[1] Abbey, J. L., David, H. T., The construction of uniformly minimum variance unbiased estimators
for exponential distributions, Ann. Math. Statist., 41 (1970), 1217–1222.
[2] Afendras, G., Papadatos, N., Papathanasiou, V., The discrete Mohr and Noll inequality with applications
to variance bounds, Sankhyã, 69 (2007), 162–189.
[3] Akhiezer, N. I., The Classical Moment Problem and Some Related Questions in Analysis, New York,
Hafner Publishing Co., 1965.
[4] Asai, N., Kubo, I., Kuo, H., Multiplicative renormalization and generating functions I, Taiwanese
J. Math., 7 (2003), 89–101.
[5] Asai, N., Kubo, I., Kuo, H., Multiplicative renormalization and generating functions II, Taiwanese
J. Math., 8 (2004), 593–628.
[6] Beale, F. S., On a certain class of orthogonal polynomials, Ann. Math. Statist., 12 (1941), 97–103.
[7] Blight, B. J. N., Rao, P. V., The convergence of Bhattacharyya bounds, Biometrika, 61 (1974), 137–
142.
[8] Bobkov, S. G., Götze, F., Houdré, C., On Gaussian and Bernoulli covariance representations,
Bernoulli, 7 (2001), 439–451.
[9] Cacoullos, T., On upper and lower bounds for the variance of a function of a random variable, Ann.
Probab., 10 (1982), 799–809.
[10] Cacoullos, T., Papathanasiou, V., Bounds for the variance of functions of random variables by orthogonal
polynomials and Bhattacharyya bounds, Statist. Probab. Lett., 4 (1986), 21–23.
[11] Cacoullos, T., Papathanasiou, V., Characterizations of distributions by variance bounds, Statist.
Probab. Lett., 7 (1989), 351–356.
[12] Chernoff, H., A note on an inequality involving the normal distribution, Ann. Probab., 9 (1981),
533–535.
[13] Diaconis, P., Zabell, S., Closed form summation for classical distributions: Variations on a theme
of De Moivre, Statist. Sci., 6 (1991), 284–302.
[14] Goldstein, L., Reinert, G., Stein’s method and the zero-bias tranformation with application to simple
random sampling, Ann. Appl. Probab., 7 (1997), 935–952.
[15] Goldstein, L., Reinert, G., Distributional transformations, orthogonal polynomials, and Stein characterizations,
J. Theoret. Probab., 18 (2005), 237–260.
[16] Kagan, A., Variance inequalities for functions of Gaussian variables, J. Theoret. Probab., 8 (1995),
23–30.
[17] Houdré, C., Pérez-Abreu, V. , Covariance identities and inequalities for functionals on Wiener and
Poisson spaces, Ann. Probab., 23 (1995), 400–419.
[18] Johnson, R. W., A note on variance bounds for a function of a Pearson variate, Statist. Decisions,
11 (1993), 273–278.
[19] Johnson, R. W., On characterizations of distributions by mean absolute deviation and variance
bounds, Ann. Inst. Statist. Math., 43 (1991), 287–295.
[20] Lefévre, C., Papathanasiou, V., Utev, S. A., Generalized Pearson distributions and related characterization
problems, Ann. Inst. Statist. Math., 54 (2002), 731–742.
[21] López-Blázquez, F., Salamanca-Miño, B., Estimation based on the winzorized mean in the geometric
distribution, Statistics, 35 (2000), 81–95.
[22] Papathanasiou, V., A characterization of the Pearson system of distributions and the associated orthogonal
polynomials, Ann. Inst. Statist. Math., 47 (1995), 171–176.
[23] Privault, N., Extended covariance identities a nd inequalities, Statist. Probab. Lett., 55 (2001), 247–
255.
[24] Riesz, M., Sur le problème des moments et le théorème de Parseval correspondant (in French), Acta
Litt. Ac. Sci. (Szeged), 1 (1923), 209–225.
[25] Schoutens, W., Orthogonal polynomials in Stein’s method, J. Math. Anal. Appl., 253 (2001), 515–
531.
[26] Seth, G. R., On the variance of estimates, Ann. Math. Statist., 20 (1949), 1–27.
[27] Stein, C. M., A bound for the error in the normal approximation to the distribution of a sum of
dependent random variables, in Proc. Sixth Berkeley Symp. Math. Statist. Probab., Univ. California
Press, Berkeley, CA, 2 (1972), 583–602.
[28] Stein, C. M., Estimation of the mean of a multivariate normal distribution, Ann. Statist., 9 (1981),
1135–1151.