Joint consistency of nonparametric item characteristic curve and ability estimation

被引:39
作者
Douglas, J
机构
[1] Department of Biostatistics, K6/438 Clinical Science Center, Madison, WI 53792-4675
关键词
item characteristic curve; kernel smoothing; large sample theory; nonparametric regression;
D O I
10.1007/BF02294778
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.
引用
收藏
页码:7 / 28
页数:22
相关论文
共 22 条
[1]  
[Anonymous], 1979, 794 U TENN DEP PSYCH
[2]  
Billingsley P., 1986, PROBABILITY MEASURE
[3]   MARGINAL MAXIMUM-LIKELIHOOD ESTIMATION OF ITEM PARAMETERS - APPLICATION OF AN EM ALGORITHM [J].
BOCK, RD ;
AITKIN, M .
PSYCHOMETRIKA, 1981, 46 (04) :443-459
[4]  
Devroye L. P, 1978, CAN J STAT, V6, P179
[5]   NONPARAMETRIC REGRESSION WITH ERRORS-IN-VARIABLES [J].
FAN, JQ ;
TRUONG, YK .
ANNALS OF STATISTICS, 1993, 21 (04) :1900-1925
[6]   MAXIMUM LIKELIHOOD ESTIMATES IN EXPONENTIAL RESPONSE MODELS [J].
HABERMAN, SJ .
ANNALS OF STATISTICS, 1977, 5 (05) :815-841
[7]  
Hardle W., 1990, APPL NONPARAMETRIC R, DOI DOI 10.1017/CCOL0521382483
[8]  
Hastie T., 1990, Generalized additive model
[9]  
HOEFFDING W, 1986, ENCY STAT SCI, V7, P222
[10]  
Nadaraya E.A., 1964, Theory Probab Its Appl, V9, P141, DOI [10.1137/1109020, DOI 10.1137/1109020]