End‐of‐Sample Instability Tests

This paper considers tests for structural instability of short duration, such as at the end of the sample. The key feature of the testing problem is that the number, m, of observations in the period of potential change is relatively small—possibly as small as one. The well‐known F test of Chow (1960) for this problem only applies in a linear regression model with normally distributed iid errors and strictly exogenous regressors, even when the total number of observations, n+m, is large. We generalize the F test to cover regression models with much more general error processes, regressors that are not strictly exogenous, and estimation by instrumental variables as well as least squares. In addition, we extend the F test to nonlinear models estimated by generalized method of moments and maximum likelihood. Asymptotic critical values that are valid as n→∞ with m fixed are provided using a subsampling‐like method. The results apply quite generally to processes that are strictly stationary and ergodic under the null hypothesis of no structural instability.     

Modified BLUEs and BLIEs of the location and scale parameters and the population mean using ranked set sampling

Ranked set sampling (RSS) is a sampling procedure that can be used to improve the cost efficiency of selecting sample units of an experiment or a study. In this paper, RSS is considered for estimating the location and scale parameters a and b>0, as well as the population mean from the family F((x?a)/b). Modified best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) are considered. Numerical computations with different location-scale distributions and different sample sizes are conducted to assess the efficiency of the suggested estimators. It is found that the modified BLIEs are uniformly higher than that of BLUEs for all distributions considered in this study. The modified BLUE and BLIE are more efficient when the underlying distribution is symmetric.     

A method for estimating parameters and quantiles of the three-parameter inverse Gaussian distribution based on statistics invariant to unknown location

The inverse Gaussian (IG) distribution, also known as the Wald distribution, is a long-tailed positively skewed distribution and a well-known lifetime distribution. In this paper, we propose an efficient method of estimation for the parameters and quantiles of the three-parameter IG distribution, which is based on statistics invariant to unknown location. Through a Monte Carlo simulation study, we then show that the proposed method performs well compared with other prominent methods in terms of bias and variance. Finally, we present two illustrative examples.     

Testing for parameter constancy in the time series direction in panel data models

We propose tests for parameter constancy in the time series direction in panel data models. We construct a locally best invariant test based on Tanaka [Time series analysis: nonstationary and noninvertible distribution theory. New York: Wiley; 1996] and an asymptotically point optimal test based on Elliott and Müller [Efficient tests for general persistent time variation in regression coefficients. Rev Econ Stud. 2006;73:907–940]. We derive the limiting distributions of the test statistics as T→∞ while N is fixed, and calculate the critical values by applying numerical integration and response surface regression. Simulation results show that the proposed tests perform well if we apply them appropriately.     

Optimal determination of the parameters of some biased estimators using genetic algorithm

In this paper, some new algorithms for estimating the biasing parameters of the ridge, Liu and two-parameter estimators are introduced with the help of genetic algorithm (GA). The proposed algorithms are based on minimizing some statistical measures such as mean square error (MSE), mean absolute error (MAE) and mean absolute prediction error (MAPE). At the same time, the new algorithms allow one to keep the condition number and variance inflation factors to be less than or equal to ten by means of the GA. A numerical example is presented to show the utility of the new algorithms. In addition, an extensive Monte Carlo experiment is conducted. The numerical findings prove that the proposed algorithms enable to eliminate the problem of multicollinearity and minimize the MSE, MAE and MAPE.     

Estimation of weibull location

A simulation study was carried out to compare the performances of two different simple estimators of the location parameter for a three-parameter Weibull distribution Both Estimators have been suggested by recent paper in the literature. Bras and mean square error are examined for many different sample-size and shape-parameter-value combinations. Strong evidence of the domination of one estimator over the other is found.     

An optimal selection of two-level regular single arrays for robust parameter experiments

Efforts have been made in the literature to find optimal single arrays which work best for the robust parameter experiments. However, examples show that in many cases the optimal designs obtained by the existing criteria cloud not attain the maximum number of clear interested effects for robust parameter experiments. In this paper, through a similar way of Zhang et al. (2008) (ZLZA, in short), an aliasing pattern to measure the confounding between the interested effects and other effects for the case of robust parameter designs is introduced. A new criterion for selecting optimal two-level regular single arrays is proposed. In the consideration of the criterion, two rank-orders of effects are suggested: one is based on the interest of experimenters and the other is under the usual effect hierarchy principle. The optimal designs are tabulated in the appendix.     

Adapting by calibration the sample size of a phase III trial on the basis of phase II data

The problem of estimating the sample size for a phase III trial on the basis of existing phase II data is considered, where data from phase II cannot be combined with those of the new phase III trial. Focus is on the test for comparing the means of two independent samples. A launching criterion is adopted in order to evaluate the relevance of phase II results: phase III is run if the effect size estimate is higher than a threshold of clinical importance. The variability in sample size estimation is taken into consideration. Then, the frequentist conservative strategies with a fixed amount of conservativeness and Bayesian strategies are compared. A new conservative strategy is introduced and is based on the calibration of the optimal amount of conservativeness – calibrated optimal strategy (COS). To evaluate the results we compute the Overall Power (OP) of the different strategies, as well as the mean and the MSE of sample size estimators. Bayesian strategies have poor characteristics since they show a very high mean and/or MSE of sample size estimators. COS clearly performs better than the other conservative strategies. Indeed, the OP of COS is, on average, the closest to the desired level; it is also the highest. COS sample size is also the closest to the ideal phase III sample size M_I, showing averages and MSEs lower than those of the other strategies. Costs and experimental times are therefore considerably reduced and standardized. However, if the ideal sample size M_I is to be estimated the phase II sample size n should be around the ideal phase III sample size, i.e. n?2M_I/3. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved likelihood-based inference for the stationary AR(2) model

An improved likelihood-based method based on Fraser et al. (1999) is proposed in this paper to test the significance of the second lag of the stationary AR(2) model. Compared with the test proposed by Fan and Yao (2003) and the signed log-likelihood ratio test, the proposed method has remarkable accuracy. Simulation studies are performed to illustrate the accuracy of the proposed method. Application of the proposed method on historical data is presented to demonstrate the implementation of this method. Furthermore, the method can be extended to the general AR(p) model.