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• W2044334429 abstract "Let $f$ be a continuous and positive unknown density on a known compact interval $mathscr{Y}$. Let $F$ denote the distribution function of $f$ and let $Q = F^{-1}$ denote its quantile function. A finite-parameter exponential family model based on $B$-splines is constructed. Maximum-likelihood estimation of the parameters of the model based on a random sample of size $n$ from $f$ yields estimates $hat{f, F}$ and $hat{Q}$ of $f, F$ and $Q$, respectively. Under mild conditions, if the number of parameters tends to infinity in a suitable manner as $n rightarrow infty$, these estimates achieve the optimal rate of convergence. The asymptotic behavior of the corresponding confidence bounds is also investigated. In particular, it is shown that the standard errors of $hat{F}$ and $hat{Q}$ are asymptotically equal to those of the usual empirical distribution function and empirical quantile function." @default.
• W2044334429 created "2016-06-24" @default.
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• W2044334429 date "1990-06-01" @default.
• W2044334429 modified "2023-10-18" @default.
• W2044334429 title "Large-Sample Inference for Log-Spline Models" @default.
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• W2044334429 doi "https://doi.org/10.1214/aos/1176347622" @default.
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