### Citations

13209 | Statistical Learning Theory - Vapnik - 1998 |

2948 |
Categorical data analysis
- Agresti
- 2002
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Citation Context .... Keywords: Generalized cross-validation function, kernel trick, logistic regression, longitudinal data, mixed-effects model, penalized likelihood. 1. Introduction Logistic regression (Amemiya, 1985; =-=Agresti, 2002-=-) is a popular method for binary classification problems. The output of a logistic regression model can be interpreted as a posterior estimate of the probability that an observation belongs to each of... |

1065 |
Advanced econometrics
- Amemiya
- 1985
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Citation Context ...posed procedure. Keywords: Generalized cross-validation function, kernel trick, logistic regression, longitudinal data, mixed-effects model, penalized likelihood. 1. Introduction Logistic regression (=-=Amemiya, 1985-=-; Agresti, 2002) is a popular method for binary classification problems. The output of a logistic regression model can be interpreted as a posterior estimate of the probability that an observation bel... |

787 |
Multivariate Models and Dependence Concepts
- Joe
- 1997
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Citation Context ...to two treatment groups. 36 patients in the first group were treated for all episodes of urine tract infection and 36 patients in the second group were treated only if two specific symptoms occurred (=-=Joe, 1997-=-). We set the probability of bacteriuria of patient i at j-th time, P (yij = 1|zij ,xij) = exp(b0 + βzij + η2(xij) + bi) 1 + exp(b0 + βzij + η2(xij) + bi) , Semiparametric kernel logistic regression w... |

732 |
Smoothing noisy data with spline functions. Estimating the correct degree of smoothing by the method of generalized cross-validation
- Craven, Wahba
- 1978
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Citation Context ...vation. Since for each candidate of hyper-parameter sets, ∑ i ni of p̂θ (−k)(x∗k)’s should be computed, selecting parameters using CV function is computationally formidable. By leaving-out-one lemma (=-=Craven and Wahba, 1979-=-), we have (yk − p̂(−k)θ (x∗k))− (yk − p̂θ(x∗k)) = p̂θ(x∗k)− p̂(−k)θ (x∗k) ≈ ∂p̂θ(x ∗ k) ∂yk (yi − p̂(−k)θ (x∗k)) and ∂p̂θ(x ∗ k) ∂yk = ∂ν̂θ(x ∗ k) ∂y∗k ∂p̂θ(x ∗ k) ∂ν̂θ(x∗k) ∂y∗k ∂yk = skk, (4.1) whe... |

394 | Functions of positive and negative type and their connection with the theory of integral equations - Mercer - 1909 |

383 |
Some results on Tchebycheffian spline functions
- Kimeldorf, Wahba
- 1971
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Citation Context ...fit on the data and the smoothness. Semiparametric kernel logistic regression with longitudinal data 387 From now we denote by Kthe n×n matrix consisting of K(xi,xj). Then the representation theorem (=-=Kimeldorf and Wahba, 1971-=-) guarantees that the minimizer of the penalized negative log-likelihood (2.3) to be ηi = ∑n j=1Kijαj + b = K1iα, where Kij = K(xi,xj), K1i is the ith row of the kernel matrix K1 = (K,1) and α = (α1, ... |

132 |
Longitudinal data analysis
- Hedeker, Gibbons
- 2006
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Citation Context ... of applications, including cancer classification and analysis of DNA binding sites. For data that are clustered and/or longitudinal, mixed-effect regression models are becoming increasingly popular (=-=Hedeker and Gibbons, 2006-=-; Wu and Zhang, 2006). Mixed-effects models constitute both fixed and random effects. In clustered data, subjects are clustered within an organization such as a hospital, school, clinic or firm. In lo... |

113 |
Econometric Analysis of Count Data.
- Winkelmann
- 2008
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Citation Context ...er effects, while for longitudinal data the random effects represent subject effects. There has been much work done on mixed-effect models for continuous responses, and non-continuous responses data (=-=Winkelmann, 2003-=-; Shim and Seok, 2008). In this paper we propose a semiparametric kernel logistic regression model (SKLR) for the binary classification of longitudinal data. The proposed model is derived by employing... |

93 | On a kernel-based method for pattern recognition, regression, approximation and operator inversion. - Smola, Scholkopf - 1998 |

33 |
Nonparametric Regression Methods for Longitudinal Data Analysis
- Wu, Zhang
- 2006
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Citation Context ... cancer classification and analysis of DNA binding sites. For data that are clustered and/or longitudinal, mixed-effect regression models are becoming increasingly popular (Hedeker and Gibbons, 2006; =-=Wu and Zhang, 2006-=-). Mixed-effects models constitute both fixed and random effects. In clustered data, subjects are clustered within an organization such as a hospital, school, clinic or firm. In longitudinal data wher... |

5 | Doubly penalized kernel method for heteroscedastic autoregressive data - Cho, Shim, et al. - 2010 |

4 |
Kernel Poisson regression for longitudinal data
- Shim, Park, et al.
- 2008
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Citation Context ...for longitudinal data the random effects represent subject effects. There has been much work done on mixed-effect models for continuous responses, and non-continuous responses data (Winkelmann, 2003; =-=Shim and Seok, 2008-=-). In this paper we propose a semiparametric kernel logistic regression model (SKLR) for the binary classification of longitudinal data. The proposed model is derived by employing the penalized likeli... |

2 | Asymmetric least squares regression estimation using weighted least squares support vector machine - Hwang - 2011 |

1 | Kernel method for autoregressive data - Hwang - 2010 |

1 |
An analysis of satisfaction index on computer education
- Pi, Park, et al.
- 2011
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Citation Context ... through examples. In Section 6 we give the conclusions. 2. Kernel logistic regression A nonlinear form of logistic regression, known as kernel logistic regression, can be obtained via kernel tricks (=-=Pi et al., 2011-=-), whereby a conventional logistic regression model is constructed in a high dimensional nonlinear feature space induced by a Mercer’s kernel (1909). More formally, given a training data, D = {(xi, yi... |