# Comparison between bootstrap percentiles confidence interval and BCa confidence interval?

I have generated a nonparametric percentiles bootstrap confidence interval ($32.27143, 51.08571$), and a BCA confidence interval ($33.26, 53.49$) with an initial sample size of $n=7$. Evidently, the BCA interval is larger than the percentiles interval. Shouldn't the BCA interval be better than the percentiles interval (and by "better" I mean "smaller")? I noticed also that when the sample size is larger, for example $n=40$, BCa confidence interval decreases.

-
BCa intervals are "better" than other types of bootstrap intervals in terms of coverage. This is, their coverage is closer to the nominal value. In some scenarios this implies that the intervals are wider or narrower than other types of bootstrap intervals. Regarding your last comment, the length of confidence intervals converges to $0$ as the sample size $N\rightarrow\infty$. Intuitively this happens because the larger the sample is, the more information it carries about the parameters and this is reflected on the "precision" of the estimation. –  user10525 Nov 15 '12 at 12:06
Following on Procrastinator's comment, one might think if the intervals were not much different it would be OK to just use the percentile interval. But a habit of doing that will get you that poorer coverage - the intervals do differ in distribution but that does not imply anything about individual instances. –  phaneron Nov 15 '12 at 19:49
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.803724467754364, "perplexity": 604.2039546519761}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164972407/warc/CC-MAIN-20131204134932-00008-ip-10-33-133-15.ec2.internal.warc.gz"}