Statistical Methodology最新文献

It is well known that the Dirichlet process (DP) model and Dirichlet process mixture (DPM) model are sensitive to the specifications of the baseline distribution. Given a sample from a finite population, we perform Bayesian predictive inference about a finite population quantity (e.g., mean) using a DP model. Generally, in many applications a normal distribution is used for the baseline distribution. Therefore, our main objective is empirical and we show the extent of the sensitivity of inference about the finite population mean with respect to six distributions (normal, lognormal, gamma, inverse Gaussian, a two-component normal mixture and a skewed normal). We have compared the DP model using these baselines with the Polya posterior (fully nonparametric) and the Bayesian bootstrap (sampling with a Haldane prior). We used two examples, one on income data and the other on body mass index data, to compare the performance of these three procedures. These examples show some differences among the six baseline distributions, the Polya posterior and the Bayesian bootstrap, indicating that the normal baseline model cannot be used automatically. Therefore, we consider a simulation study to assess this issue further, and we show how to solve this problem using a leave-one-out kernel baseline. Because the leave-one-out kernel baseline cannot be easily applied to the DPM, we show theoretically how one can solve the sensitivity problem for the DPM as well.

A step-stress accelerated life testing model is constructed that deals with type-I censored experiments for which a continuous monitoring of the tested items is infeasible and only their inspection at particular time points is possible, producing thus grouped data. A general scale family of distributions is considered for the underlying lifetimes, which allows for flexible modeling by permitting different lifetime distributions for different stress levels. The maximum likelihood estimators of its parameters and their density functions are derived explicitly only when the inspection points coincide with the points of stress-level change. In case of additional inspection points, the estimates are obtained numerically. Asymptotic, exact (whenever possible) and bootstrap confidence intervals (CIs) are considered. For the bootstrap CIs a smoothing-modification is introduced, accounting for the categorical nature of the data.

A simple robust $L2$-regression estimator is presented. The proposed method blends a minimum covariance determinant $\left(MCD\right)$ concentration algorithm with a controlled ordinary least squares regression phase. A hierarchical cluster analysis then partitions the data into main cluster of “half set” and a minor cluster of one or more groups. An initial least squares regression estimate arises from the main cluster of “half set”. Thereafter, a group-additive difference in fit statistic is used to activate the minor cluster and a controlled re-weighted least squares regression yields a robust efficient estimator with high breakdown value. Simulation experiment shows the advantage of the proposed method over the popular robust regression techniques in terms of robustness of coefficients, and blending outlier diagnostic procedure with parameter estimation.

In this paper, we develop a double acceptance sampling plan for half exponential power distribution when the lifetime experiment is truncated at a prefixed time. The zero and one failure schemes are considered. We obtain the minimum sample sizes of the first and second samples necessary to ensure the specified mean life at the given consumer’s confidence level. The operating characteristic values and the minimum ratios of the mean life to the specified life are also analyzed. Numerical example is provided to illustrate the double acceptance sampling plan.

In this paper, we employ wavelet method to propose a multivariate density estimator based on a biased sample. We investigate the asymptotic rate of convergence of the proposed estimator over a large class of densities in the Besov space, $B_{pq}^s$. Moreover, we prove the consistency of our estimator when the expectation of weight function is unknown. This paper is an extension of results in Ramirez and Vidakovic (2010) and Chesneau et al. (2012) to the multivariate case.

In the present paper, we study the properties of the multivariate discrete scalar hazard rate. Its continuous analogue introduced in the early seventies did not attract much attention because it could not be used to identify the corresponding life distribution. We find the conditions under which an $n$-variate discrete scalar hazard rate can determine the distribution uniquely. Several other properties of this hazard rate which can be employed in modelling lifetime data are discussed. Some ageing classes based on the scalar hazard function are suggested.

We consider statistical inference for partial linear additive models (PLAMs) when the linear covariates are measured with errors and distorted by unknown functions of commonly observable confounding variables. A semiparametric profile least squares estimation procedure is proposed to estimate unknown parameter under unrestricted and restricted conditions. Asymptotic properties for the estimators are established. To test a hypothesis on the parametric components, a test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we further show that its limiting distribution is a weighted sum of independent standard chi-squared distributions. A bootstrap procedure is further proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for an illustration.

In this paper, we develop a methodology for the dynamic Bayesian analysis of generalized odds ratios in contingency tables. It is a standard practice to assume a normal distribution for the random effects in the dynamic system equations. Nevertheless, the normality assumption may be unrealistic in some applications and hence the validity of inferences can be dubious. Therefore, we assume a multivariate skew-normal distribution for the error terms in the system equation at each step. Moreover, we introduce a moving average approach to elicit the hyperparameters. Both simulated data and real data are analyzed to illustrate the application of this methodology.

Multiple imputation (MI) is an appealing option for handling missing data. When implementing MI, however, users need to make important decisions to obtain estimates with good statistical properties. One such decision involves the choice of imputation model–the joint modeling (JM) versus fully conditional specification (FCS) approach. Another involves the choice of method to handle interactions. These include imputing the interaction term as any other variable (active imputation), or imputing the main effects and then deriving the interaction (passive imputation). Our study investigates the best approach to perform MI in the presence of interaction effects involving two categorical variables. Such effects warrant special attention as they involve multiple correlated parameters that are handled differently under JM and FCS modeling. Through an extensive simulation study, we compared active, passive and an improved passive approach under FCS, as JM precludes passive imputation. We additionally compared JM and FCS techniques using active imputation. Performance between active and passive imputation was comparable. The improved passive approach proved superior to the other two particularly when the number of parameters corresponding to the interaction was large. JM without rounding and FCS using active imputation were also mostly comparable, with JM outperforming FCS when the number of parameters was large. In a direct comparison of JM active and FCS improved passive, the latter was the clear winner. We recommend improved passive imputation under FCS along with sensitivity analyses to handle multi-level interaction terms.

Odds ratios and log-linear parameters are not collapsible, which means that including a variable into the analysis or omitting one from it, may change the strength of association among the remaining variables. Even the direction of association may be reversed, a fact that is often discussed under the name of Simpson’s paradox. A parameter of association is directionally collapsible, if this reversal cannot occur. The paper investigates the existence of parameters of association which are directionally collapsible. It is shown, that subject to two simple assumptions, no parameter of association, which depends only on the conditional distributions, like the odds ratio does, can be directionally collapsible. The main result is that every directionally collapsible parameter of association gives the same direction of association as a linear contrast of the cell probabilities does. The implication for dealing with Simpson’s paradox is that there is exactly one way to associate direction with the association in any table, so that the paradox never occurs.