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  2. Kernel regression - Wikipedia

    en.wikipedia.org/wiki/Kernel_regression

    In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y .

  3. Kernel (statistics) - Wikipedia

    en.wikipedia.org/wiki/Kernel_(statistics)

    In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable.

  4. Nonparametric regression - Wikipedia

    en.wikipedia.org/wiki/Nonparametric_regression

    Example of a curve (red line) fit to a small data set (black points) with nonparametric regression using a Gaussian kernel smoother. The pink shaded area illustrates the kernel function applied to obtain an estimate of y for a given value of x.

  5. Kernel smoother - Wikipedia

    en.wikipedia.org/wiki/Kernel_smoother

    Kernel average smoother example. The idea of the kernel average smoother is the following. For each data point X 0, choose a constant distance size λ (kernel radius, or window width for p = 1 dimension), and compute a weighted average for all data points that are closer than to X 0 (the closer to X 0 points get higher weights).

  6. Kernel density estimation - Wikipedia

    en.wikipedia.org/wiki/Kernel_density_estimation

    Kernel density estimation of 100 normally distributed random numbers using different smoothing bandwidths.. In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights.

  7. Multivariate kernel density estimation - Wikipedia

    en.wikipedia.org/wiki/Multivariate_kernel...

    The previous figure is a graphical representation of kernel density estimate, which we now define in an exact manner. Let x 1, x 2, ..., x n be a sample of d-variate random vectors drawn from a common distribution described by the density function ƒ. The kernel density estimate is defined to be

  8. Regularized least squares - Wikipedia

    en.wikipedia.org/wiki/Regularized_least_squares

    This demonstrates that any kernel can be associated with a feature map, and that RLS generally consists of linear RLS performed in some possibly higher-dimensional feature space. While Mercer's theorem shows how one feature map that can be associated with a kernel, in fact multiple feature maps can be associated with a given reproducing kernel.

  9. Principal component regression - Wikipedia

    en.wikipedia.org/wiki/Principal_component_regression

    Kernel PCR then proceeds by (usually) selecting a subset of all the eigenvectors so obtained and then performing a standard linear regression of the outcome vector on these selected eigenvectors. The eigenvectors to be used for regression are usually selected using cross-validation. The estimated regression coefficients (having the same ...