Stone, Charles J. Large-sample inference for log-spline models. (English) Zbl 0712.62036 Ann. Stat. 18, No. 2, 717-741 (1990). Let Y be a random variable which takes values in a subinterval \({\mathcal Y}\) of \({\mathcal R}\) and has an unknown density f on \({\mathcal Y}\). Let F be the distribution function of f and Q its quantile function. As approximations of f, for each n the author constructs finite-parameter exponential models \(\{\) f(\(\cdot;\theta)\), \(\theta \in \Theta_ n\}\) for f, based on B-splines where \(\Theta_ n\) is a convex open subset of \({\mathcal R}^ J\) and \(J\to \infty\) as \(n\to \infty.\) Next, using a sample of n independent, identically distributed replications \(Y_ 1,...,Y_ n\) of \({\mathcal Y}\), he considers maximum likelihood estimation of the parameters of the models yielding estimates \(\hat f,\) \(\hat F\) and \(\hat Q\) of f, F and Q, respectively. Then, he shows that under mild conditions these estimates achieve the optimal rate of convergence and clarifies the asymptotic behavior of the corresponding confidence bounds. Reviewer: K.-i.Yoshihara Cited in 50 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62F12 Asymptotic properties of parametric estimators 62G05 Nonparametric estimation Keywords:large-sample inference; log-spline models; functional inference; quantile function; finite-parameter exponential models; B-splines; maximum likelihood estimation; optimal rate of convergence; confidence bounds × Cite Format Result Cite Review PDF Full Text: DOI