Density Estimation for Statistics and Data Analysis

By Bernard Walter Silverman. 1987

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “A nonparametric representation of tree-structured graphical models was introduced in Song et al. (2010b). Inference in this kind of graphical model relies mostly on message passing algorithms.”
Filtering with State-Observation Examples via Kernel Monte Carlo Filter (2013, methodology): “ighbors approach (Stone, 1977) for learning the observation model. A problem here is that conditional density estimation suffers from the curse of dimensionality if observations are high-dimensional (Silverman, 1986). Vlassis et al. (2002) avoided this problem by estimating the conditional density f”
Comprehensible credit scoring models using rule extraction from support vector machines (2007, positive): “For a discrete valued input, Trepan simply uses the empirical frequencies of the various values whereas for a continuous input x, a kernel density estimation method is used to model the probability distribution f(x) as follows [27]:”
Estimating mutual information. (2003, background): “This is recommended in the literature [31], since both statistical and systematic errors would become too large for smaller values of h .”
Closing the learning-planning loop with predictive state representations (2009, methodology): “Although use of kernel density estimation for continuous observations in PSRs is not new [29], extending our algorithm to use KDE results, for the first time, in a statistically consistent learning algorithm for PSRs with continuous observations.”
Robust kernel density estimation (2008, background): “Introduction The kernel density estimator (KDE) is a well-known nonparametric estimator of univariate or multivariate densities, and numerous articles have been written on its properties, applications, and extensions (Silverman, 1986; Scott, 1992).”
Noise Estimation Using Density Estimation for Self-Supervised Multimodal Learning (2020, methodology): “Existing density estimation algorithms can be divided into two categories: (a) parametric or semi-parametric approaches such as Gaussian Mixture models (McLachlan and Krishnan 2007; Wang and Wang 2015) and probabilistic graphical models (Koller and Friedman 2009); and (b) non-parametric approaches s”
Open-Ended Learning Leads to Generally Capable Agents (2021, methodology): “We use a Gaussian kernel and Silverman’s rule to estimate its bandwidth (Silverman, 2018).”
Regional disparities in the European Union: Convergence and Agglomeration (2008, background): “window sliding across the income distribution (see e.g. Silverman 1986, Fox 1990, Scott 1979”
Decentralization and efficiency of local government (2010, methodology): “However, we may turn to kernel smoothing methods ( Silverman 1986 ) to estimate f , and therefore ˆ f would be the nonparametric kernel estimator of f . In such a case, since ˆ f = (1/(Sh)) S=1 K ((xs − x)/ h), a suitable”
A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION (2012, background): “See Silverman (1986), Fan and Gijbels (1996), and Cheng (1997) for more details.”
Estimation of Dynamic Panel Data Sample Selection Models (2001, methodology): “The smoothing was done using a standard normal kernel and the rule of thumb bandwidth suggested by Silverman (1986) for density estimation.”
Linearly Combining Density Estimators via Stacking (1999, methodology): “This is all consistent with the standard theory of kernel density estimation; as the sample size increases, for a given true density the optimal single bandwidth decreases as an inverse function of N ( Silverman, 1986 ).”
Nonparametric Density Estimation: Toward Computational Tractability (2003, methodology): “For good estimates, the exact form of turns out to be relatively unimportant, while the correct choice of is critical [ 22 , 20].”
Unified Cross-Validation Methodology For Selection Among Estimators and a General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities and Examples (2003, unknown): “Silverman (1986) refers to Scott and Factor (1981) to indicate that for densities with infinite support this leave-one-out likelihood cross-validation method for bandwidth selection in density estimation is sensitive to outliers, and to Schuster and Gregory (1981) to point out that leave-one-out…”