Combining regular and irregular histograms by penalized likelihood

Combining regular and irregular histograms by penalized likelihood

A new fully automatic procedure for the construction of histograms is proposed. It consists of constructing both a regular and an irregular histogram and then choosing between the two. To choose the number of bins in the irregular histogram, two different penalties motivated by recent work in model selection are proposed. A description of the algorithm and a proper tuning of the penalties is gi...

Constructing Irregular Histograms by Penalized Likelihood

We propose a fully automatic procedure for the construction of irregular histograms. For a given number of bins, the maximum likelihood histogram is known to be the result of a dynamic programming algorithm. To choose the number of bins, we propose two different penalties motivated by recent work in model selection by Castellan [6] and Massart [26]. We give a complete description of the algorit...

Penalized Least Squares and Penalized Likelihood

where pλ(·) is the penalty function. Best subset selection corresponds to pλ(t) = (λ/2)I(t 6= 0). If we take pλ(t) = λ|t|, then (1.2) becomes the Lasso problem (1.1). Setting pλ(t) = at + (1 − a)|t| with 0 ≤ a ≤ 1 results in the method of elastic net. With pλ(t) = |t| for some 0 < q ≤ 2, it is called bridge regression, which includes the ridge regression as a special case when q = 2. Some penal...

Penalized likelihood and multi-objective spatial scans for the detection and inference of irregular clusters

BACKGROUND Irregularly shaped spatial clusters are difficult to delineate. A cluster found by an algorithm often spreads through large portions of the map, impacting its geographical meaning. Penalized likelihood methods for Kulldorff's spatial scan statistics have been used to control the excessive freedom of the shape of clusters. Penalty functions based on cluster geometry and non-connectivi...

Penalized Likelihood Density Estimation :