Effect of missing plots in some response surface designs

The effect of one or more missing observations for response surface designs arranged in blocks are examined in this paper. The resu lts as applied to a central composite design with orthogonal blocking, and an equirdial design with orthogonal blocking, are reported.     

Information in an observation in robust designs

We consider the Information contained 1n each observation in a given design robust with respect to the estlmability of parameters and against the unavailability of observations. We compare the observations in various 1-, 2- and 3- dimensional designs on the basis of their informations.     

Sequential analysis of 3m supersaturated factorial experiments

In this paper, designs that allow for the estimation of all main effects, and the detection and estimation of significant interactions in fewer runs than used in traditional approaches are examined. Specifically, a method for sequentially analyzing data from 3m fractional factorial experiments is presented. The procedure is illustrated through two examples.     

Designs with Repeated Measurements on Any Number of Units over Varying Periods

In the usual repeated measurements designs (RMDs), the subjects are all observed for the same number of periods and the optimum RMDs require specified numbers of subjects, usually depending on the number of treatments to be used. In practice, it is sometimes not feasible to meet these requirements. To overcome this problem, alternative designs are suggested where any number of available subjects may be used and they may be observed for different periods. These designs are based on suitable serially balanced sequences which are shown to be optimal. Moreover, besides the usual direct and residual effects, the model considered has an extra term due to the interaction effect between them. The recommended designs are universally optimal in a very general class.     

Testing equality of survival distributions when the population marks are missing

This paper introduces a nonparametric approach for testing the equality of two or more survival distributions based on right censored failure times with missing population marks for the censored observations. The standard log-rank test is not applicable here because the population membership information is not available for the right censored individuals. We propose to use the imputed population marks for the censored observations leading to fractional at-risk sets that can be used in a two sample censored data log-rank test. We demonstrate with a simple example that there could be a gain in power by imputing population marks (the proposed method) for the right censored individuals compared to simply removing them (which also would maintain the right size). Performance of the imputed log-rank tests obtained this way is studied through simulation. We also obtain an asymptotic linear representation of our test statistic. Our testing methodology is illustrated using a real data set.     

Book Reviews

Books reviewed:
Anthony, Atkinson & Marco, Riani, Robust Diagnostic Regression Analysis
N., Balakrishnan & C.R., Rao, Order Statistics: Theory & Methods. Handbook of Statistics, Volume 16
N., Balakrishnan & C.R., Rao, Order Statistics: Applications. Handbook of Statistics, Volume 17
C.R., Rao & G.J., Székely, Statistics for the 21st Century: Methodologies for Applications of the Future
D.A., Nolan & T.P., Speed, Stat Labs: Mathematical Statistics Through Applications
W.N., Venables & B.D., Ripley, S Programming
Peter W.M., John, Statistical Design and Analysis of Experiments     

Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration

In this paper we compare through Monte Carlo simulations the finite sample properties of estimators of the fractional differencing parameter, d. This involves frequency domain, time domain, and wavelet based approaches, and we consider both parametric and semiparametric estimation methods. The estimators are briefly introduced and compared, and the criteria adopted for measuring finite sample performance are bias and root mean squared error. Most importantly, the simulations reveal that (1) the frequency domain maximum likelihood procedure is superior to the time domain parametric methods, (2) all the estimators are fairly robust to conditionally heteroscedastic errors, (3) the local polynomial Whittle and bias-reduced log-periodogram regression estimators are shown to be more robust to short-run dynamics than other semiparametric (frequency domain and wavelet) estimators and in some cases even outperform the time domain parametric methods, and (4) without sufficient trimming of scales the wavelet-based estimators are heavily biased.     

A bayesian approach to bioassay. technical report m498

We describe the design and analysis for a simulation experiment to compare the mean-squared errors (MSE's) of two quantile estimators defined for random walk designs. The dependence of the easily computed MSE of the first estimator on the levels of five factors is examined via multiple regression. This information is used to plan a simulation to compute the MSE of the second estimator using a fraction of a 3³5²factorial allowing uncorrelated estimates for all main effects and the two-factor interactions of a specified factor. Efficient estimation of the MSE of the second estimator is attempted through antithetic and control variate techniques of variance reduction, with modest success.     

A fractional order statistic towards defining a smooth quantile function for discrete data

This work is motivated in part by a recent publication by Ma et al. (2011) who resolved the asymptotic non-normality problem of the classical sample quantiles for discrete data through defining a new mid-distribution based quantile function. This work is the motivation for defining a new and improved smooth population quantile function given discrete data. Our definition is based on the theory of fractional order statistics. The main advantage of our definition as compared to its competitors is the capability to distinguish the uth quantile across different discrete distributions over the whole interval, u∈(0,1). In addition, we define the corresponding estimator of the smooth population quantiles and demonstrate the convergence and asymptotic normal distribution of the corresponding sample quantiles. We verify our theoretical results through a Monte Carlo simulation, and illustrate the utilization of our quantile function in a Q-Q plot for discrete data.     

Cointegration in Fractional Systems with Unknown Integration Orders

Cointegrated bivariate nonstationary time series are considered in a fractional context, without allowance for deterministic trends. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been assumed known. We allow one or more of them to be unknown real values, in which case Robinson and Marinucci (2001, 2003) have justified least squares estimates of the cointegrating vector, as well as narrow‐band frequency‐domain estimates, which may be less biased. While consistent, these estimates do not always have optimal convergence rates, and they have nonstandard limit distributional behavior. We consider estimates formulated in the frequency domain, that consequently allow for a wide variety of (parametric) autocorrelation in the short memory input series, as well as time‐domain estimates based on autoregressive transformation. Both can be interpreted as approximating generalized least squares and Gaussian maximum likelihood estimates. The estimates share the same limiting distribution, having mixed normal asymptotics (yielding Wald test statistics with χ² null limit distributions), irrespective of whether the integration orders are known or unknown, subject in the latter case to their estimation with adequate rates of convergence. The parameters describing the short memory stationary input series are √n‐consistently estimable, but the assumptions imposed on these series are much more general than ones of autoregressive moving average type. A Monte Carlo study of finite‐sample performance is included.