A Matrix Variate Closed Skew-Normal Distribution with Applications to Stochastic Frontier Analysis

In this article, we introduce the matrix extension of the closed skew-normal distribution and give two constructions for it: a marginal one and another based on hidden truncation. Important basic properties of the distribution are presented such as its closure under linear transformation and moment generating function. We also give distributional results for quadratic forms involving random matrices distributed according to two particular cases of it. Using an additive construction, we derive a submodel which can be employed to describe the compound error structure of a very general multivariate stochastic frontier model. Finally, we consider the skew-elliptical extension of the proposed distribution.     

LogXact 4.1 for Windows

Box's paper helicopter has been used to teach experimental design for more than a decade. It is simple, inexpensive, and provides real data for an involved, multifactor experiment. Unfortunately it can also further an all-too-common practice that Professor Box himself has repeatedly cautioned against, namely ignoring the fundamental science while rushing to solve problems that may not be sufficiently understood. Often this slighting of the science so as to get on with the statistics is justified by referring to Box's oft-quoted maxim that “All models are wrong, however some are useful.” Nevertheless, what is equally true, to paraphrase both Professor Box and George Orwell, is that “All models are wrong, but some are more wrong than others.” To experiment effectively it is necessary to understand the relevant science so as to distinguish between what is usefully wrong, and what is dangerously wrong.

This article presents an improved analysis of Box's helicopter problem relying on statistical and engineering knowledge and shows that this leads to an enhanced paper helicopter, requiring fewer experimental trails and achieving superior performance. In fact, of the 20 experimental trials run for validation—10 each of the proposed aerodynamic design and the conventional full factorial optimum—the longest 10 flight times all belong to the aerodynamic optimum, while the shortest 10 all belong to the conventional full factorial optimum. I further discuss how ancillary engineering knowledge can be incorporated into thinking about—and teaching—experimental design.     

Optimum Critical Value for Pre-Test Estimator

In this paper, methods are proposed in finding the robust design in both Taguchi and Standard setups when a signal factor is present. The robust design is a set of level combinations of control factors so that the effect of controllable noise factors on response is minimum. Both univariate and multivariate methods are used in finding the influential noise factors for the determination of robust designs.     

Sequential Designs for Binary Data with the Purpose to Maximize the Probability of Response

Two kinds of sequential designs are proposed for finding the point that maximizes the probability of response assuming a binary response variable and a quadratic logistic regression model. One is a parametric optimal design approach, and the other one is a nonparametric stochastic approximation approach. The suggested sequential designs are evaluated and compared in a simulation study. In summary, the parametric approach performed very well whereas its competitor failed in some cases.     

Bias-corrected confidence bands in nonparametric regression

Bias-corrected confidence bands for general nonparametric regression models are considered. We use local polynomial fitting to construct the confidence bands and combine the cross-validation method and the plug-in method to select the bandwidths. Related asymptotic results are obtained. Our simulations show that confidence bands constructed by local polynomial fitting have much better coverage than those constructed by using the Nadaraya–Watson estimator. The results are also applicable to nonparametric autoregressive time series models.     

Understanding exponential smoothing via kernel regression

Exponential smoothing is the most common model-free means of forecasting a future realization of a time series. It requires the specification of a smoothing factor which is usually chosen from the data to minimize the average squared residual of previous one-step-ahead forecasts. In this paper we show that exponential smoothing can be put into a nonparametric regression framework and gain some interesting insights into its performance through this interpretation. We also use theoretical developments from the kernel regression field to derive, for the first time, asymptotic properties of exponential smoothing forecasters.     

Dyadic regression in the presence of heteroscedasticity—An assessment of alternative approaches

Although the problem of heteroscedasticity has been the subject of much discussion in other areas of applied statistics the problem has received scant attention in the social network literature. This study attempts to remedy this situation by considering how traditional methods for significance testing in dyadic regression models, such as standard QAP tests, perform under conditions of heteroscedasticity. Moreover, the article presents two alternative methods to deal with heteroscedasticity that are both shown to perform rather well with typical social network data under conditions of both heteroscedasticity and homoscedasticity. Overall, the results of the study suggest that applied researchers using regression techniques to study dyadic data are well advised to correct for heteroscedasticity, by either of the two methods discussed here, whenever there is a reason to suspect heteroscedasticity.     

D- and V-optimal population designs for the quadratic regression model with a random intercept term

In this paper D- and V-optimal population designs for the quadratic regression model with a random intercept term and with values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. D-optimal population designs based on single-point individual designs were readily found but the derivation of explicit expressions for designs based on two-point individual designs was not straightforward and was complicated by the fact that the designs now depend on ratio of the variance components. Further algebraic results pertaining to d-point D-optimal population designs where d≥3 and to V-optimal population designs proved elusive. The requisite designs can be calculated by careful programming and this is illustrated by means of a simple example.     

Efficient Estimation of an Additive Quantile Regression Model

Abstract. In this paper, two non‐parametric estimators are proposed for estimating the components of an additive quantile regression model. The first estimator is a computationally convenient approach which can be viewed as a more viable alternative to existing kernel‐based approaches. The second estimator involves sequential fitting by univariate local polynomial quantile regressions for each additive component with the other additive components replaced by the corresponding estimates from the first estimator. The purpose of the extra local averaging is to reduce the variance of the first estimator. We show that the second estimator achieves oracle efficiency in the sense that each estimated additive component has the same variance as in the case when all other additive components were known. Asymptotic properties are derived for both estimators under dependent processes that are strictly stationary and absolutely regular. We also provide a demonstrative empirical application of additive quantile models to ambulance travel times.     

Novel quadratic programming approach for time series clustering with biomedical application

Fundamental problems in data mining mainly involve discrete decisions based on numerical analyses of data (e.g., class assignment, feature selection, data categorization, identifying outlier samples). These decision-making problems in data mining are combinatorial in nature and can naturally be formulated as discrete optimization problems. One of the most widely studied problems in data mining is clustering. In this paper, we propose a new optimization model for hierarchical clustering based on quadratic programming and later show that this model is compact and scalable. Application of this clustering technique in epilepsy, the second most common brain disorder, is a case point in this study. In our empirical study, we will apply the proposed clustering technique to treatment problems in epilepsy through the brain dynamics analysis of electroencephalogram (EEG) recordings. This study is a proof of concept of our hypothesis that epileptic brains tend to be more synchronized (clustered) during the period before a seizure than a normal period. The results of this study suggest that data mining research might be able to revolutionize current diagnosis and treatment of epilepsy as well as give a greater understanding of brain functions (and other complex systems) from a system perspective. This work was partially supported by the NSF grant CCF 0546574 and Rutgers Research Council grant-202018.