Anderson, GL, de Figueiredo, RJP. An adaptive orthogonal series estimator for probability density functions. Ann Stat 1980; 8: 347–376.
Čencov, NN. Statistical Decision Rules and Optimum Inference. New York: Springer‐Verlag; 1980.
Devroye, L, Györfi, L. Nonparametric Density Estimation: The L1 View. New York: John Wiley %26 Sons; 1985.
Devroye, L, Lugosi, G. Combinatorial Methods in Density Estimation. New York: Springer; 2001.
Efromovich, S. Nonparametric Curve Estimation: Methods, Theory and Applications. New York: Springer; 1999.
Ibragimov, IA, Khasminskii, RZ. Statistical Estimation: Asymptotic Theory. New York: Springer; 1981.
Massart, P. Concentration Inequalities and Model Selection, vol. 1896, Lecture Notes in Mathematics, New York: Springer; 2007.
Rosenblatt, M. Curve estimates. Ann Math Stat 1971; 42: 1815–1842.
Schwartz, S. Estimation of probability density by an orthogonal series. Ann Math Stat 1967; 38: 1262–1265.
Scott, DW. Multivariate Density Estimation: Theory, Practice, and Visualization. New York: John Wiley %26 Sons; 1992.
Silverman, BW. Density Estimation for Statistics and Data Analysis. London: Chapman %26 Hall; 1986.
Tapia, RA, Thompson, JR. Nonparametric Probability Density Estimation. Baltimore: Johns Hopkins University Press; 1978.
Wegman, EJ. Nonparametric probability density estimation: I. A summary of available methods. Technometrics 1972; 14: 533–546.
Scott, DW. Histogram. WIREs Comp Stat 2010; 2(1): 44–48.
Čencov, NN. Evaluation of an unknown distribution density from observations. Soviet Math. Dokl. 1962; 3: 1559–1562.
Hart, JD. Nonparametric Smoothing and Lack‐of‐Fit Tests. New York: Springer; 1997.
Walter,, GG. Wavelets and other Orthogonal Systems with Applications. London: CRC Press; 1994.
Hall, P. Orthogonal series methods for both qualitative and quantitative data. Ann Stat 1983; 11: 1004–1007.
Hendriks, H. Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions. Ann Stat 1990; 18: 832–849.
Wahba, G. Optimal convergence properties of variable knot, kernel, and orthogonal series methods for density estimation. Ann Stat 1975; 3: 15–29.
Watson, GS. Density estimation by orthogonal series. Ann Math Stat 1969; 38: 1262–1265.
Rosenblatt, M. Remarks on some non‐parametric estimates of a density function. Ann Math Stat 1956; 27: 832–837.
Hall, P. Estimating a density on the positive half line by the method of orthogonal series. Ann Inst Stat Math 1980; 32: 351–362.
Walter, GG. Properties of Hermite series estimation of probability density. Ann Stat 1977; 5: 1258–1264.
Hall, P. On trigonometric series estimates of densities. Ann Stat 1981; 9: 683–685.
Tarter, ME, Lock, MD. Model‐Free Curve Estimation. New York: Chapman %26 Hall; 1993.
Buckland, ST. Fitting density functions with polynomials. J R Stat Soc [Ser A] 1992; 41: 63–76.
Rudzkis, R, Radavicius, M. Adaptive estimation of distribution density in the basis of algebraic polynomials. Theory Probab Appl 2005; 49: 93–109.
Chicken, E, Cai, T. Block thresholding for density estimation: local and global adaptivity. J Multivar Anal 2005; 95: 75–106.
Donoho, D, Johnstone, I, Kerkyacharian, G, Picard, D. Density estimation by wavelet thresholding. Ann Stat 1996; 24: 508–539.
Härdle, W, Kerkyacharian, G, Picard, D, Tsybakov, A. Wavelets, Approximation, and Statistical Applications. New York: Springer; 1998.
Good, IJ, Gaskins, RA. Density estimation and bump‐hunting by penalized likelihood method exemplified by scattering and meteorite data, with discussion. J Am Stat Assoc 1980; 75: 42–73.
