Estimation of a Finite Population Mean under Random Nonresponse Using Kernel Weights

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Estimator</td><td class="align_center"><span style="width: 27.8761ptpx;"><svg height="21.7213pt" id="M183" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -18.4485 27.8761 21.7213" width="27.8761pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.187,-9.421)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z"></path></g><rect height="0.65243" width="8.50777" x="0" y="-14.458"></rect><rect height="0.65243" width="8.50777" x="0" y="-11.1958"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M640 650H413L406 622L438 617C475 611 483 605 463 571C422 503 346 400 296 333C264 403 215 529 199 575C189 604 191 614 228 618L262 622L271 650H30L23 622C90 615 97 609 119 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y="-11.1958"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M640 650H413L406 622L438 617C475 611 483 605 463 571C422 503 346 400 296 333C264 403 215 529 199 575C189 604 191 614 228 618L262 622L271 650H30L23 622C90 615 97 609 119 553L212 321C222 295 223 285 218 259L193 127C176 39 167 33 82 28L76 0H350L356 28C266 36 257 40 275 127L303 266C308 290 314 302 328 322C396 418 454 493 498 546C551 610 565 616 631 622L640 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.508,3.132)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g 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class="align_center">0.7164</td><td class="align_center">1.2984</td><td class="align_center">1.4249</td></tr><tr><td class="align_left">Quadratic</td><td class="align_center">0.8270</td><td class="align_center">1.4951</td><td class="align_center">2.994</td></tr><tr><td class="align_left">Sine</td><td class="align_center">1.5269</td><td class="align_center">2.5451</td><td class="align_center">4.888</td></tr><tr><td class="align_left">Exponential</td><td class="align_center">2.2958</td><td class="align_center">2.8322</td><td class="align_center">4.6016</td></tr><tr><td class="align_left">Bump</td><td class="align_center">0.9872</td><td class="align_center">1.8365</td><td class="align_center">1.9630</td></tr><tr><td class="align_left">Jump</td><td class="align_center">1.8594</td><td class="align_center">2.1297</td><td class="align_center">4.2239</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Summary results of <svg height="8.85534pt" id="M182" 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,-0.013,12.482,0)"><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> CI lengths.</div>

Journal of Probability and Statistics

tab4

Table 4

Table 4: Estimation of a Finite Population Mean under Random Nonresponse Using Kernel Weights 