# zbMATH — the first resource for mathematics

Measuring the efficiency of trigonometric series estimates of a density. (English) Zbl 0522.62029

##### MSC:
 62G05 Nonparametric estimation
Full Text:
##### References:
 [1] Anderson, G.L; De Figueiredo, R.J.P, An adaptive orthogonal-series estimator for probability density functions, Ann. statist., 8, 347-376, (1980) · Zbl 0426.62023 [2] Bosq, D; Bluez, J, Etude d’une classe d’estimateurs non-parametrique de la densité, Ann. inst. H. Poincaré sect. A (N.S.), 14, 479-498, (1978) · Zbl 0392.62029 [3] Butzer, P.L; Nessel, R.J, () [4] Carslaw, H.S, () [5] Cencov, N.N, Evaluation of an unknown distribution density from observations, Soviet math. dokl., 3, 1559-1562, (1962) · Zbl 0133.11801 [6] Elderton, W.P, () [7] Epanechnikov, V.A, Nonparametric estimation of a multivariate probability density, Theory probab. appl., 14, 153-163, (1969) · Zbl 0175.17101 [8] Hall, P, On trigonometric series estimates of densities, Ann. statist., (1981) · Zbl 0484.62057 [9] Kronmal, R; Tarter, M, The estimation of probability densities and cumulatives by Fourier series methods, J. amer. statist. assoc., 63, 925-952, (1968) · Zbl 0169.21403 [10] Lanczos, C, () [11] Petrov, V.V, () [12] Van Ryzin, J, Bayes risk consistency of classification procedures using density estimation, Sankhyā ser. A, 28, 261-270, (1966) · Zbl 0192.25703 [13] Schwartz, S.C, Estimation of probability density by orthogonal series, Ann. math. statist., 38, 1261-1265, (1967) · Zbl 0157.47904 [14] Tarter, M.E, Trigonometric maximum likelihood estimation and application to the analysis of incomplete survival information, J. amer. statist. assoc., 74, 132-139, (1979) · Zbl 0405.62032 [15] Tarter, M.E; Raman, S, A systematic approach to graphical methods in biometry, (), 199-222 [16] Wahba, G, Optimal convergence properties of variable knot, kernel, and orthogonal series methods for density estimation, Ann. statist., 3, 15-20, (1975) · Zbl 0305.62021 [17] Wahba, G, Optimal smoothing of density estimates, (), 423-457 [18] Walter, G.G, Properties of Hermite series estimation of probability density, Ann. statist., 8, 454-455, (1980) · Zbl 0451.62035 [19] Walter, G.G; Blum, J.R, Probability density estimation using delta sequences, Ann. statist., 7, 328-340, (1979) · Zbl 0403.62025 [20] Watson, G.S, Density estimation by orthogonal series, Ann. math. statist., 40, 1496-1498, (1969) · Zbl 0188.50602 [21] Zygmund, A, ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.