Estimation of Population Median under Robust Measures of an Auxiliary Variable

<div>Minimum MSE of estimators <span class="nowrap"><svg height="16.1561pt" id="M256" style="vertical-align:-5.332pt" version="1.1" viewbox="-0.0498162 -10.8241 22.0498 16.1561" width="22.0498pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.285,-5.741)"><path d="M594 262C594 419 464 546 305 546S17 419 17 262S146 -22 305 -22S594 105 594 262ZM538 262C538 131 433 25 305 25S73 131 73 262S177 499 305 499S538 393 538 262ZM489 157C489 176 480 201 468 219C415 228 387 236 336 262C387 288 415 298 468 305C480 324 489 348 488 367C472 378 446 383 424 382C390 339 369 320 321 288C323 346 329 374 350 424C339 445 322 464 305 473C289 464 271 445 261 424C281 374 287 346 290 288C242 320 221 339 187 382C165 383 140 378 122 367C122 348 131 323 143 305C196 296 224 288 275 262C224 236 196 226 143 219C131 200 122 176 123 157C139 146 165 141 187 142C221 185 242 204 290 236C288 178 282 150 261 100C272 79 289 60 306 51C322 60 341 79 351 100C330 150 324 178 321 236C369 204 391 185 424 142C446 141 472 146 489 157Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.176,3.784)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.724,3.784)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.982,3.784)"><path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.114,3.784)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

tab8

Table 8

Table 8: Estimation of Population Median under Robust Measures of an Auxiliary Variable 