seminars:stat:04162015
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| + | <WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP> | ||
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| + | ~~META:title =April 16, 2015~~ | ||
| + | <WRAP 70% center> | ||
| + | ^ **DATE:**|Thursday, April 16, 2015 | | ||
| + | ^ **TIME:**|1:15pm to 2:15pm | | ||
| + | ^ **LOCATION:**|WH 100E | | ||
| + | ^ **SPEAKER:**|Ruiqi Liu (Binghamton University) | | ||
| + | ^ **TITLE:**|Density estimation for power transformations—Paper Discussion | | ||
| + | </WRAP> | ||
| + | \\ | ||
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| + | <WRAP center box 80%> | ||
| + | <WRAP centeralign>**Abstract**</WRAP> | ||
| + | I will discuss a paper of Olga Y. Savchuk and Anton Schick. | ||
| + | Consider a random sample $X_1,...,X_n$ from a density $f$. For a positive $\alpha$, | ||
| + | the density $g$ of $t(X_1) = |X_1|^\alpha sign(X_1)$ can be estimated in two ways: by a | ||
| + | kernel estimator based on the transformed data $t(X_1),...,t(X_n)$ or by a plug- | ||
| + | in estimator transformed from a kernel estimator based on the original data. | ||
| + | In this paper, they compare the performance of these two estimators using | ||
| + | MSE and MISE. For MSE, the plug-in estimator is better in the case $\alpha > 1$ | ||
| + | when $f$ is symmetric and unimodal, and in the case $\alpha \ge 2.5$ when $f$ is right- | ||
| + | skewed and/or bimodal. For $\alpha < 1$, the plug-in estimator performs better | ||
| + | around the modes of $g$, while the transformed data estimator is better in the | ||
| + | tails of $g$. For global comparison MISE, the plug-in estimator has a faster | ||
| + | rate of convergence for $0.4 \le \alpha < 1$ and $1 < \alpha < 2$. For $\alpha < 0.4$, the plug-in | ||
| + | estimator is preferable for a symmetric density $f$ with exponentially decaying | ||
| + | tails, while the transformed data estimator has a better performance when | ||
| + | $f$ is right-skewed or heavy-tailed. Applications to real and simulated data | ||
| + | illustrated these theoretical findings. | ||
| + | </WRAP> | ||