Nonparametric iterative estimation of multivariate binary density

Wei, Liang; Krishnaiah, P. R.

doi:10.1016/0047-259x(85)90057-0

Cited by 9 publications

(11 citation statements)

References 6 publications

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“…As was shown in [4], the mean integrated square error of p,(x) to be denoted by MISE (p 0, attains its minimum upon choosing Ar= na2/(2-d +(n-1)a 2 ), r e R.…”

Section: Shrinkage Estimates Based On Walsh Functionsmentioning

confidence: 97%

“…Liang and Krishnaiah proposed such an estimate in [4] via some iteration considerations, as follows.…”

Section: Shrinkage Estimates Based On Walsh Functionsmentioning

confidence: 99%

“…The validity of (14) does not depend on the value assumed by a . Use (14) to replace (4-5) of [4], and the rest of the proof for sufficiency runs exactly along the same way as in [4].…”

Section: )mentioning

confidence: 99%

“…The proof is a slight modification of the proof of Theorem 2 in [4]. First, according to (4-3) of [4], we need only to show that…”

Section: A New Shrinkage Estimatementioning

confidence: 99%

See 3 more Smart Citations

Estimation of Multivariate Binary Density Using Orthonormal Functions.

Chen¹,

Krishnaiah²,

Liang³

1986

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“…As was shown in [4], the mean integrated square error of p,(x) to be denoted by MISE (p 0, attains its minimum upon choosing Ar= na2/(2-d +(n-1)a 2 ), r e R.…”

Section: Shrinkage Estimates Based On Walsh Functionsmentioning

confidence: 97%

“…Liang and Krishnaiah proposed such an estimate in [4] via some iteration considerations, as follows.…”

Section: Shrinkage Estimates Based On Walsh Functionsmentioning

confidence: 99%

“…The validity of (14) does not depend on the value assumed by a . Use (14) to replace (4-5) of [4], and the rest of the proof for sufficiency runs exactly along the same way as in [4].…”

Section: )mentioning

confidence: 99%

“…The proof is a slight modification of the proof of Theorem 2 in [4]. First, according to (4-3) of [4], we need only to show that…”

Section: A New Shrinkage Estimatementioning

confidence: 99%

See 2 more Smart Citations

Estimation of Multivariate Binary Density Using Orthonormal Functions.

Chen¹,

Krishnaiah²,

Liang³

1986

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“…Examples of practical situations calling for the estimation of a density can be found in the works of several authors, e.g., Murthy (1965), Singh (1977b), Liang and Krishnaiah (1985), among others.…”

Section: Introductionmentioning

confidence: 99%