Multidimensional Cramér-Rao-Leibniz lower bound for vector-measurement-based likelihood functions with parameter-dependent support

One regularity condition for the classical Cramér-Rao lower bound (CRLB) of an unbiased estimator to hold is that the support of the likelihood function (LF) should be independent of the parameter to be estimated. This has been shown to be too stringent and the CRLB has been shown to be valid for the case of parameter-dependent support as long as the LF is continuous at the boundary of its support. For the case where the LF is not continuous at the boundary of its support, a new modified CRLB-designated as the Cramér-Rao-Leibniz lower bound (CRLLB) as it relies on the Leibniz integral rule-has been presented for the scalar parameter and measurement case in [3]. The CRLLB for multidimensional parameter and measurements has been developed in [8]. The present work applies the multidimensional CRLLB to n-dimensional measurement noise with the raised fractional cosine and the truncated Laplace distributions inside an (n-1)-sphere.