Boundary Bias Correction Using Weighting Method in Presence of Nonresponse in Two-Stage Cluster Sampling

<table class="fixed-width table-group" id="tab4"><tr><td><table class="table"><colgroup><col style="width:6.86em"/><col style="width:9.23em"/><col style="width:12.56em"/></colgroup><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Data function</td><td class="align_center">Proposed Estimator</td><td class="align_center">Nadaraya-Watson Estimator</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Linear</td><td class="align_center">0.92695</td><td class="align_center">1.70934</td></tr><tr><td class="align_left">Quadratic</td><td class="align_center">0.76973</td><td class="align_center">2.93895</td></tr><tr><td class="align_left">Sine</td><td class="align_center">1.52697</td><td class="align_center">4.88850</td></tr><tr><td class="align_left">Bump</td><td class="align_center">0.97842</td><td class="align_center">2.22051</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Summary results of <svg height="8.85534pt" id="M223" style="vertical-align:-0.4673595pt" version="1.1" viewbox="-0.0498162 -8.38798 22.4913 8.85534" width="22.4913pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.241,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.527,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z"></path></g></svg> confidence interval lengths.</div>

Journal of Probability and Statistics

tab4

Table 4

Table 4: Boundary Bias Correction Using Weighting Method in Presence of Nonresponse in Two-Stage Cluster Sampling 