A simulation study on the confidence interval procedures of some mean cumulative function estimators

Recurrence data are collected to study the recurrent events in biological, physical, and other systems. Quantities of interest include the mean cumulative number of events and the mean cumulative cost of the events. The mean cumulative function (MCF) can be estimated using non-parametric (NP) methods or by fitting parametric models, and many procedures have been suggested to construct the confidence intervals (CIs) for the MCF. This paper summarizes the results of a large simulation study that was designed to compare five CI procedures for both NP and parametric estimation. When performing parametric estimation, we assume the power law non-homogeneous Poisson process (NHPP) model. Our results include the evaluation of these procedures when they are used for window-observation recurrence data where recurrence histories of some systems are available only in observation windows with gaps in between.     

A simple approach to an integrated single-vendor single-buyer inventory system with shortage

In this article, a simple approach with two basic inequalities (Cauchy–Schwarz inequality and arithmetic–geometric mean inequality) is used to solve the integrated single-vendor single-buyer inventory problem developed by Wu and Ouyang (Wu, K.-S. and Ouyang, L.-Y., 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14 (6), 555–561). Without the method of completing perfect square, the proposed approach yields the global minimum of the integrated total cost per year more easily than the algebraic approach used by Wu and Ouyang (2003 Wu, K-S and Ouyang, L-Y. 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14(6): 555–561. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In addition, for people without the background of calculus, it is more useful to determine the buyer's economic order quantity and the vendor's optimal number of deliveries.     

Penalized weighted composite quantile regression in the linear regression model with heavy-tailed autocorrelated errors

In this paper, a penalized weighted composite quantile regression estimation procedure is proposed to estimate unknown regression parameters and autoregression coefficients in the linear regression model with heavy-tailed autoregressive errors. Under some conditions, we show that the proposed estimator possesses the oracle properties. In addition, we introduce an iterative algorithm to achieve the proposed optimization problem, and use a data-driven method to choose the tuning parameters. Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least squares based method when there are outliers in the dataset or the autoregressive error distribution follows heavy-tailed distributions. Moreover, the proposed estimator works comparably to the least squares based estimator when there are no outliers and the error is normal. Finally, we apply the proposed methodology to analyze the electricity demand dataset.     

Some unbiased estimators versus mean per unit and ratio estimators in finite population sample surveys

We present some unbiased estimators at the population mean in a finite population sample surveys with simple random sampling design where information on an auxiliary variance x positively correlated with the main variate y is available. Exact variance and unbiased estimate of the variance are computed for any sample size. These estimators are compared for their precision with the mean per unit and the ratio estimators. Modifications of the estimators are suggested to make them more precise than the mean per unit estimator or the ratio estimator regardless of the value of the population correlation coefficient between the variates x and y. Asymptotic distribution of our estimators and confidnece intervals for the population mean are also obtained.     

Contrast analysis for scale differences

Research on tests for scale equality, that are robust to violations of the distributional normality assumption, have focused exclusively on an overall test statistic and have not examined procedures for identifying specific differences in multiple group designs. The present study compares four contrast analysis procedures for scale differences in the single factor four group design. Two data transformations are considered under several conbinations of variance difference, sample sizes, and distributional forms.The results indicate that no single transformation or analysis procedure is uniformly superior in controlling the familywise error rate or in statistical power. The relationship between sample size and variances is a major factor in selecting a contrast analysis procedure.     

A note on some conditions for optimality of certain ridge estimators

Consider the linear regression model, y = Xβ + ε in the usual notation with X'X being in the correlation form. Galpin(1980) claimed that the ridge estimators of Hoerl, Kennard and Baldwin(1975) and Lawless and Wang(1976) give guaranteed lower mean squared error than the least squares estimator when X'X has at least two very small eigen values. We show that the arguments of Galpin(1980) leading to the above claim are incorrect, and hence the claim itself is unsubstantited. A Monte Carlo study shows that Galpin's claim is not correct in general.     

A formal bayes multiple shrinkage estimator

A new minimax multiple shrinkage estimator is constructed. This estimator which can adaptively shrink towards many subspace targets, is formal Bayes with respect to a mixture of harmonic priors. Unbiased estimates of risk and simulation results suggest that the risk properties of this estimator are very similar to those of the multiple shrinkage Stein estimator proposed by George (1986a). A special case is seen to be admissible.     

A note on the distribution of mean square error of forecasting

Simulation has been a very important and widely used method in the study of misspecification or order determination in time series analysis. Mean square error of forecasting (MSEF) has been a major criterion for comparing the performance of different models. In simulation studies, standard deviations of MSEF's are calculated from the computed values of the MSEF's, In this note, the distribution of MSEF from simulation studies is established. Exact variance of the MSEF can be obtained from the prespecified values of the model selected for simulation. This variance should be a more appropriate criterion for evaluating the performance between models.     

A likelihood ratio test for the equality of proportions of two normal populations

In sampling inspection by variables, an item is considered defective if its quality characteristic Y falls below some specification limit L₀. We consider switching to a new supplier if we can be sure that the proportion of defective items for the new supplier is smaller than the proportion defective for the present supplier.

Assume that Y has a normal distribution. A test for comparing these proportions is developed. A simulation study of the performance of the test is presented.