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1

An approximate necessary condition for the optimal bandwidth selector in kernel density estimation

100%

Gajek L., Lenic A.

Applicationes Mathematicae

|

1993-1995

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tom 22

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nr 1

123-138

EN

An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.

2

Optimal streams of premiums in multiperiod credibility models

81%

Gajek L., Miś P., Słowińska J.

Applicationes Mathematicae

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2007

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tom 34

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nr 2

223-235

EN

Optimal arrangement of a stream of insurance premiums for a multiperiod insurance policy is considered. In order to satisfy solvency requirements we assume that a weak Axiom of Solvency is satisfied. Then two optimization problems are solved: finding a stream of net premiums that approximates optimally 1) future claims, or 2) "anticipating premiums". It is shown that the resulting optimal streams of premiums enable differentiating between policyholders much more quickly than one-period credibility premiums.

3

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An improper Cramer-Rao lower bound

50%

Gajek L.

Applicationes Mathematicae

|

1987

|

tom 19

|

nr 2

241-256

Ograniczanie wyników

3 Applicationes Mathematicae

3 Gajek L.

1 Lenic A.

1 Miś P.

1 Słowińska J.

1 2007

1 1993

1 1987

An approximate necessary condition for the optimal bandwidth selector in kernel density estimation

Optimal streams of premiums in multiperiod credibility models

An improper Cramer-Rao lower bound