Testing for exponentiality against monotone failure rate average alternatives

We propose a test for exponentiality against the class of non-exponential distributions having monotone failure rate averages. The test statistic, which is a U-statistic and hence asymptotically normally distributed, is much simpler than its competitors yet compares favorably with them in efficiency and power comparisons.     

Pooled Panel Unit Root Tests and the Effect of Past Initialization

This paper analyzes the role of initialization when testing for a unit root in panel data, an issue that has received surprisingly little attention in the literature. In fact, most studies assume that the initial value is either zero or bounded. As a response to this, the current paper considers a model in which the initialization is in the past, which is shown to have several distinctive features that makes it attractive, even in comparison to the common time series practice of making the initial value a draw from its unconditional distribution under the stationary alternative. The results have implications not only for theory, but also for applied work. In particular, and in contrast to the time series case, in panels the effect of the initialization need not be negative but can actually lead to improved test performance.     

The Local Power of the CADF and CIPS Panel Unit Root Tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.     

A Seemingly Unrelated Nonparametric Additive Model with Autoregressive Errors

This article considers a nonparametric additive seemingly unrelated regression model with autoregressive errors, and develops estimation and inference procedures for this model. Our proposed method first estimates the unknown functions by combining polynomial spline series approximations with least squares, and then uses the fitted residuals together with the smoothly clipped absolute deviation (SCAD) penalty to identify the error structure and estimate the unknown autoregressive coefficients. Based on the polynomial spline series estimator and the fitted error structure, a two-stage local polynomial improved estimator for the unknown functions of the mean is further developed. Our procedure applies a prewhitening transformation of the dependent variable, and also takes into account the contemporaneous correlations across equations. We show that the resulting estimator possesses an oracle property, and is asymptotically more efficient than estimators that neglect the autocorrelation and/or contemporaneous correlations of errors. We investigate the small sample properties of the proposed procedure in a simulation study.     

Robust signed-rank estimation and variable selection for semi-parametric additive partial linear models

A fully nonparametric model may not perform well or when the researcher wants to use a parametric model but the functional form with respect to a subset of the regressors or the density of the errors is not known. This becomes even more challenging when the data contain gross outliers or unusual observations. However, in practice the true covariates are not known in advance, nor is the smoothness of the functional form. A robust model selection approach through which we can choose the relevant covariates components and estimate the smoothing function may represent an appealing tool to the solution. A weighted signed-rank estimation and variable selection under the adaptive lasso for semi-parametric partial additive models is considered in this paper. B-spline is used to estimate the unknown additive nonparametric function. It is shown that despite using B-spline to estimate the unknown additive nonparametric function, the proposed estimator has an oracle property. The robustness of the weighted signed-rank approach for data with heavy-tail, contaminated errors, and data containing high-leverage points are validated via finite sample simulations. A practical application to an economic study is provided using an updated Canadian household gasoline consumption data.     

On the Critical Value Behaviour of Multiple Decision Procedures

In this paper we investigate the asymptotic critical value behaviour of certain multiple decision procedures as e.g. simultaneous confidence intervals and simultaneous as well as stepwise multiple test procedures. Supposing that n hypotheses or parameters of interest are under consideration we investigate the critical value behaviour when n increases. More specifically, we answer e.g. the question by which amount the lengths of confidence intervals increase when an additional parameter is added to the statistical analysis. Furthermore, critical values of different multiple decision procedures as for instance step-down and step-up procedures will be compared. Some general theoretic results are derived and applied for various distributions.     

Testing for No Effect by Cosine Series Methods

The properties of three lack-of-fit tests that are related to non-parametric cosine regression analysis are examined in the context of testing for a constant mean function. Analytic power comparisons of these tests vs a most powerful test are made using intermediate asymptotic relative efficiency. In particular, a data-driven test is produced which is asymptotically as efficient as the most powerful test over a class of alternatives. A small scale simulation experiment is conducted to ascertain the extent that the large sample comparisons are applicable to finite samples.     

Variance estimation based on blocked 3×2 cross-validation in high-dimensional linear regression

In high-dimensional linear regression, the dimension of variables is always greater than the sample size. In this situation, the traditional variance estimation technique based on ordinary least squares constantly exhibits a high bias even under sparsity assumption. One of the major reasons is the high spurious correlation between unobserved realized noise and several predictors. To alleviate this problem, a refitted cross-validation (RCV) method has been proposed in the literature. However, for a complicated model, the RCV exhibits a lower probability that the selected model includes the true model in case of finite samples. This phenomenon may easily result in a large bias of variance estimation. Thus, a model selection method based on the ranks of the frequency of occurrences in six votes from a blocked 3×2 cross-validation is proposed in this study. The proposed method has a considerably larger probability of including the true model in practice than the RCV method. The variance estimation obtained using the model selected by the proposed method also shows a lower bias and a smaller variance. Furthermore, theoretical analysis proves the asymptotic normality property of the proposed variance estimation.     

Doubly adaptive biased coin designs with heterogeneous responses

Doubly adaptive biased coin design (DBCD) is an important family of response-adaptive randomization procedures for clinical trials. It uses sequentially updated estimation to skew the allocation probability to favor the treatment that has performed better thus far. An important assumption for the DBCD is the homogeneity assumption for the patient responses. However, this assumption may be violated in many sequential experiments. Here we prove the robustness of the DBCD against certain time trends in patient responses. Strong consistency and asymptotic normality of the design are obtained under some widely satisfied conditions. Also, we propose a general weighted likelihood method to reduce the bias caused by the heterogeneity in the inference after a trial. Some numerical studies are also presented to illustrate the finite sample properties of DBCD.