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Questions and Answers
What governs the shape of a histogram?
What governs the shape of a histogram?
- The kernel function and bandwidth
- The origin and bandwidth (correct)
- The choice of x and the kernel density estimator
- The averaging method and kernel function
What is the kernel density estimator formula based on?
What is the kernel density estimator formula based on?
- Averaged shifted histograms
- The choice of x and the kernel function
- Kernel function and bandwidth (correct)
- The origin and averaging method
What is the purpose of the kernel function in the kernel density estimator?
What is the purpose of the kernel function in the kernel density estimator?
- It governs the choice of x
- It is used for averaging shifted histograms
- It is the weighing function (correct)
- It determines the shape of the histogram
What is the drawback of the histogram despite the use of averaged shifted histograms?
What is the drawback of the histogram despite the use of averaged shifted histograms?
What is the kernel density estimator formula influenced by?
What is the kernel density estimator formula influenced by?
What governs the shape of a histogram?
What governs the shape of a histogram?
What is the purpose of the kernel function in the kernel density estimator?
What is the purpose of the kernel function in the kernel density estimator?
What is the drawback of the histogram despite the use of averaged shifted histograms?
What is the drawback of the histogram despite the use of averaged shifted histograms?
What is the kernel density estimator formula influenced by?
What is the kernel density estimator formula influenced by?
What does the kernel density estimator formula depend on?
What does the kernel density estimator formula depend on?
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Study Notes
Histogram and Kernel Density Estimator
- The shape of a histogram is governed by the number of bins and the width of each bin
- The kernel density estimator (KDE) formula is based on the kernel function, which is a weighting function that determines the influence of each data point on the estimate
- The purpose of the kernel function in the KDE is to assign weights to each data point, with more weight given to points closer to the estimation point
- Despite the use of averaged shifted histograms, the drawback of histograms is that they can be sensitive to the choice of bin width and can be misleading if the bin width is not chosen carefully
- The kernel density estimator formula is influenced by the choice of kernel function, bandwidth, and the data points themselves
- The kernel density estimator formula depends on the kernel function, bandwidth, and the data points, which determines the estimated density at a given point.
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