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Under the context of empirical bayes a prior density estimate is obtained by using Bsplines. In this approach, there are two smoothing parameters, the number of basis functions and usual regularization parameter found in the context of penalized least squares problem. An algorithm is provided to get estimates of the two parameter as well as the prior density. 1. PRIOR SELECTION Usually, a lot of attention is paid on a particular parametric classes of priors using the data to assist in estimation of the prior hyperparameters or various functions thereof. The nonparametric empirical Bayes approach supposes that a large amount of data is available to estimate the prior, and hence places no (or minimal) restrictions on the form of the prior. One can try direct estimation of the prior doing the following: Let Π(0) be prior distribution and let f(-\9) be a likelihood density of the data ΛΊ, . . . , Xn given Θ. Suppose we do not know the form of the prior distribution Π and there is considerable information available in data such that it is possible to obtain ra the marginal density of the data. Then, we can estimate m by nonparametric methods of curve estimation such as, Logspline [7], H-spline [5], Smoothing spline density estimation [6], etc. Thus, making use of the integral relationship

Prior selection by an adaptive smoothing splines approach