Wahba, G. Data‐based optimal smoothing of orthogonal series density estimates. Ann Stat 1981; 9: 146–156.
Tarter, ME, Kronmal, RA. An introduction to the implementation and theory of nonparametric density estimation. Am Stat 1976; 30: 105–112.
Diggle, PJ, Hall, P. The selection of terms in an orthogonal series density estimator. J Am Stat Assoc 1986; 81: 230–233.
Hart, JD. On the choice of truncation point in Fourier series density estimation. J Stat Comput Simul 1985; 21: 95–116.
Hall, P. Cross‐validation and the smoothing of orthogonal series density estimators. J Multivar Anal 1987; 21: 189–206.
Scott, DW, Terrell, GR. Biased and unbiased cross‐validation in density estimation. J Am Stat Assoc 1987; 82: 1131–1146.
Kronmal, RA, Tarter, ME. The estimation of probability densities and cumulatives by Fourier series methods. J Am Stat Assoc 1968; 63: 925–952.
Crain, BB. A note on density estimation using orthogonal expansions. Ann Stat 1973; 2: 454–463.
Efromovich, S. Nonparametric estimation of a density with unknown smoothness. Theory Probab Appl 1985; 30: 557–568.
Hall, P, Kerkyacharian, G, Picard, D. Block threshold rules for curve estimation using Kernel and wavelet methods. Ann Stat 1998; 26: 922–942.
Rigollet, P. Adaptive density estimation using the blockwise Stein method. Bernoulli (Andover) 2006; 12: 351–370.
Efromovich, S. Density estimation for the case of supersmooth measurement error. J Am Stat Assoc 1997; 92: 526–535.
Efromovich, S. Adaptive estimation of and oracle inequalities for probability densities and characteristic functions. Ann Stat 2008; 36: 1127–1155.
Efromovich, S. Adaptive orthogonal series density estimation for small samples. Comput Stat Data Anal 1996; 22: 599–617.
Catoni, O. Statistical Learning Theory and Stochastic Optimization, vol. 1851, Lecture Notes in Mathematics. New York: Springer; 2004.
Nemirovski, A. Topics in Non‐Parametric Statistics, vol. 1738, Lecture Notes in Mathematics, New York: Springer; 2000.
Rigollet, P, Tsybakov, A. Linear and convex aggregation of density estimators. Math Methods Stat 2007; 16: 260–280.
Samarov, A, Tsybakov, A. Aggregation of density estimators and dimension reduction. In: Nair, V, ed. Advances in Statistical Models and Inference, Essays in Honor of Kjell Doksum. Singapore: World Scientific; 233–251, 2007.
Yang, Y. Mixing strategies for density estimation. Ann Stat 2000; 28: 75–87.
Efromovich, S. Density estimation under random censorship and order restrictions: from asymptotic to small samples. J Am Stat Assoc 2001; 96: 667–685.
Gajek, L. On improving density estimators which are not bona fide functions. Ann Stat 1986; 14: 1612–1618.
Efromovich, S. Lower bound for estimation of Sobolev densities of order less 1/2. J Stat Plan Inference 2009; 139: 2261–2268.
Golubev, GK. Nonparametric estimation of smooth probability densities in L2. Prob Inform Transm 1992; 28: 44–54.
Efromovich, S. Adaptive estimation of error density in nonparametric regression with small sample size. J Stat Plan Inference 2007; 137: 363–378.
Marron, JS, Wand, MP. Exact mean integrated squared error. Ann Stat 1992; 20: 712–736.
Efromovich, S. Density estimation for biased data. Ann Stat 2004; 32: 1137–1161.
Efromovich, S. Estimation of the density of regression errors. Ann Stat 2005; 33: 2194–2227.
Efromovich, S. Optimal nonparametric estimation of the density of regression errors with finite support. Ann Inst Stat Math 2007; 59: 617–654.
Efromovich, S. Conditional density estimation. Ann Stat 2007; 35: 2504–2535.