GOODNESS-OF-FIT TESTS BASED ON A NEW CHARACTERIZATION OF THE EXPONENTIAL DISTRIBUTIONHenze, Norbert; Meintanis, Simos G.
doi: 10.1081/STA-120013007pmid: N/A
The characteristic function of a random variable X with exponential density , satisfies the equation , where u(t) and v(t) denote the real and the imaginary part of , respectively. We study a new class of consistent tests for exponentiality based on a suitably weighted integral of , where is the maximum-likelihood estimate of θ, and u n and v n denote the empirical counterparts of u(t) and v(t), respectively. As the decay of the weight function tends to infinity, the test statistic approaches the square of a linear combination of the first two nonzero components of Neyman's smooth test for exponentiality. The new tests are compared with other omnibus tests for exponentiality.
VARIANCE ESTIMATION IN THE ERROR COMPONENTS REGRESSION MODELKnapp, Guido
doi: 10.1081/STA-120013008pmid: N/A
In a regression model with a random individual and a random time effect explicit representations of the nonnegative quadratic minimum biased estimators of the corresponding variances are deduced. These estimators always exist and are unique. Moreover, under normality assumption of the dependent variable unbiased estimators of the mean squared errors of the variance estimates are derived. Finally, confidence intervals on the variance components are considered.
SECOND-ORDER ASYMPTOTICS FOR SCORE TESTS IN HETEROSKEDASTIC t REGRESSION MODELSBarroso, Lúcia P.; Cordeiro, Gauss M.; Vasconcellos, Klaus L. P.
doi: 10.1081/STA-120013009pmid: N/A
This paper develops corrected score tests for heteroskedastic t regression models, thus generalizing results by Cordeiro, Ferrari and Paula[1] and Cribari-Neto and Ferrari[2] for normal regression models and by Ferrari and Arellano-Valle[3] for homoskedastic t regression models. We present, in matrix notation, Bartlett-type correction formulae to improve score tests in this class of models. The corrected score statistics have a chi-squared distribution to order n −1, where n is the sample size. We apply our main result to a few special models and present simulation results comparing the performance of the usual score tests and their corrected versions.
THE DISTRIBUTION OF STOCHASTIC SHRINKAGE PARAMETERS IN RIDGE REGRESSIONRubio, Hernán; Firinguetti, Luis
doi: 10.1081/STA-120013010pmid: N/A
In this article we derive the density and distribution functions of the stochastic shrinkage parameters of three well known operational Ridge Regression (RR) estimators by assuming normality. The stochastic behavior of these parameters is likely to affect the properties of the resulting RR estimator, therefore such knowledge can be useful in the selection of the shrinkage rule. Some numerical calculations are carried out to illustrate the behavior of these distributions, throwing light on the performance of the different RR estimators.
TREE-BASED REGRESSION FOR A CIRCULAR RESPONSELund, Ulric J.
doi: 10.1081/STA-120013011pmid: N/A
The application of conventional statistical methods to directional data generally produces erroneous results. Various regression models for a circular response have been presented in the literature, however these are unsatisfactory either in the limited relationships that can be modeled, or the limitations on the number or type of covariates admissible. One difficulty with circular regression is devising a meaningful regression function. This problem is exacerbated when trying to incorporate both linear and circular variables as covariates. Due to these complexities, circular regression is ripe for exploration via tree-based methods, in which a formal regression function is not needed, but where insight into the general structure and relationship between predictors and the response may be obtained. A basic framework for regression trees, predicting a circular response from a combination of circular and linear predictors, will be presented.
POINTWISE CONVERGENCE OF THE WAVELET REGULARIZED ESTIMATORSAngelini, C.; De Canditiis, D.
doi: 10.1081/STA-120013012pmid: N/A
The classical nonparametric regression problem is considered under the hypothesis of nonnecessarily equispaced deterministic design, white noise, and regression functions belonging to Sobolev spaces. A linear shrinkage wavelet estimator is considered. We prove that this estimator reaches the optimal rate of convergence in the MSE (Mean Squared Error) at any given point. The performance of the estimator is illustrated on a set of standard test functions.
ANALYSIS OF MASKED DATA IN A DEPENDENT COMPETING RISKS MODEL UNDER UNKNOWN ENVIRONMENTNagai, Yoshimitsu
doi: 10.1081/STA-120013013pmid: N/A
System failure data is often analyzed to estimate component reliabilities. Due to cost and time constraints, the exact component causing the failure of the system cannot be identified in some cases. This phenomenon is called masking. Further, it is sometimes necessary for us to take account of the influence of the operating environment. Here we consider a series system, operating under unknown environment, of two components whose failure times follow the Marshall-Olkin bivariate exponential distribution. We present a maximum likelihood approach for obtaining estimators from the masked data for this system. From a simulation study, we found that the relative errors of the estimates are almost well behaved even for small or moderate expected number of systems whose cause of failure is identified.
A NOTE ON THE HOMOGENETIC ESTIMATE FOR THE VARIANCE OF THE KAPLAN–MEIER ESTIMATEShen, Pao-sheng
doi: 10.1081/STA-120013014pmid: N/A
The Greenwood estimate (GE) is commonly employed for estimating the variance of the Kaplan–Meier estimate (KME) even though it underestimates the variance. To reduce the bias of the GE, Zhao (1996) proposed an alternative, called the homogenetic estimate (HE). In this note, we point out that the HE actually esimates the variance of the reduced sample estimate (RE) and can seriously overestimate that of the KME. We also derive the explict relationship between the HE and the GE and discuss the use of the HE.