NONPARAMETRIC KERNEL REGRESSION SUBJECT TO MONOTONICITY CONSTRAINTS

2001

280 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/28e2be532d66694d3fe3486671f5c0217f58892d

Citations in the corpus

• A variable selection approach to monotonic regression with Bernstein polynomials (2011, unknown): “Hall and Huang [29] develop a method that monotonizes standard kernel smoothers by the inclusion of a discrete probability distribution on the values of the predictor variable.”
• Bayesian Isotonic Regression for Discrete Outcomes (2003, unknown): “A variety of frequentist approaches have been proposed for monotone curve estimation (Mammen, 1991; Lee, 1996; Ramsay, 1998; Hall and Huang, 2001; Mammen et al., 2001) and testing of monotonicity (Ghosal, Sen, and van der Vaart, 2000; Doveh, Shapiro, and Feigen, 2002).”
• Monotonicity Preserving Approximation of Multivariate Scattered Data (2005, unknown): “These methods do not incorporate monotonicity, although some attempts to enforce monotonicity of kernel based approximation (in the univariate case) and of the neural networks have been made [24,26].”
• Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints (2012, unknown): “Theorem 2 is the multivariate, multi-constraint, hyperplane subset generalization of the univariate, single constraint, single point violation setting considered in Hall and Huang (2001) having dispensed with probability weights and power divergence distance measures of necessity. The theory in Hall”
• Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications (2010, unknown): “For example, we can also impose the constraint d[̂σ 2(x)]/dx ≥ 0 or d2 [̂σ 2(x)]/dx2 ≥ 0 to ensure monotonicity (Hall and Huang 2001) or convexity of the estimated variance function as may be needed.”
• Measuring the price responsiveness of gasoline demand: Economic shape restrictions and nonparametric demand estimation (2011, unknown): “As Härdle and Marron (1991) showed using the Bonferroni inequality, the resulting intervals over the full grid form simultaneous confidence intervals at a level of at least 1 − α.”
• Multivariate convex regression with adaptive partitioning (2011, unknown): “The latter has been studied extensively with many approaches; for examples, see Brunk (1955), Hall & Huang (2001), Neelon & Dunson (2004) and Shively et al. (2009).”
• Constrained penalized splines (2012, unknown): “Hall & Huang (2001) provided a monotone kernel regression estimator.”
• Subgroup Identification and Variable Selection from Randomized Clinical Trial Data. (2013, unknown): “Details can be found in Hardle et al. [1993]. With the inclusion of the penalty term in (2.4), β̂ becomes a function of λn, so in addition to h, a value of λn must be chosen if β̂ is to be obtained. Throughout this paper, we refer to the method of estimating β and η without a monotonicity constraint”
• Bayesian Semiparametric Isotonic Regression for Count Data (2005, unknown): “Various frequentist approaches have been proposed in the literature for monotone curve estimation (Mammen 1991; Lee 1996; Ramsay 1998; Hall and Huang 2001; Mammen, Marron, Turlach, and Wand 2001) and monotonicity testing (Ghosal, Sen, and van der Vaart 2000; Doveh, Shapiro, and Feigen 2002).”
• Nonparametric Instrumental Variable Estimation Under Monotonicity (2015, unknown): “…been studied; see, for example, Mukerjee (1988), Cheng and Lin (1981), Wright (1981), Friedman and Tibshirani (1984), Ramsay (1988), Mammen (1991), Ramsay (1998), Mammen and Thomas-Agnan (1999), Hall and Huang (2001), Mammen, Marron, Turlach, and Wand (2001), and Dette, Neumeyer, and Pilz (2006).”