A New Ridge Regression Causality Test in the Presence of Multicollinearity

The VAR lag structure applied for the traditional Granger causality (GC) test is always severely affected by multicollinearity due to autocorrelation among the lags. Therefore, as a remedy to this problem we introduce a new Ridge Regression Granger Causality (RRGC) test, which is compared to the GC test by means of Monte Carlo simulations. Based on the simulation study we conclude that the traditional OLS version of the GC test over-rejects the true null hypothesis when there are relatively high (but empirically normal) levels of multicollinearity, while the new RRGC test will remedy or substantially decrease this problem.     

Simultaneous estimation of ordered parameters

The problem of estimating ordered parameters is encountered in biological, agricultural, reliability and various other experiments. Consider two populations with densities f₁(x₁-ω₁) and f₂(x₂-ω₂) where ω₁#ω₂. The estimation of ω₁,ω₂) with the loss function, the sum of squared errors, is studied. when f_i is the f_i(,_i,,_i ²) density with ,_i known, i=1,2; we obtain a class of minimax estimators. When ω₁ #ω₂ we show some of these estimators are improved by the maximum likelihood estimator. For a general f_i we give sufficient conditions for the minimaxity of the analogue of the Pitman estimator.     

Estimation of parameters of the gamma distribution in the presence of outliers

The maximum likelihood estimators and moment estimators are derived for samples from the Gamma distribution in the presence of outliers. These estimators are compared empirically when all the three parameters are unknown and when one of the three parameters is known; their bias and mean square error (MSE) are investigated with the help of numerical technique.     

Large sample theory for a multivariate structural relationship with replication

For a multivariate structural relationship, where the replicated observations are available and the covariance matrix of the observational error is not restricted to diagonal, we consider the generalized least-squares estimators of the unknown structural parameters. The estimators are proved to be asymptotically normally distributed using the Liapunov central limit theorem under mild conditions on the incidental parameters. Their asymptotic covariance matrix is also derived.     

Robust estimation of the ratio of scale parameters for positive random variables

An estimator of the ratio of scale parameters of the distributions of two positive random variables is developed for the case where the only difference between the distributions is a difference in scale. Simulation studies demonstrate that the estimator performs much better, in terms of mean squared error, than the most popular one among those estimators currently available.     

MULTI-LEVEL FACTORIAL DESIGNS WITH MINIMUM NUMBERS OF LEVEL CHANGES

The order of experimental runs in a fractional factorial experiment is essential when the cost of level changes in factors is considered. The generalized foldover scheme given by [1] Coster, D. C. and Cheng, C. S. 1988. Minimum cost trend free run orders of fractional factorial designs. The Annals of Statistics, 16: 1188–1205. [Crossref], [Web of Science ®] , [Google Scholar]gives an optimal order to experimental runs in an experiment with specified defining contrasts. An experiment can be specified by a design requirement such as resolution or estimation of some interactions. To meet such a requirement, we can find several sets of defining contrasts. Applying the generalized foldover scheme to these sets of defining contrasts, we obtain designs with different numbers of level changes and then the design with minimum number of level changes. The difficulty is to find all the sets of defining contrasts. An alternative approach is investigated by [2] Cheng, C. S., Martin, R. J. and Tang, B. 1998. Two-level factorial designs with extreme numbers of level changes. The Annals of Statistics, 26: 1522–1539. [Crossref], [Web of Science ®] , [Google Scholar]for two-level fractional factorial experiments. In this paper, we investigate experiments with all factors in slevels.     

Economical process adjustment with measurement error

Srivastava and Wu (1997) considered a random walk model with sampling interval and measurement error which was assumed to be white noise. In this paper, we consider the situation in which the measurement error is also a random walk. It is assumed that there is a sampling cost and an adjustment cost. The cost of deviating from the target value is assumed to be proportional to the square of the deviations. The long-run average cost rate is evaluated exactly in terms of the first four moments of a randomly stopped random walk. Using approximations of those moments, optimum, values of the control parameters are given.