Density deconvolution with associated stationary data

Le Thi Hong Thuy; Cao Xuan Phuong

Applications of Mathematics (2023)

  • Volume: 68, Issue: 5, page 685-708
  • ISSN: 0862-7940

Abstract

top
We study the density deconvolution problem when the random variables of interest are an associated strictly stationary sequence and the random noises are i.i.d. with a nonstandard density. Based on a nonparametric strategy, we introduce an estimator depending on two parameters. This estimator is shown to be consistent with respect to the mean integrated squared error. Under additional regularity assumptions on the target function as well as on the density of noises, some error estimates are derived. Several numerical simulations are also conducted to illustrate the efficiency of our method.

How to cite

top

Thuy, Le Thi Hong, and Phuong, Cao Xuan. "Density deconvolution with associated stationary data." Applications of Mathematics 68.5 (2023): 685-708. <http://eudml.org/doc/299356>.

@article{Thuy2023,
abstract = {We study the density deconvolution problem when the random variables of interest are an associated strictly stationary sequence and the random noises are i.i.d. with a nonstandard density. Based on a nonparametric strategy, we introduce an estimator depending on two parameters. This estimator is shown to be consistent with respect to the mean integrated squared error. Under additional regularity assumptions on the target function as well as on the density of noises, some error estimates are derived. Several numerical simulations are also conducted to illustrate the efficiency of our method.},
author = {Thuy, Le Thi Hong, Phuong, Cao Xuan},
journal = {Applications of Mathematics},
keywords = {associated process; density deconvolution; nonstandard noise density},
language = {eng},
number = {5},
pages = {685-708},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Density deconvolution with associated stationary data},
url = {http://eudml.org/doc/299356},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Thuy, Le Thi Hong
AU - Phuong, Cao Xuan
TI - Density deconvolution with associated stationary data
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 5
SP - 685
EP - 708
AB - We study the density deconvolution problem when the random variables of interest are an associated strictly stationary sequence and the random noises are i.i.d. with a nonstandard density. Based on a nonparametric strategy, we introduce an estimator depending on two parameters. This estimator is shown to be consistent with respect to the mean integrated squared error. Under additional regularity assumptions on the target function as well as on the density of noises, some error estimates are derived. Several numerical simulations are also conducted to illustrate the efficiency of our method.
LA - eng
KW - associated process; density deconvolution; nonstandard noise density
UR - http://eudml.org/doc/299356
ER -

