Multivariate and Semiparametric Kernel Regression

Härdle, Wolfgang Karl; Müller, Marlene

doi:10.1002/9781118150658.ch12

Cited by 42 publications

(25 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the extreme situation in which and are independent, is not a function of at all and consequently there exists no solution to (30). We thus conclude that as the statistical dependence between and decreases, the variance of increases without bound.…”

Section: Estimation With Density Knowledge Via Obliquenessmentioning

confidence: 79%

“…A drawback of the obliqueness approach in the present setting, which did not exist in model M1, is that there is generally no closed form solution to (30). Nevertheless, it is possible to approximate the oblique estimator based on sets of examples of the type shown in Fig.…”

Section: Estimation With Density Knowledge Via Obliquenessmentioning

confidence: 99%

“…Like the oblique method under model M1, the approach taken here is also related to instrumental variable regression. Specifically, an equation very similar to (30) was studied in the context of instrumental variable estimation in nonparametric models [20]. In particular, it was shown that uniqueness of the solution to (30) requires when the distribution of belongs to the exponential family.…”

Section: Estimation With Density Knowledge Via Obliquenessmentioning

confidence: 99%

“…Proof: Substituting , the left-hand side (LHS) of (30) becomes (32) Using (31), this expression reduces to (33) so that the MMSE estimator satisfies (30).…”

Section: A Best Case Analysismentioning

confidence: 99%

“…It merely states that when (31) holds, at least one of the solutions satisfying the obliqueness requirement (30), is the MMSE estimator.…”

Section: A Best Case Analysismentioning

confidence: 99%

See 4 more Smart Citations

Hidden Relationships: Bayesian Estimation With Partial Knowledge

Michaeli

Eldar

2011

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-We address the problem of Bayesian estimation where the statistical relation between the signal and measurements is only partially known. We propose modeling partial Bayesian knowledge by using an auxiliary random vector called instrument. The statistical relations between the instrument and the signal and between the instrument and the measurements, are known. However, the joint probability function of the signal and measurements is unknown. Two types of statistical relations are considered, corresponding to second-order moment and complete distribution function knowledge. We propose two approaches for estimation in partial knowledge scenarios. The first is based on replacing the orthogonality principle by an oblique counterpart and is proven to coincide with the method of instrumental variables from statistics, although developed in a different context. The second is based on a worst-case design strategy and is shown to be advantageous in many aspects. We provide a thorough analysis showing in which situations each of the methods is preferable and propose a nonparametric method for approximating the estimators from a set of examples. Finally, we demonstrate our approach in the context of enhancement of facial images that have undergone unknown degradation and image zooming.Index Terms-Bayesian estimation, instrumental variables, minimax regret, nonparametric regression, partial knowledge.

show abstract

Section: Estimation With Density Knowledge Via Obliquenessmentioning

confidence: 79%

Section: Estimation With Density Knowledge Via Obliquenessmentioning

confidence: 99%

Section: Estimation With Density Knowledge Via Obliquenessmentioning

confidence: 99%

“…Proof: Substituting , the left-hand side (LHS) of (30) becomes (32) Using (31), this expression reduces to (33) so that the MMSE estimator satisfies (30).…”

Section: A Best Case Analysismentioning

confidence: 99%

“…It merely states that when (31) holds, at least one of the solutions satisfying the obliqueness requirement (30), is the MMSE estimator.…”

Section: A Best Case Analysismentioning

confidence: 99%

See 3 more Smart Citations

Hidden Relationships: Bayesian Estimation With Partial Knowledge

Michaeli

Eldar

2011

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

Bibliography

2015

Nonparametric Statistical Methods

View full text Add to dashboard Cite

Aalen, O. O. (1978). Nonparametric inference for a family of counting processes. Annals of Statistics 6, 701-726. Abdushukurov, A. A. (1987). Nonparametric estimation in the proportional hazards model of random censorship. Akad Nauk UzSSR, Tashkent VINITI No. 3448-V. Adichie, J. N. (1967). Estimates of regression parameters based on rank tests. Annals of Mathematical Statistics 38, 894-904. Adichie, J. N. (1974). Rank score comparison of several regression parameters. Annals of Statistics 2, 396-402. Adichie, J. N. (1976). Testing parallelism of regression lines against ordered alternatives. Communications in Statistics: Theory and Methods 5,

show abstract

Is the KOSPI 200 Options Market Efficient? Parametric and Nonparametric Tests of the Martingale Restriction

Guo

Han

Ryu

2012

Journal of Futures Markets

View full text Add to dashboard Cite

A number of studies on the S&P 500 index options market claim that the no‐arbitrage assumption cannot be rejected for this market because either the martingale restriction defined in Longstaff (1995) cannot be rejected by the data, or, even when it is rejected, a large proportion of the violation can be explained by market friction factors. The present study singles out the effect of market inefficiency from market friction by testing the martingale restriction for the KOSPI 200 index options market, which is the most liquid and active options market in the world. Not only using the parametric methods adopted in previous studies but also using the nonparametric methods that enable us to avoid the model misspecification problem, we empirically present clear evidence of a violation of the martingale restriction. In addition, in contrast to the S&P 500 options market, regression analyses and robustness tests indicate that market friction factors can explain only a small portion of the percentage differences between option‐implied and market‐observed index prices. Overall, the results do not support the basic no‐arbitrage assumption or the market efficiency in the KOSPI 200 options market.

show abstract

Multivariate and Semiparametric Kernel Regression

Cited by 42 publications

References 47 publications

Hidden Relationships: Bayesian Estimation With Partial Knowledge

Hidden Relationships: Bayesian Estimation With Partial Knowledge

Bibliography

Is the KOSPI 200 Options Market Efficient? Parametric and Nonparametric Tests of the Martingale Restriction

Contact Info

Product

Resources

About