Ridge regression estimators in the linear regression models with non-spherical errors

The present paper considers a family of ordinary ridge regression estimators in the linear regression model when the disturbances covariance matrix depends upon a few unknown parameters. An asymptotic expansion for the distribution of the ridge regression estimator is developed and under the quadratic loss function its asymptotic risk is compared with that of the feasible GLS estimator.     

Distribution and density functions of the feasible generalized ridge regression estimator

In this paper, we derive the distribution and density functions of the feasible generalized ridge regression (GRR) estimator. It is shown that when the absolute value of a regression coefficient is close to zero, the distribution of the feasible GRR estimator is bimodal and has thinner tails than that of the OLS estimator.     

Time series count data regression

The count data model studied in the paper extends the Poisson model by al-lowing for overdispersion and serial correlation. Alternative approaches to esti-mate nuisance parameters, required for the correction of the Poisson maximum likelihood covariance matrix estimator and for a quasi-likelihood estimator, are studied. The estimators are evaluated by finite sample Monte Carlo experi-mentation. It is found that the Poisson maximum likelihood estimator with corrected covariance matrix estimators provide reliable inferences for longer time series. Overdispersion test statistics are wellbehaved, while conventional portmanteau statistics for white noise have too large sizes. Two empirical illustrations are included.     

A note on asymptotics for quantile smoothing splines

When cubic smoothing splines are used to estimate the conditional quantile function, thereby balancing fidelity to the data with a smoothness requirement, the resulting curve is the solution to a quadratic program. Using this quadratic characterization and through comparison with the sample conditional quan-tiles, we show strong consistency and asymptotic normality for the quantile smoothing spline.     

A cubic smoothing spline based lack of fit test for nonlinear regression models

The use of a statistic based on cubic spline smoothing is considered for testing nonlinear regression models for lack of fit. The statistic is defined to be the Euclidean squared norm of the smoothed residual vector obtained from fitting the nonlinear model, The asymptotic distribution of the statistic is derived under suitable smooth local alternatives and a numerical example is presented.     

Interval-valued data regression using partial linear model

Semi-parametric modelling of interval-valued data is of great practical importance, as exampled by applications in economic and financial data analysis. We propose a flexible semi-parametric modelling of interval-valued data by integrating the partial linear regression model based on the Center & Range method, and investigate its estimation procedure. Furthermore, we introduce a test statistic that allows one to decide between a parametric linear model and a semi-parametric model, and approximate its null asymptotic distribution based on wild Bootstrap method to obtain the critical values. Extensive simulation studies are carried out to evaluate the performance of the proposed methodology and the new test. Moreover, several empirical data sets are analysed to document its practical applications.     

Dimension reduction via local rank regression

Outer product of gradients (OPG) achieves dimension reduction via estimating the gradients of the regression function. In this paper, we propose two novel OPG estimators via local rank regression: the rank OPG estimator and the Walsh-average OPG estimator. Both proposals guard against a wide range of error distributions, and are safe alternatives to existing OPG estimators based on local linear regression or local L1 regression. The effectiveness of the new proposals are demonstrated via extensive numerical studies.     

Bayesian variable selection with spherically symmetric priors

We propose that Bayesian variable selection for linear parametrizations with Gaussian iid likelihoods should be based on the spherical symmetry of the diagonalized parameter space. Our r-prior results in closed forms for the evidence for four examples, including the hyper-g prior and the Zellner–Siow prior, which are shown to be special cases. Scenarios of a single-variable dispersion parameter and of fixed dispersion are studied, and asymptotic forms comparable to the traditional information criteria are derived. A simulation exercise shows that model comparison based on our r-prior gives good results comparable to or better than current model comparison schemes.     

Chain pooling model selection for two-level fixed effects factorial experiments

As many as three iterated statistical model deletion procedures are considered for an experiment.Population model coeff cients were chosen to simulate a saturated 2⁴experiment having an unfavorable distribution of parameter values.Using random number studies, three model selection strategies were developed, namely, (1) a strategy to be used in anticipation of large coefficients of variation (neighborhood of 65 percent), (2) strategy to be used in anticipation of small coefficients of variation (4 percent or less), and (3) a security regret strategy to be used in the absence of such prior knowledge     

James - stein regression estimation in a prediction context

Two types of shrunken estimators of regression coefficients are studied in the context of stochastic predictor variables. Emphasis is placed on the choice of the shrinkage parameters, using a ‘deleted-observation’ concept which is motivated by predictive ability.