive asymptotic properties of the marginal and copula parameter estimators and compare performance of the estimation procedures based on Monte Carlo simulations. At low and moderate dependence structures the two-stage estimation has comparable performance as the maximum likelihood estimation. In addition we propose a parametric pseudo-likelihood ratio test for copula model selection under the two-stage procedure. We apply the proposed methods to an environmental data set.