References

top
  1. Bagai, I., Rao, B. L. S. Prakasa, 10.1007/BF00773461, Ann. Inst. Stat. Math. 47 (1995), 253-266. (1995) Zbl0833.62036MR1345422DOI10.1007/BF00773461
  2. Birkel, T., 10.1214/aop/1176991591, Ann. Probab. 16 (1988), 1685-1698. (1988) Zbl0658.60039MR0958210DOI10.1214/aop/1176991591
  3. Butucea, C., Tsybakov, A. B., 10.1137/S0040585X97982840, Theory Probab. Appl. 52 (2008), 24-39. (2008) Zbl1141.62021MR2354572DOI10.1137/S0040585X97982840
  4. Carrasco, M., Florens, J.-P., 10.1017/S026646661000040X, Econom. Theory 27 (2011), 546-581. (2011) Zbl1218.62025MR2806260DOI10.1017/S026646661000040X
  5. Carroll, R. J., Hall, P., 10.2307/2290153, J. Am. Stat. Assoc. 83 (1988), 1184-1186. (1988) Zbl0673.62033MR0997599DOI10.2307/2290153
  6. Chesneau, C., 10.1016/j.jkss.2012.01.005, J. Korean Stat. Soc. 41 (2012), 423-436. (2012) Zbl1296.62079MR3255347DOI10.1016/j.jkss.2012.01.005
  7. Comte, F., Dedecker, J., Taupin, M.-L., 10.3103/S1066530708020014, Math. Methods Stat. 17 (2008), 87-112. (2008) Zbl1282.62087MR2429122DOI10.3103/S1066530708020014
  8. Comte, F., Rozenholc, Y., Taupin, M.-L., 10.1002/cjs.5550340305, Can. J. Stat. 34 (2006), 431-452. (2006) Zbl1104.62033MR2328553DOI10.1002/cjs.5550340305
  9. Dedecker, J., Prieur, C., 10.1007/s00440-004-0394-3, Probab. Theory Relat. Fields 132 (2005), 203-236. (2005) Zbl1061.62058MR2199291DOI10.1007/s00440-004-0394-3
  10. Delaigle, A., Meister, A., 10.5705/ss.2009.082, Stat. Sin. 21 (2011), 1065-1092. (2011) Zbl1232.62057MR2827515DOI10.5705/ss.2009.082
  11. Devroye, L., 10.2307/3314852, Can. J. Stat. 17 (1989), 235-239. (1989) Zbl0679.62029MR1033106DOI10.2307/3314852
  12. Esary, J. D., Proschan, F., Walkup, D. W., 10.1214/aoms/1177698701, Ann. Math. Stat. 38 (1967), 1466-1474. (1967) Zbl0183.21502MR0217826DOI10.1214/aoms/1177698701
  13. Fan, J., 10.1214/aos/1176348248, Ann. Stat. 19 (1991), 1257-1272. (1991) Zbl0729.62033MR1126324DOI10.1214/aos/1176348248
  14. Fortuin, C. M., Kasteleyn, P. W., Ginibre, J., 10.1007/BF01651330, Commun. Math. Phys. 22 (1971), 89-103. (1971) Zbl0346.06011MR0309498DOI10.1007/BF01651330
  15. Groeneboom, P., Jongbloed, G., 10.1111/1467-9574.00225, Staat. Neerl. 57 (2003), 136-157. (2003) Zbl1090.62527MR2035863DOI10.1111/1467-9574.00225
  16. Hall, P., Meister, A., 10.1214/009053607000000028, Ann. Stat. 35 (2007), 1535-1558. (2007) Zbl1147.62031MR2351096DOI10.1214/009053607000000028
  17. Lehmann, E. L., 10.1214/aoms/1177699260, Ann. Math. Stat. 37 (1966), 1137-1153. (1966) Zbl0146.40601MR0202228DOI10.1214/aoms/1177699260
  18. Levin, B. Y., 10.1090/mmono/150, Translations of Mathematical Monographs 150. AMS, Providence (1996). (1996) Zbl0856.30001MR1400006DOI10.1090/mmono/150
  19. Liu, M. C., Taylor, R. L., 10.2307/3315482, Can. J. Stat. 17 (1989), 427-438. (1989) Zbl0694.62017MR1047309DOI10.2307/3315482
  20. Masry, E., 10.1109/18.87002, IEEE Trans. Inf. Theory 37 (1991), 1105-1115. (1991) Zbl0732.60045MR1111811DOI10.1109/18.87002
  21. Masry, E., 10.1006/jmva.1993.1003, J. Multivariate Anal. 44 (1993), 47-68. (1993) Zbl0783.62065MR1208469DOI10.1006/jmva.1993.1003
  22. Masry, E., 10.1016/0304-4149(93)90094-K, Stochastic Processes Appl. 47 (1993), 53-74. (1993) Zbl0797.62071MR1232852DOI10.1016/0304-4149(93)90094-K
  23. Masry, E., 10.1109/TIT.2003.818415, IEEE Trans. Inf. Theory 49 (2003), 2941-2952. (2003) Zbl1302.62085MR2027570DOI10.1109/TIT.2003.818415
  24. Meister, A., 10.1088/0266-5611/24/1/015003, Inverse Probl. 24 (2008), Article ID 015003, 14 pages. (2008) Zbl1143.65106MR2384762DOI10.1088/0266-5611/24/1/015003
  25. Meister, A., 10.1007/978-3-540-87557-4, Lecture Notes in Statistics 193. Springer, Berlin (2009). (2009) Zbl1178.62028MR2768576DOI10.1007/978-3-540-87557-4
  26. Oliveira, P. E., 10.1007/978-3-642-25532-8, Springer, Berlin (2012). (2012) Zbl1249.62001MR3013874DOI10.1007/978-3-642-25532-8
  27. Pan, J., 10.1360/02ys9082, Sci. China, Ser. A 45 (2002), 749-760. (2002) Zbl1098.62549MR1915886DOI10.1360/02ys9082
  28. Pensky, M., Vidakovic, B., 10.1214/aos/1017939249, Ann. Stat. 27 (1999), 2033-2053. (1999) Zbl0962.62030MR1765627DOI10.1214/aos/1017939249
  29. Rudin, W., Real and Complex Analysis, McGraw-Hill, New York (1987). (1987) Zbl0925.00005MR0924157
  30. Stefanski, L. A., Carroll, R. J., 10.1080/02331889008802238, Statistics 21 (1990), 169-184. (1990) Zbl0697.62035MR1054861DOI10.1080/02331889008802238
  31. Es, B. van, Spreij, P., Zanten, H. van, 10.3150/bj/1065444813, Bernoulli 9 (2003), 451-465. (2003) Zbl1044.62037MR1997492DOI10.3150/bj/1065444813
  32. Zanten, H. van, Zareba, P., 10.1007/s11203-007-9013-0, Stat. Inference Stoch. Process. 11 (2008), 207-219. (2008) Zbl1204.62051MR2403107DOI10.1007/s11203-007-9013-0
  33. Volkonskij, V. A., Rozanov, Y. A., 10.1137/1104015, Theor. Probab. Appl. 4 (1959), 178-197. (1959) Zbl0092.33502MR0121856DOI10.1137/1104015

NotesEmbed ?

top

You must be logged in to post comments.