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Statistics is the science of extracting useful information from data, and a statistical model is
used to provide a useful approximation to some of the important characteristics of the …

Many math and some statistics departments offer a one-semester graduate course in
statistical theory using texts such as Casella and Berger (2002), Bickel and Doksum (2007) …

Abstract Olive (Internat J Stat Probab 2: 90–100, 2013) developed a large sample 100 (1-
δ)\% 100 (1-δ)% nonparametric prediction region for a future m * 1 m× 1 test vector y _f yf …

This paper suggests a method for bootstrapping the multiple linear regression model Y= β
_1+ β _2 x_2+ ⋯+ β _p x_p+ e Y= β 1+ β 2 x 2+⋯+ β pxp+ e after variable selection. We …

Data splitting divides the training data set into two sets H and the validation set V. Data
splitting can give valid inference for complicated data sets. We suggest a data split-ting …

Consider the multiple linear regression model Y= β _1+ β _2 x_2+ ⋯+ β _p x_p+ e= x^ T β+
e Y= β 1+ β 2 x 2+⋯+ β pxp+ e= x T β+ e with sample size n. This paper compares the six …

Consider a regression model, Y| x∼ D (x), where D is a parametric distribution that depends
on the p× 1 vector of predictors x. Generalized linear models, generalized additive models …

Inference after model selection is a very important problem. This paper derives the
asymptotic distribution of some model selection estimators for autoregressive moving …

Perhaps the first nonparametric, asymptotically optimal prediction intervals are provided for
univariate random walks, with applications to renewal processes. Perhaps the first …